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dissertation entitled
A GENERALIZED VISCOSITY MODEL
FOR THE COOKING EXTRUSION OF STARCH BASED PRODUCTS

presented by

Kevin Lewis Mackey

has been accepted towards fulﬁllment
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PhD. Food Science

 

 

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A GENERALIZED VISCOSITY MODEL
FOR THE COOKING EXTRUSION OF ST ARCH BASED PRODUCTS

By

Kevin Lewis Mackey

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Food Science and Human Nutrition

1989

ABSTRACT

A GENERALIZED VISCOSITY MODEL
FOR THE COOKING EXT RUSION OF STARCH BASED PRODUCTS

By
Kevin Lewis Mackey

A generalized model has been developed for predicting the extrudate viscosity of
low to intermediate moisture content starch based products during cooking extrusion.
The model incorporates the effects of shear rate, temperature, moisture content, time-
temperature history and main history.

The model was tested using doughs of potato ﬂour, corn starch and whole wheat
flour. Equipment used included an Instron Capillary Rheometer attached to a Model
4202 Instron Universal Testing Machine and an APV Baker MPF 50 D/25 co-rotating
twin screw extruder. Die lengths of the capillary rheometer were 6.35 x 103 m and 2.54
x 10" or while the diameters were 3.18 x 10'3 m and 1.59 x 10‘3m. Extruder dies of 6.35
x 10" m in length and diameters of 2.54 x 10‘2 m and 3.18 10'3 m were used.

Experiments with potato ﬂour were conducted at temperatures of 25, 50, 65, and
95°C. Cook times within the capillary rheometer were 0 to 12 minutes after compression.
Moisture contents of 0.282, 0.507, and 0.772 g water per g solids (22.0%, 33.7%, and
43.6% wb, respectively) were used in the capillary rheometer, while the moisture con-
tents in the extruder were 0.67 and 1.0 g water per g solids (40% and 50% wb). Shear
rates ranged from 1-10000 s“.

In potato dough, shear rate was described by the power law model. Time-
temperature history and strain histOry did not inﬂuence viscosity. The ﬁnal predictive
model incorporates shear rate, temperature and moisture content and yielded an R2 of
0.95 1.

Corn starch dough moisture contents were 0.359, 0.476, and 0.572 g water per g
starch (26.4%, 32.0%, and 36.4% wb, respectively) for capillary rheometer tests and 0.5
and 0.6 g water per g starch (33.0% and 37.5% wb) for extrusion tests. In the capillary
rheometer, barrel temperatures were held at 50, 55, 60, 75, 85, 95, and 110°C at cook
times of 1, 2, 3, 6, 12, and 24 minutes.

In corn starch dough, slip analysis was inconclusive. Shear rate was modelled by
the equation proposed by Ofoli et a1. (1988). Viscosity was found to be a function of
cook temperature and moisture content, but not cook time. Observed versus predicted
viscosities gave an R2 of 0.95 after accounting for shear rate, temperature, moisture con-
tents and time-temperature history in the capillary rheometer. Contrary to tests for porato
doughs, extrusion tests indicated that strain history was important for highly puffed corn
starch exu'udates (R’=0.79 before strain history con'ection). Strain history was modelled
as a function of mechanical energy input (shaft work). After correction for strain history,
the ﬁt of the model improved to an n2 of 0.85..

Whole wheat ﬂour tests were conducted at the same temperature and cook times as
those for corn starch, but at moisture contents of 0.333, 0.337, 0.385, and 0.426 g water
per g solids (25.0%, 25.2%, and 29.9% wb, respectively). As obseved for corn starch slip
conection gave inconclusive results. Shear rate was best modelled by the Herschel-
Bulkley model. Overall ﬁt of the model steadily improved with corrections for tempera-
ture, moisture content and time-temperature history. Viscosity of cooked doughs were
found to be a function of moisture content, cook time and temperature. The ﬁt (R’=0.56)
was not as good for whole wheat flour as was observed for corn starch (R’=0.95) and
potato flour (R2=0.95). The lower R2 may have been due to the presence of flour compo—
nents such as bran, gluten (protein) viscoelastic effects and lipids which were not
accounted for by the model. Incorporation of gelatinization kinetics alone in the

time-temperature effects was inadequate to totally model the viscosity.

ACKNOWLEDGMENTS

I would like to thank the United States Department of Agriculture for their provid-
ing me with a fellowship which enabled me to pursue my studies. Also many thanks to
the Departments of Food Science and Human Nutrition and Agricultural Engineering for
their financial and adminstrative support while I was working on my degree.

Many thanks to Dr. Ronnie Morgan for his initial guidance, encouragement, and
advice in deciding on a dissertation t0pic and selecting of my coursework and committee.
Thank also to Drs. Edwards, Markakis, and Uebersax for their willingness to serve on my
guidance committee and for the many ﬁne suggestions they have provided.

Special thanks to Dr. Jim Steffe for his help in teaching me more about rheology,
for having conﬁdence in my abilities as a scientist and teacher and for his advice on
career choices. I would also like to thank him for his excellent editorial skills.

To Dr. Bob Ofoli I give my heart felt thanks for his advice, for his willingness to
become my advisor after the departure of Dr. Morgan, and for all the hard work he did in
helping me prepare this dissertation.

Finally, I wish to acknowledge the support of my family and friends for their
encouragement. I especially want to thank Julie, my wife, for her love, support, and
understanding during this long and sometimes difﬁcult process. Without you and your

love this dissertation would have been much more difﬁcult.

iv

Preface
This dissertation was written in an alternative format to aid the author in preparing
portions of the dissertation for publication. The ﬁrst three chapters feature an introduc-
tion, literature review and the model development. Chapters 4, 5, and 6 consist of time
papers to be submitted for publication while chapters 7 and 8 are the conclusions and
suggestions for future research. I hope that writing the dissertation in this format will not
confuse the reader and will, perhaps, allow the reader to understand and apply the infor-

mation in an easier manner.

Kevin L. Mackey
December, 1988 -

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................ ix °

LIST OF FIGURES .......................................................................................... x

NOMENCLATURE .......................................................................................... xii
CHAPTER 1 INTRODUCTION AND OBJECTIVES ......................................... 1

J 1.1. Introduction ............................................................................................ (i,
1.2. Objectives. ............................................................................................... 2
CHAPTER 2 LITERATURE REVIEW ................................................................. 3
2.1. Starch ........................................................................................................ 3

v 2.1.1. Introduction ................................................................................ (3)
2.1.2. Structure of the starch granule ........................................................ 6
2.1.2.1. External structure of the starch granule. .................... 6
2.1.2.2. Internal structure of the starch granule. .................................... 6
2.1.3. Physical and Chemical Changes ...................................................... 7
2.1.3.1. Physical changes ..................................................................... 8

2.1.3.2. Chemical changes .................................................................... 10

2.1.4. Measurement Methods .................................................................... 13

2.1.4.1. Light Microscopy .................................................................... 13

2.1.4.2. Polarized Light Microscopy .................................................... 14

2.1.4.3. Electron Microscopy ............................................................... 15

2.1.4.3.1. Scanning Electron Microscopy (SEM) ........................... 15

2.1.4.3.2. Transmission Electron Microsc0py (TEM) .................... 16

2.1.4.4. Viscometers ............................................................................. 16

2.1.4.5. Thermal Analysis .................................................................... 17

2.1.4.5.1. Differential Scanning Calorimetry (DSC) ...................... l8

2.1.4.5.2. Thermal Mechanical Analysis (TMA) ............................ 18

2.1.4.6. Others ...................................................................................... 19

2.1.4.6.1. Enzyme ........................................................................... 19

2.1.4.6.2. X-ray diffraction ............................................................. 19

vi

2.1.4.6.2. Nuclear Magnetic Resonance ......................................... 20

2. 2. Rheology ................................................................................................... 21
/ 2.2.1. introduction ..................................................................................... .2112
2. 2. 2. Models For Rheological Modelling of Food .................................... 21
2.3. Extrusion .................................................................................................. 25 -
V 2.3.1. introduction ...................................................................................... <25;
2.3.2. Viscosity Models Used in Extrusion ............................................... 27
CHAPTER 3 MODEL DEVELOPMENT ............................................................. 29
3.1. Effect of Shear Rate on Viscosity ............................................................. 29
3.2. Effect of Temperature .............................................................................. 30
3.3. Effect of Moisture .................................................................................... 31
3.4. Eﬁ‘ect of Time-Temperature History ....................................................... 31
3.5. Effect of Strain History ............................................................................ 36
3.6. A procedure for determining the parameters in Eq.[3.20]. ....................... 40
CHAPTER 4 EXTRUSION MODELLING OF PREGELATINIZED POTATO
FLOUR ................................................................................................................... 42
4.1. Abstract .................................................................................................... 42
v4.2. Introduction .............................................................................................. <4L
4.3. Model Development ................................................................................. 45
4.4. Materials and Methods .............................................................................. 47
4.5. Results and Discussion ............................................................................. 50
4.6. Conclusions .............................................................................................. 57
4.7. Nomenclature ............................................................................................ 58
CHAPTER 5 EXTRUSION MODELING or CORN STARCH .......................... 59
5.1. Abstract ..................................................................................................... 5%
1/ 5.2. Introduction ............................................................................................... 5 L602
5.3. Model Development .............................................................. , ................... 62
5.4. Materials and Methods ............................................................................. 65
5.5. Results and Discussion ............................................................................. 71
5.6. Conclusions .............................................................................................. 92
5.7. Nomenclature ............................................................................................ 94
CHAPTER 6 A RHEOLOGICAL MODEL FOR NATIVE WHOLE WHEAT
FLOUR DOUGH EXTRUDATES ........................................................................ 97
6.1. Abstract ................... 9‘1
\/6. 2. Introduction ............................................................................................... Q98 :
6. 3. Materials and Methods .............................................................................
6. 4. Results and Discussion .............................................................................. 105
6.5. Conclusions .............................................................................................. 119
6.6. Nomenclature ........................................................................................... 121

vii

CHAPTER 7 SUMMARY AND CONCLUSIONS ............................................... 123

7.1. Overall Summary ..................................................................................... 123
7.2. Conclusions ............................................................................................... 126
CHAPTER 8 SUGGESTIONS FOR FUTURE RESEARCH ............................... 127
8.1. Effects of non-starch ingredients. ................ ’. ........................................... 127
8.2. Development of methods to quantify time-temperature history effects. .. 128
8.3. Development of equipment for measuring strain history. ........................ 129
8.4. Investigation of slip or friction within the capillary die. .......................... 129
LITERATURE CITED ........................................................................................... 130
APPENDICES ........................................................................................................ 138
Appendix 1. Temperatme, moisture, cook time, shear stress, shear rate, and
observed viscosity of potato flour doughs. ........................................................ 138
Appendix 2. Moisture content, temperaturre, cook time, die LID, shear
stress, and shear rate of corn starch .................................................................... 140
Appendix 3. Temperature, moisture content, cook time, shear stress, shear
rate, observed viscosity of whole wheat ﬂour doughs. ..................................... 169

viii

LIST OF TABLES

Table 2.1. Properties of whole granular starches. .................................................. 5
Table 2.2.1. Rheological models and their parameters used to characterize fluid
food behavior. ......................................................................................................... 23
Table 3.1. Model parameters and what they describe. .......................................... 39
Table 3.2. Flow chart for determining the model parameters. .............................. 41
Table 4.1. Screw conﬁgurations of APV-Baker twin- screw extruder. ................. 49
Table 4. 2. Summary of model parameters and comparison with values from the
literature. ................................................................................................................. 56
Table 5.1. Screw conﬁguration for extrusion test on APV Baker 50 mm twin

screw extruder. ....................................................................................................... 70

Table 5.2. Temperature andmoisture parameters as determined by linear regres-

sion with viscosity measured at a shear rate of 100 s" ............................................ 74
Table 5.3. Values of constants a and B as a function of temperature. ................... 80

Table 5.4. Stepwise regression of observed viscosity versus temperature, shear
rate, moisture content and time-temperature history corrections for corn starch

 

doughs. .................................................................................................................... 83
Table 5.5. Data from twin screw extrusion tests on corn starch doughs. ............... 85
Table 5.6. List of model parameters for Eq. 5.22. ................................................. 91
Table 6.1. Screw conﬁguration for extrusion tests on an APV Baker 50 mm twin
screw extruder. ........................................................................................................ 104
Table 6. 2. Temperature and moisture correction parameters for whole wheat

ﬂour at 100 s. ........................................................................................................ 106
Table 6.3. Results of stepwise regression for whole wheat ﬂour doughs. ............ 115
Table 6.4. List of parameters for Eq. 6.1. .............................................................. 118

LIST OF FIGURES

Figure 4.1. Corrected viscosity of potato ﬂour doughs (adjusted to 35% MC and

shear rate of 100 s ) versus reciprocal temperature. .............................................. 51
Figure 4. 2. Corrected viscosity of potato ﬂour dough (adjusted to T=50 C and

shear rate of 100 ) versus moisture content. .......................................................... 52
Figure 4.3. Viscosity versus shear rate for cook times of 0 to 12 minutes at 95

C. ............................................................................................................................ 53
Figure 4.4. Observed versus predicted viscosity via Eq. [4.5] for capillary
rheometer (CR) and extruder dies ('1‘ SE) for potato ﬂour doughs. ......................... 55
Figure 5.1. Capillary rheometer assembly. ............................................................. 66

Figure 5.2. Observed versus predicted viscosities of corn starch doughs after
shear correction for all temperatures, moisture contents and time-temperature
histories. .................................................................................................................. 72

Figure 5.3. Apparent observed and predicted viscosities of corn starch doughs
versus shear rate at a moisture content of 0.476 g water/ g corn starch. ................ 73

Figure 5.4. Observed versus predicted viscosities, of corn starch doughs after
shear rate and temperature corrections, for all moisture contents and time-
temperature histories. ............................................................................................. 75

Figure 5.5. Observed versus predicted viscosities of corn starch doughs, after
shear rate, temperature and moisture corrections, for all time-temperature histo-
ries. ......................................................................................................................... 77

Figure 5.6. Average apparent viscosity versus cook time for cook temperatures
of 75, 85, 95, and 110 C (MC=O.476 g/g db) for corn starch doughs. ................... 78

Figure 5.7. Observed versus predicted viscosities corrected for shear rate,
temperature, moisture, and time-temperature history for corn starch doughs. ....... 82

Figure 5.8 Observed versus predicted viscosities corrected for shear rate,
temperature, moisture, and time-temperature history in extruder dies for corn
starch. ...................................................................................................................... 86

Figure 5.9. Observed viscosity at 150 s", moisture content of 0.476 g/g and
temperature of 50 C for corn starch doughs. .......................................................... 89

Figure 5.10. Observed versus predicted viscosities corrected for shear rate,
temperature, moisture, time-temperature, and strain history in extruder dies for
corn starch. ............................................................................................................. 90

Figure 6.1. Capillary rheometer assembly. ............................................................ 101

Figure 6.2. Observed versus predicted viscosities corrected for shear rate for all
temperatures, moisture contents and time-temperature history for whole wheat
flour doughs. ........................................................................................................... 108

Figure 6.3. Observed versus predicted viscosities corrected for shear rate and
temperature for all moisture contents and time-temperature history for whole
wheat flour doughs. ................................................................................................ 109

Figure 6.4. Observed versus predicted viscosities corrected for shear rate, tem-
perature, and moisture content for all time-temperature histories for whole wheat
flour doughs. ........................................................................................................... 110

Figure 6.5. Observed versus predicted viscosities corrected for shear rate,
temperature, moisture, and time-temperature history for whole wheat ﬂour 1 3
doughs. ................................................................................................................... 1

Figure 6.6. Observed versus predicted viscosities corrected for shear rate,
temperature, moisture, and time-temperature history in extruder dies for whole
flour doughs. ........................................................................................................... 1 16

xi

NOMENCLATURE

A, A’, material constant describing effects of cook temperature and product moisture

A:
b

Cp
cn

Cs

gnu

BF‘FFfoB‘

content on viscosity at \v = co, dimensionless

rate constant of effect of moisture content on viscosity, dimensionless
protein concentration, decimal dry basis
capillary rheometer

starch concentration, wet basis decimal

rate constant of effect of strain history ((9) on viscosity, s
capillary diameter, in

mechanical energy supplied by the extruder, Jm"
Planck’s constant,

consistency coefﬁcient, Pa 3

consistency coefﬁcient (Mizrahi-Berk), Pa“ sIII
reaction transmission coefﬁcient, s" “K"
Boltzman’s constant,

transmission coefficient,

capillary length, m

power index (Mizrahi-Berk), dimensionless
moisture content, dry basis decimal

reference moisture content, dry basis, decimal
power indices, dimensionless

volumetric flow rate, m’ls

universal gas constant, 1.987 cal/g mole
capillary radius, or

xii

time, 3

temperature, 'K

reference temperature, ‘K

twin screw extruder

material constant describing polymer entanglement, dimensionless

material constant describing effect of strain history on viscosity at 41 = co, dimen-
sionless

material constant describing effects of temperature on gelatinization, dimension-
less

material exponent for describing effect of moisture content on protein denatura-
tion, dimensionless ‘

shear rate, 3"

shear rate at the wall, 3'1

free energy of activation, kcal/g mole
energy of gelatinization, kcal/g mole
pressure drop, Pa

apparent viscosity, Pa 3

normalized apparent viscosity ratio, dimensionless

time-temperature history, s 'K
strain history, dimensionless
shear stress, Pa

shear stress at wall, Pa
yield stress, Pa

yield suess, Pa

xiii

K“ yield stress-related parameter (Mizrahi—Berk), Pa °"

11 Newtonian viscosity, Pa s

ll. high shear limiting viscosity, Pa s

1].. change in apparent viscosity due to gelatinization at \v = on, Pa 3

no high shear limiting viscosity (Bingham plastic), Pa 8

Subscripts ofn

pre

y,T,MC
¢

iT
-‘y,r,Mc

i.T.MC.v

i.T.MC.v.¢

apparent viscosity corrected for shear rate, Pa 3

contribution to viscosity by gelatinization

predicted apparent viscosity, Pa 3

viscosity at \v = co, Pa 3

apparent viscosity before gelatinization, Pa 8

apparent viscosity at q) = «t, Pa s '

apparent viscosity conected for shear rate and temperature, Pa 3

apparent viscosity corrected for shear rate, temperture and moisture con-
tent, Pa 3

apparent viscosity corrected for shear rate, temperture, moisture content
and time-temperature history, Pa 8

apparent viscosity corrected for shear rate, temperture, moisture content,
time- -temperature history and strain history, Pa 3

xiv

CHAPTER 1 INTRODUCTION AND OBJECTIVES

1.1. Introduction.

The predominant ingredient in extruded snack and ready to eat (RTE) cereals is
starch (Harper, 1986). Many of these products do not use puriﬁed starch but rather deg-
errrred cereal grits which also contain some protein, fat, and ﬁber. The starch granule can
undergo many changes leading to increased molecular rearrangement during extrusion,
including loss of crystallinity, degradation and formation of amylose lipid complexes.
These changes almost always will signiﬁcantly affect viscosity. Therefore, temperature,
moisture, shear, and feed composition are important factors accounting for changes in
starch structure during extrusion (Harper, 1986).

Extrusion cooking of starch based foods is increasing each year due to the versatil-
ity, high productivity, low production costs, high product quality, increased energy efﬁ-
ciency and lack of product efﬂuent of extrusion processes (Harper, 1981). However, the
full economic exploitation of extrusion is currently constrained by a lack of
understanding of the eﬁ'ects of ingredients and process conditions on product quality, and
difﬁculties in process design and scale-up.

A general viscosity model would be useful for process engineering analyses.
Harper (1986) states that there is no single model that incorporates starch gelatinization,
viscoelastic behavior, density and thermal properties as functions of time, temperature,
shear rate, and moisture content. Modeling in cooking extrusion needs more research,
since models can be used to simplify complex processes in a cooking extruder, predict
changes in product quality, and obtain a basis for new product development (Janssen,
1986). Most models proposed so far are empirical and limited to observed experimental

conditions.

1.2. Objectives.

The overall goal of this research is to obtain an understanding of the interactions of
shear rate, temperature, moisture content, time-temperature history and strain history on
the viscosity of extruded starch-based doughs. To achieve this goal, the speciﬁc objec-
tives of the study are to:

1. Develop a generalized viscosity model incorporating effects of time-temperature
history, moisture content, temperature, strain history, and shear rate during extrusion of
low moisture starch based foods.

2. Evaluate the model with data obtained from capillary viscometry and twin screw
extrusion for three dough systems: corn starch, potato ﬂour and wheat ﬂour.

3. Assess the effects of starch gelatinization during extrusion on rheological prop-

erties.

CHAPTER 2 LITERATURE REVIEW
2.1 Starch
2.1.1. Introduction

Starch is the major storage form of glucose (energy) in plants. In cereal grains,
starch contents range from 60 to 70% of the weight of the grain (Hoseney, 1986).
Besides being an excellent source of energy for plants and animals, starch also provides
important physical properties to foods. Pr0perties that are most important to the food sci-
entist include gelling of puddings, thickening of gravies, setting of cakes, breads and
other baked goods, and as a source of glucose for many sweeteners.

In higher plants (eg. cereal grains), starch is formed in the plastids. All starch is
stored in the form of granules. Starch granules made in the chloroplasts of leaves are
considered transitory because at nightfall, the granule is broken up and the glucose is
transferred to other portions of the plant. Reserve starch granules are usually formed in
amyloplasts, though starch can be formed in chloroplasts which have lost their lamellar
structure and therefore begin to produce large amounts of storage starch (Shannon and
Garwood, 1984). In general, one plastid produces one starch granule except for rice and
oat plants which produce compound granules (Hoseney, 1986).

If examined under polarized light, intact starch granules show a distinct birefrin-
gence pattern consisting of a Maltese cross. The presence of birefringence is an indica-
tion of a high degree of order within the granule. Gelatinization is often deﬁned as the
loss of birefringence.

Starch granules are also made up of semicrystalline materials as indicated by the
classical studies of Katz (1928) and his co-workers using X-ray diffraction. Katz (1928)
showed that intact starch granules gave three types of X-ray diffraction patterns (A, B, or

C) depending on the source. Cereal starches (i.e corn, wheat, barley) give the A pattern,

tuberous starches (potato) give the B pattern and smooth starches (pea and bean) give the
C pattern. The C pattern is thought to be a mixture of both A and B patterns. Gelatiniza-
tion of starches result in a loss of crystallinity and the appearance of the V type X-ray
diffraction.

Starch consists mainly of two large polysacchanide molecules, amylose and amy-
lopectin, consisting of long chains of glucose. Amylose is considered to be primarily a
linear ar(1-4) glucan with a molecular weight of 150,000-1,000,000 depending upon the
source. Early research indicated that amylose was linear, as determined by enzyme

studies (ﬁt-amylase) but later research indicates that the [i-amylase used contained some

a-amylase and/or debranching enzymes. Present research indicates that some limited
branching is present in the amylose molecule (Banks and Greenwood, 1975). Amylose
content ranges from 20-30% among biological sources (Table 2.1.), however, there are
genetic hybrids in which there is an increase or decrease of the amylose content available.
Amylopectin differs from amylose in both its molecular weight and its highly
branched structure. The amylopectin molecule is made up of glucose units with a—(1-4)
glycosidic, a-(1-6) glycosidic or both a-(1-4) and or-(l-6) glycosidic bonds. The average
chain length is 20-25 glucose units and random branches give this molecule its high
molecular weight. Evidence is mounting that amylopectin is the principal crystalline
component of the starch granule (Lineback, 1984). Bireﬁingence and X-ray diffraction
patterns of waxy maize starches containing no amyloseare similar to those of normal
maize starch. High amylose maize starches are less birefringent and show less crystallin-
ity than normal starches. Lineback (1984) also suggests that amylopectin is responsible
for the crystalline structure, because amylose is released into solution when starches are

exposed to gelatinization temperatures while amylopectin is not.

 

Table 2.1. Properties of whole granular starches;

 

 

Source

Barley

Triticale
Wheat
Rye
Oats

Potato
Corn

Waxy maize
Broad bean
Sorghum

Rice
High-
amylose
maize

Gelatinization Granule shape Granule

Temperature

range
('0

51-60

55-62
58-64

57-60

53-59
59-68
62-72

63-72
64-67
68-78
68-78
67-90

round or
elliptical
round
lenticular
or round
round or
lenticular
polyhedral
oval
round or
polyhedral
round
oval
round
polygonal
round
irregular

Amylose
Size Content
(run) (%)
20-25 22
2-6
19 23-24
20-35 26(23-27)
2-10
28 27
3-10 23-24
40(15-100) 23
15 28
15(5-15) 1
30 24
35 25(23-28)
3-8 17-19
25 52

 

Source: Lineback (1984).

 

2.1.2.8tructure of the starch granule
2.1.2.1. External structure of the starch granule.

Starch granules from different plant sources have different morphologies (Table
2.1). The morphology depends on the structure and biochemistry of the starch producing
chloroplast or amyloplast (Badenhuizen, 1969). These differences enable trained person-
nel to determine which plant produced the starch.

The granule grows via apposition, i.e., addition of material to the outer layers. This
growth gives the characteristic ring structures seen in potato starch. These growth rings
can also be seen in other starches after acid treatment of the starch granules. Scanning
electron microscopy indicates that undamaged, unmodiﬁed granules have relatively
smooth surfaces free of pores, cracks or ﬁssures (Whistler et a1. 1984).
2.1.2.2. Internal structure of the starch granule.

While the use of optical and scanning electron microscopy has enabled researchers
to determine the general surface morphology of starch granules, the internal structure has
been much more difficult to determine. The development and use of transmission elec-
tron microscOpy (TEM) has provided researchers with greater resolution. Acid treatment
(7% HCl for 35 days) has shown corn and waxy maize starch granules to have similar
well-deﬁned lamellar structures with alternating concentric electron-dense and electron-
transparent rings (Mussulman and Wagoner, 1968). Rings occur at irregular intervals of
1200-4000 A and suggest that the overall length of individual amylopectin molecules are
of this length (Y amaguchi et a1. 1979). Yamaguchi et a1. (1979) proposed that a single
amylopectin molecule starts at one growth ring and ﬁnishes at the next, with each mole-
cule made up of many 70 A clusters. It is interesting to note that high amylose corn
starches do not reveal ring structures after acid or enzyme treatment, but instead show a

heterogeneous internal su'ucture.

Hood (1982) states that the molecular structure of starch corresponds with the crys-
talline structure of the starch, and that it is well accepted that starch molecules are
radially oriented within the granule. Pairs of the outer chains of amylopectin can form
double helices which also contribute to the crystalline properties (Kainuma and French,
1972). Kassenbeck (1978) used TEM and ultrathin sections of starch granules to present
ftu'ther evidence that radial orientation of amylopectin molecules exists. He also pres-
ented three possible types of molecular organization: (1) a radially aligned, ﬁbrillar
arrangement of amylose in ordered regions; (2) amylose in amorphous regions where the
amylose was degraded by the preparative method and appears in the form of precipitates;,
and (3) an arrangement of amylopectin in crystalline regions where it appears as periodi-
cally ananged block-like areas in radial sections, with crystallites in tangential lamellae.

French (1984) states that there is no sharp line separating the crystalline and amor-
phous sections of the starch granules and that some or all of the starch molecular chains
continuously change from one phase to another. He also states that there is no deﬁnite
evidence that amylose contributes to the crystalline structtue of the starch granule. Amy-
lose not contributing to crystallinity would explain why amylose molecules are seen out-
side the granule early in the gelatinization process and amylopectin molecules are not.
2.1.3. Physical and Chemical Changes

Increase in viscosity of dilute solutions of starch and water is attributed to the
starch granule taking up water and a concurrent swelling of the granule (Hoseney, 1986).
As the granule swells, starch molecules are leached out causing further increases in vis-
cosity.

Gelatinization minimally entails (1) loss of crystallinity of the granule as measured
by loss of birefringence and its X-ray diffraction patterns; (2) an uptake of heat as the

conformation of starch changes; and (3) hydration of starch accompanied with granule

swelling (Donovan, 1979). A more detailed summary of gelatinization is given by Olkku
and Rha (1978) and is presented as follows:

tion:

(1) Granules hydrate and swell to several times their original size.

(2) Granules lose their birefringence.

(.3) Clarity of the mixture increases.

(4) Marked, rapid increase in consistency occurs and reaches a peak.

(5) Linear molecules dissolve and diﬁ‘use from ruptured granules. .

(6) Mixture retrogrades to a paste-like mass or gel.

Atwell et al. (1988) recently proposed the following deﬁnition of starch gelatiniza-

Starch gelatinization is the collapse (disruption) of molecular orders within the
starch granule manifested in irreversible changes in properties such as granular
swelling, native crystallite melting, loss of birefringence, and starch solubilization.
The point of initial gelatinization and the range over which it occurs is governed
by starch concentration, method of observation, granule type, and heterogeneities

within the granule population under observation.

This deﬁnition best describes what is occurring during the process of gelatinization and
will be used in this work.
2.1.3.1. Physical changes

In the presence of sufficient water and at temperatures below gelatinization, water

is slowly and reversibly taken up by the granule (Olkku and Rha, 1978). Once gelatiniza-

tion temperatures are reached, the granules begin to swell and become distorted (Sterling,
1978; Christianson et al., 1982). The granule’s ability to polarize light and diffract

X-rays is lost at this time (Sterling, 197 8; Hoseney, 1986; Olkku and Rha, 197 8; Dono-
van, 1979). Sterling (1978) reports that a three to six fold increase in volume is seen
when starch granules begin to gelatinize. This increase is conﬁrmed by Christianson et
al. (1982), where a three and a half fold increase in com starch granule size was seen.
The starch granule swells in a tangential direction during the gelatinization process.
When temperatures increase beyond gelatinization temperatures, the granule continues to
swell and may increase up to 25-30 fold, followed by a gradual collapse (Sterling, 197 8).

Christianson et a1. (1982) presented excellent SEM photographs of corn starch
granules at various stages of gelatinization. As the temperature increases, the granules
begin to swell radially (65'C), ridges are formed at the surface (67'C), the granules
become more angular in structure (70'C) and, at higher temperatures, the granules melt
into thin ﬂat disks. Different sections of the granule appear to swell at different times,
and Sterling (197 8) postulated that differences in molecular structure cause this phenom-
enon. Christianson et al. (1982) conﬁrmed this when the amorphous regions were seen to
swell at lower temperatures than the regions of the more highly ordered portion of the
granule.

Along with this swelling, solubilization of starch molecules is occurring and by the
time a temperature of 70'C has been attained, approximately 10% of the starch has left
the corn starch granule (Christianson et al., 1982). The granules seem to pass a transition
at 80‘C where melting or softening of the granule occurs (Christianson et al., 1982).
Twenty per cent of the starch is soluble at 85 'C and the granule appears smooth and more
fluid than what is seen at lower temperatures. Wheat starch granules show a more
ordered swelling as described by both Bowles et al. (1980) and Miller et al. (1973).

It is interesting that both Miller et aL (1973) (wheat starch) and Christianson et al.

(1982) (corn starch) have reported that maximum viscosity of starch suspensions heated

10

in the presence of excess water occurs after the majority of granule swelling has stopped.
This is an indication that granule swelling is not the only reason an increase in viscosity
is seen.

Christianson et al. (1982) also compared viscosity data and SEM micrographs of
starch dispersions of varying concentration and exposrue to different temperatures. At
‘65'C and under low shear, granules swelled but retained birefringence and exhibited dila-
tant behavior. When exposed to high shear, shear thinning occurred After loss of bire-
fringence (67-70'C) softening of the granules occurred so that shear thinning occurred at
all shear rates.

In their review on the gelatinization of starch, Olkku and Rha (197 8) discussed the
effects of various ingredients on gelatinization. Proteins are believed to inhibit escape of
soluble portions from the granule but do not appear to affect swelling. The same conclu-
sion is drawn for the effects of oils and surface active agents. Pentosans are thought to
compete for water and therefore inhibit gelatinization and granule swelling. Addition of
salt can increase the granule’s ability to swell, while addition of sucrose retards hydration
of the starch granule (Olkku and Rha, 1978; Bean and Yamazaki, 1978).
2.1.3.2. Chemical changes

Along with the physical changes occurring in the starch granule, the chemical
structure is also changing during the gelatinization process. The inuamolecular hydrogen
bonds are disrupted upon heating and the structural integrity of the granule is lost. Once
disruption of hydrogen bonds occur, the amorphous regions of the granule are the ﬁrst to
hydrate (Hood, 1982). This swelling of the amorphous phase can contribute to the dis-
ruption of crystalline regions by pulling molecules away from the crystals (French, 1984).
Blanshard (1979) proposed that in addition to diffusion of water and swelling, a
hydration-facilitated helix-coil transition which is a melting process also occurs.

11

Miller et al. (1973) showed that amylose leached from the granule during heating
and formed an extra granular network which contributed to increased viscosity. Approx-
imately 10% of the starch has been solubilized at 70'C and by 80'C, 20% of the starch
has been solubilized (Christianson et al., 1982). Using proton magnetic resonance (PMR)
Jaska (1971) found water mobility to reversibly decrease with increased temperature until
gelatinization temperatures are attained. This decrease in mobility indicates adsorption of
water to starch molecules. When gelatinization occurs, an increase in water mobilization
occurs which indicates a transfer of soluble starch (about 90% of total) into solution
(Jaska, 1971). Jaska (1971) concluded that some of the starch is in solution inside the
granule before it leaves the granule and that soluble starch solubilizes over a narrow tem-
perature range.

Various methods of thermal analysis have been used to study starch gelatinization
(Hoseney, 1984; Nakazawa et al. 1984; Wootton and Bamunuarachchi, 1979a; Wootton
and Bamunuarachchi, 1979b; Stevens and Elton, 1971; Biliaderis et al., 1980; Ghiasi et
al., 1982a; Donovan, 1979), the effects of low moisture conditions (Wootton and Bamu-
nuarachchi, 1979; Takahashi, et al., 1982; Burt and Russell, 1983; Sweat et al. 1984;
Eliasson, 1980; Collison and Chilton 1974; Biliaderis et al., 1986), protein concentration
(Eliasson, 1983), lipid and lipid-like substances (Harbitz, 1982; Kugimiya et al., 1980;
Ghiasi et al. 1982b), and solute concenuation on gelatinization (Ghiasi et al., 1983; Spies
and Hoseney, 1982; Evans and Haisman, 1982; Oosten, 1982). These methods of ther-
mal analysis include diﬁ'erential thermal analysis, differential scanning calorimetry, and
thermal mechanical analysis.

When gelatinization of starch is measured by differential scanning calorimetry
(DSC) under low moisture conditions, two endotherms are observed. When excess water

is present, the DSC curve shows only one endotherm indicating that water content

12

directly affects gelatinization kinetics. Various models have been proposed for this phe-
nomenon. Donovan (1979) suggests that upon hydration/swelling of the amorphous por-
tions of the granule and due to coupling with crystallites, melting of the latter occurs as
long as water is present in excess. He postulated that when the amount of water is
insufficient for complete melting, the remaining crystallites melt at a higher temperature
and thus support the second DSC peak.

Another hypothesis for starch gelatinization at low to intermediate moisture con-
tents is proposed by Evans and Haisman (1982). They propose that two endothermic
peaks reﬂected two types of melting: granules containing less stable crystallinity melt
ﬁrst; upon melting, the polysacchanide chains absorb more water making less water
available for the remaining ungelatinized granules, causing these granules to melt at
higher temperatures.

Biliaderis et a1. (1986) have proposed a third explanation for starch gelatinization
under low to intermediate moisture conditions. They postulate that the DSC curve is not
representative of the initial crystallite proﬁle, but rather the composite thermal effect of
several processes that occur simultaneously during heating: melting, annealing and crys-
tallization. They proposed that the order-disorder phase transitions of starch-water mixes
are analogous to those of semicrystalline synthetic polymers. The thermomechanical
properties of starch polymers can be altered by the presence of small amounts of water as
a plasticizer. In the presence of a plasticizer. the glass transition temperatures of the gra-
nule’s amorphous portion are decreased which in turn facilitates melting or reorganiza-
tion of the starch crystallite and the amylose-lipid complexes to occur at lower
temperatures. ‘

Wootton and Bamunuarachchi (1979b) and Eliasson (1980) report a linear relation-
ship between moisture content and enthalpy of gelatinization when measured with a

DSC. This change in enthalpy may be caused by a change in enu'opy and not in the

13

energy of activation, in accordance with the proposed mechanism of gelatinization by
Biliaderis et al. (1986). Eyring and Steam (1939) also report that the change in enthalpy
seen at diﬁerent moisture contents of protein materials was due to differences in entropy
and not due to a change in activation energy. Eliasson (1980) also reports that the tem-
perature of the ﬁrst endotherm does not vary signiﬁcantly with water content.

Thermal analysis of starch-water mixtures with varying levels of solute concentra-
tions (salt or sucrose) shows increased thermal transition temperatures and a narrowing of
the gelatinization temperature range. It is believed that these constituents compete with
starch for water and therefore make water unavailable for gelatinization (Ghiasi et al.,
1983; Spies and Hoseney, 1982; Evans and Haisman, 1982; Oosten, 1982). Eliasson
(1983) indicates that increased levels of gluten lowered the gelatinization enthalpy and
increased the gelatinization temperature. This is similar to results reported by Ghiasi et
al. (1982a). It is believed that prorein inhibits migration of water into the starch granule.
Gelatinization of starch in the presence of lipids or surfactants indicate a lowering of gel-
atinization temperatures and increase in gel strength (Harbitz, 1983; Kugimiya et al.,
1980; Ghiasi et al. 1982b). This is most likely due to the formation of an amylose lipid
complex.

2.1.4. Measurement Methods

Many methods of measuring starch gelatinization are discussed in the literature.
These methods include light microscopy, polarized light microscopy, electron micros-
copy, viscosity changes, X-ray diffraction, thermal analysis, and enzymatic methods.
2.1.4.1. Light Microscopy

The use of a microscope allows the researcher to observe swelling duration, degree
of swelling, swollen granule integrity and size (Zobel, 1984). Freke (1971), Collison and
Chilton (1974) and Bean and Yamazaki (1978) all utilized a microscope to study starch

14

gelatinization. Both Freke (1971) and Bean and Yamazaki (1978) used a microscope
equipped with a stage heater and a camera loaded with high contrast black and white
ﬁlm, while Collison and Chilton (197 4) exposed the starch solution to heat and then
observed the results under a microscope. When heating on a microscope, care must be
taken to prevent dehydration. This can be done by sealing the cover slop with mineral oil
(Bean and Yamazaki, 1978) or silicone grease (Freke, 1971). Starch concentration of
less than 1% were used by Freke (1971) and Bean and Yamazaki (1973) to reduce the
number of granules in the ﬁeld of observation. Snyder (1984) discussed the use of vari-
ous stains (iodine, methylene blue, etc.) to aid in the determination of granule morphol-
ogy. Chlorazol violet R on heat treated starch was used by Collison and Chilton (1974)
to aid in determining damaged starch granules. Bean and Yamazaki (1978) also
measured granule swelling by photographing a scale and then superimposing this scale.
2.1.4.2. Polarized Light Microscopy

As previously mentioned, ungelatinized starch granules exhibit birefringence (a
Maltese cross) when viewed under polarized light. Use of a polarized microscope to
determine gelatinization is described by Snyder (1984), Burt and Russell (1983), Ghiasi
et al. (1982a), Bean and Yamazaki (1978), Lelievre (1973) and Miller et al. (1973).

Two methods are discussed: (1) use of a stage heater with the microscope while
taking pictures at selected temperature intervals (Bean and Yamazaki, 197 8; Lelievre,
1973) and (2) controlled heating of the starch to a desired temperature, rapid cooling and
then observation under a microscope (Ghiasi et al. 1982a; Burt and Russell, 1983;
Miller et al. 1973). Heating rates ﬁ'om l'C per 30 min (Lelievre, 1973), to l'C per min
(Bean and Yamazalci, 197 8) to lO'C per min (Burt and Russell, 1983, Ghiasi et al. 1982a)
have been used. As in unpolarized high microscopy the attachment of a camera and use
of high contrast black and white ﬁlm aid in the analysis.

15

2.1.4.3. Electron Microscopy

Use of electron microscopy to study changes in granule structure during gelatiniza—
tion has advantages over light microscopy techniques. These advantages include a
greater depth of ﬁeld and a higher resolution (about 70 A). Two types of electron
microscopy have been used in observing starch granules: (1) Scanning (SEM) and (2)
Transmission (TEM). SEM has been used to observe surface changes during gelatiniza-
tion and TEM has been utilized to help discern the internal structure of the starch granule.

2.1.4.3.1. Scanning Electron Microscopy (SEM)

Preparation of the samples for study by SEM is very important The samples must
be dry to enable coating of the surface with a heavy metal (usually a 60:40 mix of gold-
palladium). Gelatiniud or partially gelatinized starch samples have been prepared in an
amylograph (Holmes and Soeldner, 1981; Hill and Dronzak, 1973; Miller et al., 1973;
Christianson et al., 1982) or similar instrument, or by gently stirring (100 RPM) in a
water bath (V arriano-Marston et al., 1985).

Freeze drying the samples after heat treatment has been used extensively; however,
the methods of preparation vary widely. Some authors directly froze the starch pastes in
liquid nitrogen (Holmes and Soeldner, 1981; Miller et al. 1973) while others centrifuged
the paste and decanted the supernate (Christianson et al., 1982; Varriano-Marston et al.,
1985). Christianson et al. (1982) washed these pastes several times to remove minor
amounts of exudate.

Freeze-drying methods also vary from freezing inside a round-bottom ﬂask using
an ethanol-dry ice bath (Christianson et al., 1982) and freezing in a -20'C freezer, to
immersion in liquid nitrogen or liquid isopentane (V arriano-Marston et al., 1985).
Varriano—Marston et a1. (1985) report that rapid freezing followed by rapid freeze drying
caused more damage than slow or rapid freezing and slow freeze drying.

16

Upon drying, starch granules are then placed on double stick tape and coated with a
gold or goldzpalladium (60:40) mix to a thickness of 200-300 A. The coated samples are
then placed in the SEM and pictures are taken following the manufacturer’s instructions.
2.1.43.2. Transmission Electron Microscopy (TEM)

While giving higher resolution capabilities, sample preparation for TEM is much
more difﬁcult and can yield artifacts resulting in atypical morphologies. This occrn's
because the granules are not easily inﬁltrated by the embedding media (Lineback, 1984).
Because of these difﬁculties, partial degradation of the granules using acid or enzymes,
staining, or freeze fracturing have been used (Mussulman and Wagoner, 1968; Chabot et
al. 1978; French, 1984).

Stains that react speciﬁcally with certain components of the granule are called posi-
tive stains while those that provide an electron-dense outline of an otherwise electron-
transparent object are called negative stains. These stains must be of high electron
density and they must be non-crystalline (phosphotungstic acid or uranyl acetate) in order
to be usable.

Freeze fracture consists of rapidly freezing the sample in liquid nitrogen and then
impact fracturing and evaporation at low temperatures. Coating of freeze fractured sam-
ples is done ﬁrst with carbon and metal. The carbon and metal ﬁlms are cleaned by
destroying the original object by chromic acid.
2.1.4.4. Viscometers

Gelatinization of starches and effects of different treatments on starch or the pres-
ence of various food ingredients (eg. fats, protein, sugar, salt) on gelatinization can be
measured by changes in viscosity. The use of the Brabender Viscoamylograph is a
traditional method for measuring starch gelatinization. Steffe et a1. (1988) have pro-

posed an alternative to the Brabender Viscoamylograph using a Brookﬁeld viscometer

17

with a small sample adapter, mixer paddle, and two water baths. This alternate method
gave similar cru'ves compared to the Viscoamylograph but required signiﬁcantly lower
sample sizes and data collections.

Amylograph procedures are described extensively in the Amylograph Handbook
(Shuey and Tipples, 1980). Brieﬂy, the amylograph measures the torque required to bal-
ance the viscosity that is deve10ped when a starch slurry is exposed to a programmed
heating and cooling cycle. Depending on the type of starch, a known weight (eg. 40 g
wheat, 15 g potato) is added to 500 ml of water and placed in the amylograph.

The slurry is equilibrated to 50°C and then the heating cycle is started. The sample
is heated at 1.5'C/min to 95'C, held at 95'C for 1 hour and then cooled at 1.5'Clmin to
50'C. From this curve, the gelatinization temperature, pasting (i.e. maximum viscosity)
peaks, ability to withstand shear (shear thinning) and extent of setback or gel formation
upon cooling can be quantiﬁed. Addition of carboxymethylcellulose to the starch slurry
permits detection of initial gelatinization temperatures which are difﬁcult to see in some
starch slur-ries.

Viscosity of starch pastes using standard concentric cylinder, cone and plate, and
parallel plate geometries have been reported by DeKee et al. (1980), Christianson and
Bagley (1983), Christianson and Bagley (1984), Evans and Haisman (1979) and many
others. Generally, the starches are gelatinized in other apparatus and placed in the vis-
cometer to measure the viscosity.

2.1.4.5. Thermal Analysis

Use of thermal analysis to study gelatinization has become increasingly popular in
the last ten years, primarily because small sample sizes are required and gelatinization
temperatures and enthalpies of transition can be determined easily.

18

2.1.4.5.1. Differential Scanning Calorimetry (DSC)
Differential scanning calorimetry (DSC) has been used by numerous authors to

study the eﬂ‘ects of moisture levels, protein content, salt (N aCl) content, sucrose content,
and lipids or surfactants on gelatinization (Eliasson, 1983; Lund, 1983; Lelievre, 1976;
Donovan, 1979; Nakazawa et al., 1984; Wootton and Bamunuarachchi, 1979a; Stevens
and Elton, 1971; Biliaderis et al. 1980; Wootton and Bamunuarachchi, 1979b; Sweat et
al., 1984; Eliasson, 1980; Biliaderis et al., 1986; Evans and Haisman, 1982; Ghiasi et al.,
1982b; Spies and Hoseney, 1982; Kugimiya et al., 1980; Harbitz, 1983; Colonna and
Mercier, 1985; Hoseney, 1984).

Approximately 20 mg of a starch-water solution is placed in a tared DSC pan. The
starch may be input dry and water added with a syringe, or a starch slurry may be used.
The pans are then hermetically sealed and equilibration is allowed to occur, usually over
one hour. A DSC scan is then performed using an empty pan as reference at the rate of
10‘C per min from 20'C to a maximum of 150'C. Temperatures greater than 150'C
require a pressurized system because of the possibility of pan failure. Once the endo-
therm is obtained, the peak corresponding to gelatinization (50-85'C) is then integrated to
give the enthalpy of the transition.

2.1.4.5.2. Thermal Mechanical Analysis (TMA)

Thermal mechanical analysis (TMA) measures the volume expansion of materials
as they are heated at a certain rate. Biliarderis et al. (1986) used TMA to examine the
expansion of 50% starch-water mixtures. Two hundred and ﬁfty milligrams of rice starch
were ﬁrmly packed in the TMA’s quartz cell and covered with a thin layer of sand-
parafﬁn oil (5:1, w/w) and placed in the TMA. A heating rate of TC per min was used

over a temperature range of 25 to 97 'C. Weight loss due to evaporation of water and

l9

normalization to a standard weight were then performed using the TMA’s software.
TMA indicated a two-stage swelling pattern, the ﬁrst associated with the onset of gela-

tinization, the second with the melting of starch crystals.
2.1.4.6. Others

Other important, but relatively minor methods (in terms of use) have also been
used to measure starch gelatinization. These include X- ray diffraction, Nuclear magnetic
resonance (NMR), and enzyme digestibility. X-ray diffraction and NMR are used infre-
quently because of the cost of equipment and difﬁculty of use. Enzyme digestibility can
be used to quantify starch gelatinization, but it gives little information about the exact
structural and physical changes occurring.
2.1.4.6.]. Enzyme

Chiang and Johnson (1977a, 1977b) report a method used to quantify the amount

of gelatinized starch in ﬂour or starch containing foods. Based on the fact that digestion
of starch is easily performed by the enzyme glucoamylase to form glucose, this method
uses spectrophotomenic methods to determine the total and gelatinized starch.

The method is as follows: 1) disperse 20 mg of the sample in a 50 ml centrifuge
tube and 3-5 ml water, 2) add 25 ml of glucoamylase solution and incubate 30 minutes at
40’C, 3) add 2 ml of 25% nichloracetic acid to inactivate the enzyme and precipitate pro-
teins, 4) centrifuge for 5 minutes (16000 X g’s), 5) place 0.5 ml in test tubes containing
4.5 ml 0-toluidine reagent, 6) boil for 10 minutes then cool, 7) add 5 ml of glacial acetic
acid and measure absorbance at 630 nm. Other methods are reported by Zobel (1984)
and will not be discussed here.

2.1.4.6.2. X-ray diffraction

X-ray diffraction was ﬁrst used by Katz (1928) to measure changes of starch from
native to gelatinized to retrograded forms. Hellman et al. (1954) and Yang et al. (1985)

20

have also used X—ray diffraction to measure changes in the starch granules. By exposing
starch granules and starch gels to X-rays, the researcher can determine the crystalline
structure of the material. Yang et al. (1985) used small angle X-ray scattering to measure
changes in birefringence of starch granules during heating, cooling and storage. French
(1984) also lists many researchers who utilized X-ray diffraction and their ﬁndings about
the native starch granules.

2.1.4.6.3. Nuclear Magnetic Resonance

Nuclear magnetic resonance (NMR) measures starch gelatinization at a molecular
level using either high-resolution or wide-line proton magnetic techniques. Jaska (1971)
followed the hydration and solubilization of starches using wide-line techniques.
Lelievre (1975) used pulsed NMR to measure water mobility during gelatinization. It
was determined that mobility decreased as hydration of the starch occurred at the onset of
gelatinization, and as heating progressed beyond gelatinization temperatmes, the starch
chain mobility increased. Both of these studies suggest that gelatinization is a melting

process. Actual procedures depend upon the equipment being used.

21

2.2. Rheology

2.2.1. Introduction

Rheology is the study of deformation and flow of matter (New American Heritage
Dictionary, 1982). Measurement of rheological properties for food products is important
because they can be used to describe basic physical properties of the food material, there-
fore eliminating subjective terms such as gumminess or crunchiness, and enabling better
process and quality control. Szczesniak (1987) stresses that the measurement of
rheological properties should be performed in an instrument where the nature and magni-
tude of the acting forces and the sample dimensions are well known, and the results can
be expressed in fundamental units.

2.2.2. Models For Rheological Modelling of Food

In an ideal system, there would be just two types of materials: solids and liquids.
The solids would follow Hooke’s law when stress is applied, and liquids would follow
Newton’s law of constant viscosity. However, many food materials exhibit properties of
both solids and liquids, making it difﬁth to measure rheological properties of foods.
Foods can be either viscoelastic solids, elastico-viscous (elastic) liquids or inelastic ﬂu-
ids.

Walters (1975) deﬁnes viscoelastic solids as materials that do not continually
change their shape when subjected to stresses, and elastic liquids as those which change
their shape continually when subjected to stress, irrespective of how small the stress may
be. Prentice (1984) expands Walters’ (197 5) deﬁnitions by deﬁning viscoelastic foods
as those which behave as if they had a solid structure (i.e. elastic), but whose deformation
is modiﬁed by viscous behavior; and elastico-viscous foods as those which show some

kind of elastic behavior (such as recoil) when flow ceases.

22

There are many models used to describe viscosity of ﬂuid and semi-ﬂuid foods.
The simplest model which describes viscosity is Newton’s law (Table 2.2.1). However,
there are very few foods which exhibit Newtonian behavior (among them ﬂuid milk, and
dilute corn syrup solutions); therefore more complex models are necessary.

Common rheological models which are used to describe viscosity of ﬂuid foods are
the power law or Ostwald-de Waele (Reiner, 1949), Casson (Casson, 1959), Bingham
(Bingham, 1922) and Herschel-Bulkley (Herschel and Bulkley, 1926). Of these, the
model that is most widely used is the power law model because of its simplicity and ease
of parameter estimation. Simple log-log transformation of shear stress and shear rate data
allows one to estimate the parameters via linear regression provided a value for yield
stress is given. The power law model has some drawbacks, however. F‘u'st, as shear rate
increases towards inﬁnity, viscosity approaches a value of zero. A second drawback is
that as shear rate approaches zero the viscosity becomes inﬁnite. However, within these
limitations the power law has been found to adequately describe many food products.

Food products may exhibit a yield stress. Yield stress is deﬁned as the minimum
mess that must be applied to initiate ﬂow. Barnes and Walters (1985) recently ques-
tioned if there was a yield stress or whether it is the inability of the instrumentation to
measure ﬂow. However, over the short time frame a producer or consumer is concerned
with, many foods do exhibit a yield stress (e g. Mayonnaise, ketchup, molten chocolate).

The simplest model which includes a yield stress is the Bingham model (Bingham,
1922). This model assumes that once the yield stress has been exceeded. normal Newto-
nian behavior occurs. Butter and margarine are examples of Bingham foods, but in gen-

eral the Bingham model is of little use because very few foods behave this simply.

23

 

Table 2.2.1 Rheological models and their parameters used to
characterize ﬂuid food behavior (Ofoli et al., 1987).

 

 

Model Shear Stress Apparent viscosity
Newtonian o = ll 11 = p,
Powerlaw 0:19?- n=KfYr-l
Bingham o = on + a = "'1
Herschel- = °
Bulkley O O°+KY| =--+K'Y"l
.5 .5 ° .5 2
‘Y
if?” °”=K«M “W n=tK.Mt*"K.t"°‘r’
Heinz- = ' a ' 1
Cl 5111 0” 024-0107) [[00]! n]'
n = . -" + “'0
Y
Ofoli “1

0 =c?+u.i" ,, '3:
THU-0.1] +tt_"y"-"]

 

 

24

The Herschel-Bulkley (Herschel and Bulkley, 1926) model is used with a wide
range of food products. The model is a generalized power law model, with a yield stress
added. The same drawbacks that are observed with the power law model at high shear
rates are also seen with the Herschel-Bulkley model.

Measurement of the value of the yield stress generally presents difﬁculties. The
most common method is to extend shear stress versus shear rate curves to zero shear rate.
Another method is to estimate the value of the yield stress, utilizing some form of curve
ﬁtting computer program. Osorio and Steffe (1985) have proposed a back extrusion
method to quantify the yield stress for ﬂuid foods. Given the limitations, the Herschel-
Bulkley model is useful in determining rheological properties of the food material.

Another model which has found wide use in the confectionery chocolate industry is
the Casson model (Casson, 1959). Casson developed the model for use with pigment
suspensions. It is important to note that the drawbacks seen with other models (zero vis-
cosity at inﬁnite shear rates, and inﬁnite viscosity at zero shear rates) do not apply to.the
Casson model. However, due to the ﬁxed exponent of all the terms, the equation may not
accurately describe all sections of the shear stress versus shear rate curve. Another modi-
ﬁcation of the Casson model is the Mizrahi-Berk model (Mizrahi and Berk, 1972).

Ofoli et al. (1987 ) have proposed another model which allows for a yield stress,
variable shear-thinning and limiting viscosity at high shear rates. Disadvantages are the
mathematical complexity of the model and the difﬁculty in obtaining model parameters
without sophisticated computer programs.

2.3. Extrusion
2.3.1. Introduction

Ram or piston type extruders were used to stuff sausage casing and other processed
meats early in the history of food processing. An early application of the single screw
exn'uder was as a continuous pasta press in the 1930’s (Harper, 1981). Single screw
extruders were developed in the 1940’s for the purpose of making puffed snacks from
cereal ﬂours or grits (Harper, 1986). By the late 1950’s, extrusion cooked pet food had
replaced other methods of production (Harper, 1981). In the 1960’s, ready to eat (RTE)
breakfast cereals and textured soy protein products were being produced in cooking
extruders (Harper, 1981).

Reasons for the increased use of cooking extruders are listed below and discussed
in detail by Harper (1981):

l. Versatility: many foods can be produced with the same or similar equipment.

2. High productivity: extruders provide a continuous processing system, having
greater production capacity.

3. Low cost: labor and ﬂoor space requirements are reduced.

4. Product shapes: a wide variety of shapes are available which are not possible
with other production methods.

5. High product quality: cooking extrusion is basically a high temperature short
time process.

6. Energy efﬁcient: extruders operate at lower moisture contents, reducing heat
requirements for drying.

7. Production of new foods: modiﬁcation of proteins, starches and other food
materials can be achieved in exn'uders to produce new food products.

8. Low efﬂuents: little or no waste is produced, therefore costly waste treatment is
avoided.

Two types of extruders are used by the food industry today. The one that has been

in use the longest is the single screw extruder. In the last few years, twin screw extruders

26

have been used increasingly in the food indusn'y. While single screw extruders have the
ability to manufacture a wide range of food products (eg. breakfast cereals, pet foods,
puffed snacks, etc.), use of twin screw machines is increasing because of their expanded
range of applications and operational capabilities (Harper, 1986).

Single screw extruders consist of a ﬂighted screw rotating in a closely ﬁtting bar-
rel. The barrel is usually equipped with heating/cooling jackets in order to add or remove
heat to the product as it passes through the extruder. The raw material is fed into the
screw and as the material is conveyed through the transition section, the screw ﬂights and
barrel wall work and mix the material. Through viscous energy dissipation, the food
material is heated and cooked. In the metering section of the extruder, pressure is built
up before the material exits the die(s).

The screw is a single piece with varying compression ratios and pitches, or a
splined shaft which allows screw elements of differing conﬁgurations to be used (Harper,
1986). The splined shaft design allows for more ﬂexibility in terms of maintenance and
product variation. Single screw extruders often require pro-conditioners or pre-mix
equipment to mix the dry and liquid ingredients and allow an equilibrium to be reached
before feeding the material into the extruder.

Twin screw extruders, as their name implies, consist of two screws inside a barrel
which can be heated or cooled. There are two types: co-rotating or counter rotating. The
co-rotating type is the most widely used by the food industry. The screws feature many
geometries and can be used in any number of conﬁgurations. Unlike single screw
exu'uder elements, the screws and paddles are self-wiping; therefore, there is less
build-up of material. The high degree of mixing in twin screw extruders make them well
suited for use as heat exchangers for highly viscous food materials (Harper, 1986).

27

Twin screw exn'uders have a higher initial cost than single screw exn'uders. The
overall operating costs may be less, however, due to lower ﬂoor space requirements, little
or no need for premixing equipment, ability to run at lower moisture contents (lower
post-process drying requirements), and greater ﬂexibility in types of products made.
These factors give twin screw extruders an advantage over single screw extruders.

2.3.2. Viscosity Models Used in Extrusion

Several rheological models for extrusion of ﬂour or protein doughs have been
reported in the literature. One of the earliest rheological models was by Harper et al.
(1971), who modeled the viscosity as a function of inverse temperature, moisture, and
shear rate as described by the power law model.

Bhattacharya and Hanna (1986a) proposed an empirical model derived statistically
for corn gluten meal and soy protein concentrates. Dough viscosity Was modeled as a
function of moisture content and shear rate; temperature, time-temperature history and
strain history were not incorporated. Therefore, the model is machine-and ingredient-
speciﬁc and of limited general use. Effects of moisture content, barrel temperature, shear
rate, residence time and shear strain on extrusion cooked waxy and non-waxy corn grits
were studied by Bhattacharya and Hanna (1986b), who presented statistical models which
indicated that moisture content and temperature are the most signiﬁcant variables. How-
ever, the authors stated that higher moistures reduce the degree of gelatinization, in con-
trast to research results of several starch chemists studying starch gelatinization
(Donovan, 1979; Eliasson, 1980; Biliarderis et al., 1986).

The reduction in degree of gelatinization as moisture content increases is also in
conﬂict with research by Chiang and Johnson (1977a) and Owusu-Ansah et al., (1983)

both of which indicate that degree of gelatinization increases with moisture content. This

28

illustrates a problem with relying on statistical models for predicting viscosity changes in
extrusion. Bhattacharya and Hanna (1986b) did n0t include strain or time-temperature
history in their model.

Jao et al. (1978) and Cervone and Harper (1978) also developed empirical models
incorporating moisture content, temperature and shear rate, but time-temperature and
shear history effects were not considered.

Two models which included time-temperature history have been proposed by Rem-
sen and Clark (1978) and Morgan et al. (1988). The model proposed by Remsen and
Clark (197 8) included parameters for moisture content, shear rate and time-temperature
history. Remsen and Clark (1978) did not study time-temperature history at low to inter-
mediate moisttne concentrations, but assumed that relative increases in viscosity due to
cooking were the same as for suspensions containing 70-75% moisture. Their model also
exponentially approaches inﬁnity for large time-temperature histories.

This is in contrast to Morgan et al. (1988) who provided experimental data indicat-
ing that protein dough viscosities approach some ﬁnite maximum value for time-
temperature histories and shear rates encountered in extrusion. The model by Morgan et
al. (1988) includes time-temperature history as well as shear rate, moisture content, and
temperature. J anssen (1986) incorporates shear rate, temperature and time-temperature
history in a model utilizing the power law relationship. However, moisture content and

strain history were not incorporated.

29

CHAPTER 3 MODEL DEVELOPMENT
3.1. Effect of Shear Rate on Viscosity

Many of the studies discussed previously use the power law model to characterize
shear rate aﬁ‘ects on the viscosity (Bhattacharya and Hanna 1986; Janssen 1986; Cervone
and Harper 1978; Jao et al. 1978; and Remsen and Clark, 1978). While data shows good
ﬁt using the power law equation, the model itself has several drawbacks. The most
important one is that it does not accommodate a yield stress. Other serious drawbacks are
that it predicts unlimited decreasing apparent viscosity with increasing shear rate, and for
a given shear thinning index it predicts zero or inﬁnite viscosities at zero and inﬁnite
shear rates, respectively.

Barnes and Walters (1985) contend that there is no such thing as a yield stress.
Theoretically this may be true, but relative to the process time of most extrusion opera-
tions, dough does not ﬂow unless some minimum force is applied. Therefore, a yield
stress may be deﬁned as a material property in terms of the relative time frame of the
process system involved. For example, cookie dough does not ﬂatten out when put on a
table before other quality parameters such as microbial acceptability are exceeded.

Luxenburg et al. (1985) modeled soy doughs using Bingham plastic and Herschel-
Bulkley models with good results. The Bingham plastic model does not allow for vari-
able shear thinning index, and the Herschel-Bulkley model has a variable shear thinning
index but approaches zero viscosity for large shear rates. This may present problems

since shear rates encountered in extrusion may span 3 to 4 decades.

30

Morgan et al. (1988) used the Casson model to characterize soy protein doughs
extruded in a capillary rheometer. The Casson model worked well, but it does not allow
for a variable shear thinning index. Ofoli et al. (1987) have proposed a generalized rheo-
logical model for the characterization of inelastic ﬂuid foods. The model incorporates a
variable shear thinning index, yield stress, and high shear limiting viscosity:

L

H .1
.. "o as":
n-IITY] +lr_y ] [3.1]

Advantages of this model are that it incorporates a yield stress, variable shear thin-
ning indices and high-shear limiting viscosity. Equation [3.1] is the model used in this
study to quantify shear rate effects.

3.2. Effect of Temperature

Viscosity of Newtonian and non-Newtonian ﬂuids are usually affected by tempera-
ture. In general, as temperature increases, viscosity decreases. The relationship between

viscosity and temperature can be represented by the equation of Glasstone et al. (1941):

i(1"‘-T:')

nr =nte ’ [3.2]

where AB, is deﬁned as the molar "free energy of activation" in a stationary ﬂuid (Bird et

al. 1960). The free energy of activation (AE,)is related to the amount of energy required
for a molecule to escape its surroundings and move into an adjoining molecular site.
Morgan et al. (1988) proposed that a shear rate dependency (such as shown in Eq. 3.1)
could be combined with Eq. 3.2, if Metzner’s (1959) assumption that the shear thinning
index is not affected by temperature is applied. In addition, one must assume that n2 is

not aﬁ‘ected by temperature. The combined equation is

31

I‘l “r i r_ r
le.r=[[;;-] +u_,-an-~t] ash" 77) [3.3]

3.3. Effect of Moisture

The effect of moisture content on viscosity has been described using a logarithmic
mixing rule (Cervone and Harper, 1978; Harper et al., 1971; and Morgan et al., 1979).
The logarithmic model is given by

ﬂuent/Wan) [3“]

Morgan et al. (1988) combined Eqs. 3.3 and 3.4 to give a relationship which

combines shear rate, temperature and moisture content effects on apparent viscosity:

JI-

‘1 . _ T'T‘J'," +b(MC-MC,)
“mac =[[%—:| +1.1.le H] 9 ( ) [3.5]

3.4. Effect of Time-Temperature History

When starch and water are heated together, an increase in viscosity can be
observed on an amylograph (Shuey and Tipples, 1980). The extent of this increase
depends on the temperature and the time of exposure of the starch granule to that temper-
ature. If starch granules are exposed to temperatures below the temperature required for
gelatinization to start, no change in viscosity is seen until the threshold temperature is
exceeded. Therefore incorporation of time-temperature history requires use of an activa-
tion or threshold temperature.

Increases in viscosity of dilute starch solutions is attributed to the starch granule
taking up water and a concurrent swelling of the granule (Hoseney, 1986). As the gran-
ule swells, starch molecules are leached out causing further increases in viscosity.
Gomez and A guilera (1984) found that this classic gelatinization model of granule

swelling and release of starch polymers was inadequate for high-shear extrusion cooking.

32

This was based on a previous work (Gomez and Aguilera, 1983) which found that, as
extrusion moisture content decreased, "dextrinization" (i.e. shortening of polymer chains
due to mechanical breakdown) appeared to become the predominant mechanism of starch
degradation. They proposed a model that assumes the coexistence of three ptue states:
raw, gelatinized and dexninized starch. In theory, the actual state of degradation is the
sequence:

raw -> gelatinized -> dextrr’nr’zed.

A more complex model includes intermediate states of mechanically damaged
granules, free polymers, and oligosaccharides and sugars. Different states are due to
time-temperature history and shear-strain history in the extruder.

When gelatinization of starch is measured by differential scanning calorimetry
(DSC) under low moisture conditions, two endotherms are observed. When excess water
is present, the DSC curve shows only one endotherm indicating that water content
directly affects gelatinization kinetics. .

Various models have been proposed for this phenomenon. Donovan (1979) sug-
gests that, upon hydration and swelling of the amorphous portions of the granule and due
to coupling with crystallites, melting of the latter occurs as long as water is present in
excess. He postulated that when the amount of water is insufﬁcient for complete melting
the remaining crystallites melt at a higher temperature and thus support the second DSC
peak.

Another hypothesis for starch gelatinization at low to intermediate moisture con-
tents is given by Evans and Haisman (1982). They proposed that two endothermic peaks
reﬂected two types of melting: granules containing less stable crystallinity melt ﬁrst,

33

and, upon melting, the polysacchanide chains absorb more water, making less water
available for the remaining ungelatinized granules thus causing these granules to melt at
higher temperatures.

Biliaderis et al. (1986) have proposed a third explanation for starch gelatinization
under low to intermediate moisture conditions. They provided evidence showing that the
DSC curve is not representative of the initial crystallite proﬁle, but rather the composite
thermal effect of several processes that occur simultaneously during heating: melting,
annealing and crystallization. They proposed that the order-disorder phase transitions of
starch-water mixes are analogous to those of semicrystalline synthetic polymers. The
thermomechanical properties of starch polymers can be altered by the presence of small
amounts of water as a plasticizer. In the presence of a plasticizer. the glass transition
temperatures of the granule’s amorphous portion are decreased which in turn facilitates
melting or reorganization of the starch crystallite and the amylose-lipid complexes at
lower temperatures.

In this study, it is assumed that starch granules are analogous to semicrystalline
synthetic polymers, as proposed by Biliaderis et al. (1986). Completely crystalline poly-
mers follow ﬁrst order kinetics for melting while purely glassy polymers follow second-
order kinetics. A pseudo-ﬁrst order kinetic model will be used in this study for
time-temperature effects of starch gelatinization on the apparent viscosity. Harper et al.
(197 8) and Morgan et al. (1979) used this approach with heat setting bovine plasma pro-
tein suspensions and soy doughs, respectively.

Pseudo ﬁrst order polymerization assumes that concentration of one reactive spe-
cies will remain constant and predicts disappearance of the monomer species. Starch gel-
atinization is a much more complex reaction than ﬁrst order; however, this simpliﬁcation
is used to approximate the "average-overall-viscosity" effect caused by gelatinization.

Further development of this model is based on Gomez and Aguilera’s (1984) proposed

34

model. They assumd that increases in viscosity are due to the swelling granule and/or
leaching of starch polymers outside the granule. This swelling and leaching is assumed
to be similar to the viscosity increases caused by an increase in the "effective polymer
molecular weight" during a plastic polymerization process (Morgan et al., 1988).
Development of a time-temperature history function based on pseudo ﬁrst order
plastic polymerization processes was done by Morgan et al. (1988) for protein based
doughs. Modiﬁcation of this function for starch based doughs yields an equation for the

effects of time-temperature history on viscosity due to gelatinization:

na=B.(Cs)“(1—e"v)“ ‘ [3.61
Morgan et al. (1988) assumed that viscosity of a denaturing protein dough could be

described by '

n =nt,r,nc+ne [371

Where “in“: represents the undenatured viscosity and no represents the increase in vis-

cosity due to gelatinization of the starch granules.

Use of Eq. 3.6 is only valid at constant temperature. In extrusion, the temperature
will increase to a maximum with time and may decrease before exiting the die. There-
fore, there is a need to incorporate variable time-temperature histories into Eq. 3.6. Mor-

gan et al. (1979) proposed the use of an integrated time-temperature history, w, deﬁned
by

3 fl 3
“1:1. T(t)e" 0dr [3'8]
0

when T(t) is greater than the threshold temperature. Equation 3.8 is then related to Eq.
3.6 by

k, = katv [3.9]

35

where k.=(k,k.,/h) and represents a reaction transmission coefﬁcient for the material
source, =Boltzman’s constant, k,=transmission coefﬁcient, and h=Planck’s constant.

Combining Eqs. 3.6 and 3.9 yields

na=B.(Cs>°‘(t-e"-")° [3.101
which relates the change in viscosity to time-temperature history.

Morgan et al. (1988) assumed that if the protein dough is held long enough at vari-
ous temperatures, each treatment will approach the same viscosity. Kubota et al. (1979)
studied the gelatinization rate of rice and potato starches and found the maximum
viscosity to be a function of time. Similar results were found by Bakshi and Singh (1980)
for gelatinization in rice kernels. Using differential scanning calorimetry (DSC) Lund
and Wirakartusumah (1984) developed a model for starch gelatinization. Comparison of
. enthalpy values versus cook time at different temperatures gave results similar to both
Bakshi and Singh (1980) and Kubota et al. (1979). Kubota et al. (1979), Bakshi and .
Singh (1980) and Lund and Wirakartusumah (1984) worked with high moisture systems.

Dolan et al. (1988) found that viscosities collected at different time-temperature

histories could be normalized by

 

11 " Tlo
“"‘m-n. [3.111
It is important to note that all viscosities are speciﬁc to the cook temperature after
either correction or normalization to the same temperature. In other words, the inﬁnite
viscosity term is the viscosity after inﬁnite time at one cook temperature; if the cook tem-
perature is changed, then a different inﬁnite viscosity must be used. Dolan et al. (1988)

also worked under high moisture (about 90%) conditions.

36
Dolan et al. (1988) stated that the change in viscosity caused by gelatinization is
described by

no =A(l - e""')° [3.12]

Combining Eqs. 3.7 and 3.12 gives:

“w = "in: 1 +A(l - e4‘VJa] [3.13]

iftv -) co then Eq. 3.13 becomes:

 

n- = “71.11%“ + A] [3.14]

and therefore A becomes:

A = n- - 1 [315]
“tram:

By combining Eqs. [3.5], and [3.13] we get a model that incorporates temperature,

shear rate, moisture content, and time-temperature history:

JI-

‘1 __ 1'1 r"-r," +bwc-uc, a
ﬂy,r,uc,y=[[1—;] +1.67”: 1"] e ‘ ( ) [1+A(l—e4‘v)] [3-15]

3.5. Effect of Strain History

With increasing time of shear, the viscosity of dispersed starch solutions decreases.
As starch granules swell they become more susceptible to mechanical degradation.
There is much evidence that there is degradation of the starch granule during extrusion
(Mercier, 1977; Colonna et al., 1984; Gomez and Aguilera, 1983; Gomez and Aguilera,
1984; Davidson et al., 1984; Diosady et al., 1985; Doublier et al., 1986). In each case the
products of starch breakdown have been measured. Two different models for mechanical
degradation of wheat starch have been proposed by Davidson et al. (1984) and Diosady

37

(1985). A serious drawback to both models is that they require the measurement of the
extent of starch degradation by gel permeation chromatography (Davidson et al., 1984) or
the degree of cook (Diosady, 1985). Anather drawback is that both techniques measure
degradation and do not allow for predicting what the degradation may be. What is
needed is an equation that can be used regardless of system geometries, conditions and
raw materials.

Pinto and Tadmor (1970) have proposed the following for quantifying total strain-
history effects on transport properties of polymers:

<I> = [0‘th [3°17]

Morgan et al. (1988) proposed a similar model :

' Viscosity will decrease as the value of 4) increases until a ﬁnite limiting viscosity is
obtained. The value of the ﬁnite limiting viscosity depends on both the shear rates
obtained within the extruder and the length of time at each shear rate.

An equation describing strain history effects on viscosity was proposed by Morgan
et al. (1988) and is given by
n=1-B(1-e“’) [3.19]
When this equation is incorporated into Eq 3.16, the ﬁnal equation now incorporates
shear rate, temperature, moisture content, time-temperature history, and strain history:

1.
n “r

, 1:, ”5..., ;3(r‘-r';‘)+bwc -Mc,)
“ture.”: TY” l+llJY e

[1+A(1_e*-*)°][1-B(1—e“’)] [3.20]

38

There are two important differences between Eq. [3.20] and the one proposed by
Morgan et al. (1988): 1) the time-temperature history term has been modiﬁed to reﬂect
the differences between protein denaturation and starch gelatinization; and 2) the general-
ized Casson model was replaced with the model proposed by Ofoli et al. (1987) for
describing shear rate effects. Table 3.1 lists the individual terms of the model.

Limitations of the model include:

1. Difﬁculty in obtaining a yield stress value and the lack of an adequate non-
linear regression computer program to determine the power indices and high shear limit-
ing viscosity for the shear rate term.

2. The order in which one determines the moisture content and temperature effects
on viscosity may yield different values for the respective parameters.

3. Determination of the moisture content and temperature effects above gelatiniza-
tion temperatures may yield different numerical values than if quantiﬁed below gelatini-
zation temperatures.

4. Evaluation of time-temperature history parameters is difﬁcult if the heat transfer
through the material is rapid; yet, this must be accomplished to allow comparison of data
collected at different cook times and cook temperatures.

5. Strain history parameters may be functions of time-temperature history as well

as shear rate and time.

39

 

Table 3.1. Model parameters and what they describe.

 

 

Shear rate effects

Temperature effects

Moisture content effects

Time-temperature history effects

Strain history effects

t " .-
11= 7‘] +1147”

b(MC -uc,)
e

[1+A(1_ [5‘0“]

[13(1 - e'“)l

l.
‘r

 

 

40

3.6. A procedure for determining the parameters in Eq.[3.20].

Choose a reference temperature (below the gelatinization temperature) and mois-
ture content and then collect shear stress versus shear rate data to obtain a relationship to
describe the effects of shear rate on viscosity. Next, vary the temperature (again below
gelatinization temperature) and hold the shear rate and moisture content constant to
obtain the effects of temperature on viscosity.

Vary moisture content at a temperature below the gelatinization temperature and
quantify the effects of moisture on viscosity. Now vary both cook time and cook temper-
ature and measure the effects of time-temperature history on viscosity. Finally, vary the
strain history and quantify the effects of strain history on viscosity. A ﬂow chart for

determining the model parameters is shown in Table 3.2.

 

41

Table 3.2. Flow chart for determining model dependencies.

 

Shear rate dependency

Hold T=Tr, MC=MC,, \ll=0 and ¢=0.
Collect viscosity versus shear rate data to determine shear rate effects.
Establish 11 =f(y) See Eq. [3.1]

 

Temperature dependency

Hold at MC=MC,; \|I=0; and 41:0. .
Vary temperature and collect viscosity data with f(y) given by [3.1];
Establish n = f(y, T) See Eq. [3.3]

 

Moisture dependency

Hold w=0 and ¢=0. .
Vary moisture and collect viscosity data with f(y, T) given by [3.3]
Establish n =f(y,T,MC) See Eq. [3.5]

 

Time-temperature history dependency

Vary cook time and temperature and collect viscosity data with f('°y, T, MC) given by

[3.5] and ¢=o.
Establish 1] =f(‘°y,T,MC,\|I) See Eq. [3.16]

 

Strain history dependency

Vary strain history and collect viscosity with ﬂy, T,MC,\V) given by [3.16]
Establish n =f(y,T,MC,\]I, 4)) See Eq. [3.20]

 

 

 

42

CHAPTER 4 EXTRUSION MODELLING OF PREGELATINIZED
POTATO FLOUR

4.1. Abstract
A generalized model is proposed for predicting the effects of shear rate, tempera-

ture, moisture content, time-temperature history and strain history on the apparent viscos-
ity of low to intermediate moisture starch-based doughs during cooking extrusion. The
model was evaluated for potato ﬂour doughs using an Instron Capillary Rheometer and a
50 mm APV Baker co-rotating twin screw extruder for all effects except strain history.
The power law model adequately described shear rate effects in the range 10-10000 sec“.
The generalized model ﬁt observed data for temperatures of 25-95'C and moisture con-
tents (wet basis) ranging from 22 to 50%. Time-temperature history variables were not
quantiﬁed because the potato ﬂour was pregelatinized. Strain history had no signiﬁcant

inﬂuence on the viscosity.

43

4.2. Introduction

The predominant ingredient in most extruded snacks and ready to eat (RTE) cereals
is starch (Harper, 1986). During cooking extrusion, starch granules undergo many
changes leading to increased molecular rearrangement, including loss of crystallinity,
degradation and formation of amylose lipid complexes. Changes in the starch granule
during gelatinization may signiﬁcantly affect viscosity. Therefore, the role of tempera-
ture, moisture, shear, and feed ingredient composition are important factors involved in
changing starch structure during cooking extrusion (Harper, 1986).

Commercialization of extrusion processes is signiﬁcantly constrained by lack of
adequate scale-up information. Two important elements needed for improving food
extrusion scale-up and design are effective process engineering analysis methods, and
adequate rheological models. Currently, there is no single rheological model which
incorporates starch gelatinization, viscoelastic behavior, density and thermal properties as
functions of time, temperature, shear rate, and moisture content (Harper, 1986).

Several extrusion models for ﬂour and protein doughs have been reported in the lit-
erature (Bhattacharya and Hanna, 1986; Cervone and Harper, 1978; Janssen, 1986; Jao et
al., 197 8; Remsen and Clark, 197 8). However, only the model proposed by Remsen and
Clark (197 8) incorporates effects of temperature, shear rate, time-temperature history and
moisture content.

More recently, Morgan et al. (1988) proposed a generalized viscosity model to
describe the rheological changes which occur during the cooking extrusion of protein
doughs. This work presents the most comprehensive rheological model yet. The mathe-
matical relationship predicts viscosity as a function of temperature-time history, strain

history, temperature, shear rate and moisture content.

44

Dolan et al. (1988) used the model by Morgan et al. (1988) as the basis for predict-
ing changes in starch viscosity during the gelatinization of high moisture starch solutions.
The model was found to predict changes in viscosity due to different time-temperature
histories when shear rate, moisture content, temperature and strain history are held con-
stant. While the changes that occur in the starch granule are different for high moisture
systems than low moisture systems, it is important to note that time-temperature history is
an important factor contributing to viscosity changes in both systems.

The purpose of this study is to extend the work of Morgan et al. (1988) and Dolan
et al. (1988) to develop a generalized viscosity model for low to intermediate moisture
starch-based foods for use in extrusion. The model will incorporate the effects of time-

temperature history, moisture content, temperature, shear-strain history, and shear rate.

45

4.3. Model Development

The model presented by Morgan et al. (1988), with some modiﬁcations, was used
to describe the viscosity of extruded starch based products. The power law model was
found to be adequate to describe shear rate effects on the potato ﬂour dough. The effect
of time-temperature history on viscosity was modiﬁed to account for starch gelatinization

kinetics. The resulting expression is

7] =1+A(1_ 12""): . [4.1]
Incorporating the above changes, the generalized model of Morgan et al. (1988) for
extrusion of protein doughs takes the following form for starch-based doughs:

ﬁgure»... = [eéﬁ'hlf’ﬁbwc '"CJ (“.Y)[1 +A(1 _ ft”)? [1 - B(1 - £45] [4.2]

The ﬁrst term incorporates the effects of temperature and moisture content on vis-
cosity. It is important to note that AEJR is not a measure of gelatinization kinetics but
rather of how temperature affects the ﬂow of the material. Lubricating effects of water
are described by the term b(MC-MC,). The K?) term represents any apparent shear rate
dependent viscosity function (power law, Casson, Herschel-Bulkley, etc.) of the dough at
the reference temperature and moisture content and with \v = 4) = 0. The next term
describes the effects of gelatinization on the ﬁnal viscosity of the starch dough. Time-
temperature history (w) can range from zero for temperatures below gelatinization tem-
peratures to inﬁnity for either very high temperatures, long exposure time or a
combination of the two. Also included are: the energy of activation for gelatinization
(A5,) which may be affected by moisture content and or, an indicator of granule swelling
and molecular entanglement. The ﬁnal term incorporates strain history (it), which is a

46

measure of the effects of irreversible shear thinning. As strain history increases, the vis-
cosity approaches a ﬁnite value (11.). If any of the variables is constant, the term that

incorporates that variable reduces to unity.

47

4.4. Materials and Methods
Potato ﬂour (Lamb-Weston, Portland, Oregon) was mixed at room temperature

with tap water to 25, 35, and 45% moisture (wb) in a large institutional kitchen mixer.
The doughs were allowed to equilibrate at 7’C overnight in Ziploc Bags (Dow Chemical,
Indianapolis, Indiana). Final moisture content of the doughs were determined by drying
in a vacuum oven overnight at 70’C and 686 mm Hg.

An Instron Capillary Rheometer and a Model 4202 Instron Universal Testing
Machine (Instron Corp., Canton, Massachusetts) were used to measure the apparent vis-
cosity of the doughs. Die lengths of 50.8 mm (2 in) and 6.35 m (1/4 in) and diameters
of 0.49 m (1/8 in) and 1.59 mm (1/16 in) were used, giving L/D values ranging from 2
to 32. Two replicates for each plunger velocity and L/D were performed. Force versus
plunger displacement curves were collected and force at the die entrance was calculated
by extrapolation of the force versus displacement curves to the die as described by Bin?-
hom and Turetzky (1964). Barrel drag was then subtracted from the conected force.

A correction for entrance effects was made using the technique described by
Bagley (1957). Shear rate and shear stress were then calculated using the Rabinowitsch
equation (Whorlow, 1980)

 

 

. di
7.. = 3Q, + ‘t,[ 11] [4.3]
“R, dot”
and the standard expression for shear stress at the wall of a capillary:
_ APR, 4
r, — 2L [ -4]

Slip analysis was performed using the method described by Darby (1976).
Temperatures used in this study were 25, 50, 65, and 95'C. At 50 and 65'C,

doughs were compressed in the capillary barrel and were held for 10 minutes. Moisture

48

contents used were 25, 35 , and 45%, wet weight basis. Tests were conducted at 50'C for
25% (wb) moisture samples. Cook times of 2, 4, 6 and 12 min at 95'C were performed
on 35% (wb) moisture samples after compression. The 45% moisture samples were
cooked for 4 and 12 minutes after compression. Effects of temperature (A5,) on viscosity
was determined by linear regression of log viscosity versus inverse temperature; the
effect of moisture content (b) on viscosity was determined by linear regression of log vis-
cosity versus moisture content at constant temperature.

Experimental extrusion tests were conducted using an APV Baker MPF 50D (APV
Baker, lnc., Grand Rapids, Michigan) co-rotating twin screw extruder with the screw
conﬁguration shown in Table 4.1. Moisture contents were 40 and 50% (wb) and temper-
atures at the die ranged from 40 to 75°C depending on exn'uder operating conditions.
Feed rates were 1.26 x 10", 2.00 x 102, and 8.69 x 10'3 kg/s; and screw speeds used were
100, 220, and 350 RPM. Die diameter was 3.17 x 103 m and die lengths were 4.00 x
10’, 1.50 x 10'2 and 2.60 x 102 m. Pressure drop and extrudate temperature at the die
were recorded two minutes after extruder operating conditions had been changed, to
allow equilibrium conditions to be attained. Equilibrium conditions were assumed to
exist when die pressure and barrel zone temperatures stabilized.

Viscosities of the exn'udates were calculated by measuring the pressure drop at the
die. Plotting pressure drop versus the three different die L/D’s with constant temperature,
moisture, and mass ﬂow rate allowed correction for end effects as described by Bagley
(1957) for capillary dies. Shear rate was calculated using the Rabinowitsch equation
(Whorlow, 1980) and shear stress was calculated using Eq. [4.4] for each die, tempera-8
ture, moisture and mass ﬂow rate. Temperature and moisture correction on exu'uder data

was performed using AE, and b estimated from the capillary rheometer.

49

 

Table 4.1. Screw conﬁgurations of MPF-50D/25 APV Baker twin screw extruder.

 

 

 

Exn'uder L/D:15
Screw Conﬁguration
Length (cm) Screw Type
17.2 FS Feed Inlet
7.6 30F
7.6 FS
5.1 30F
2.5 45F
5.1 FS
6.2 30F
5.1 FS
5.1 30F
12.7 SL Extruder die

Key to Notation:

FS Feed Screw

30F 30 degrees Forwarding Paddles
45F 45 degrees Forwarding Paddles
SL ' Single Lead screw

 

 

50

4.5. Results and Discussion

There was apparent slip at some moisture contents, temperatures and shear rates as
indicated by the presence of a "shark skin" on the extrudate. Slip analysis was conducted
but results were not meaningful. Therefore, no further attempt was made to correct for
slip. Inability to correct for slip may be due to a friction coefﬁcient between the wall of
the capillary die and the food material which could not be measured. Another cause may
be due to a combination of both slip and friction or "slip-stick" where the material sticks
until the friction coefﬁcient is exceeded and then slips.

The effect of temperatme on viscosity of 0.507 moisture samples is shown in Fig.
[4.1]. An Arrhenius relationship was followed over the temperatures covered by these
experiments. Over the temperatures encountered during extrusion, a linear relationship
between viscosity an inverse temperature is usually observed.

Actual moisture content of the 25 , 35 , and 45% doughs was determined to be 0.282
(22% wb), 0.507 (33.7% wb), and 0.772 (43.6% wb) g water per g potato ﬂour, respec-
tively. Moisture content effects at 50’C and 100 s" are shown in Fig. 4.2. As illustrated,
a simple logarithmic relationship may not be adequate for broad ranges of moisture
content. This is similar to the data for defatted soy ﬂour adjusted to 95'C from Morgan et
al. (1988).

The power law model was used to describe shear rate effects for this study. Appar-
ent viscosity versus shear rate for potato ﬂour cooked at 95'C for 2, 4, 6, and 12 minutes
are plotted in Figure 4.3. Data for 2, 4, and 6 minutes show similar slopes (ﬂow behavior
indices) and apparent viscosities. The 12 minute cook data exhibits more shear thinning.
This is, in all likelihood, due to degradation of overcooked starch. Therefore, the time-
temperature parameter \[I of Eq. [4.1] was set to inﬁnity. In the process of making potato
ﬂour the potato starch is pregelatinized and therefore it would be expected that cooking

51

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Loose ecu 0: Ron 3 “.3338 .50: 332. .3. 3.333 ooaootoo .5. 0.53...
7v. .oeauSanmﬁ omega.

 

385 38.0 88.0 286
- L L L L L [— b L b b L l.- L b L [D [1r 00F
02 “a“ mo o
0: «En mo n
o: 5.? mo 4
62 non mme . 0
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p
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10 on: a
O
m.
o no.4
\
- .\.\. o d
o \\m\ rodeo. M
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M\

 

rrvo+moé

52

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0:0 oomnp 0a 032.203 canoe .50: 330a .0 33033 0302.00 .m.¢ 239.“.

x .02 .2380 8322..

 

 

 

md m.o to ,n.o «.0 mo
_ a L L L e L a [— t _V
0: «Nu mo o
0: 5.8 mo n T
o: 5.3 m0 4 f O
o: Roe mme o ... m
0: «on mm; .. to. m
0
a m.
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He. m
3
I 4 r m
. «A.
race. moo
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S
w¢o+m_

53

.o no «0 «3:58 a. 3 o e0 35: x000 no. 30..
50cm 523 20:00 .50: 330a .0 35035 .n.¢ 0.59.“.

Tm .301 nomcm
¢o+up 000— 00— OF =
L b L

F

 

:30 0552 o 0
380 3:52 a n
x000 3552 e 0
:30 05:5 m o
u/ :30 05:3 up a row
Too—
ﬁooo.

 

 

i¢o+up

s—od ‘Krgsoosm

54

of potato ﬂour should show an increase in viscosity. Comparison of the "coo " data
with uncooked viscosities adjusted to the same temperature and moisture veriﬁes that the
potato ﬂour is pregelatinized. Therefore, the parameter A in Eq. 4.1, which is an indica-
tor of the relative contribution of gelatinization to viscosity, is zero. Strain history did
not signiﬁcantly affect the viscosity of the potato ﬂour and therefore this parameter was
also set to unity and excluded from further analysis.

All Instron Capillary Rheometer and twin-screw extrusion data plotted were then
ﬁt into the ﬁnal model

. _1 ﬂ:-"(r"‘.1';‘)+b(1trc-rrc,)
nm=KY e

Equation 4.5 gives an R2 of 0.951. Best ﬁt parameter values are given in Table 4.2 along

[45]

with the physical description of each term.

As indicated by Table 4.2 the values for AE, free energy of activation, b, and shear

thinning index (n) are within the ranges observed by other researchers for other cereal
and soy products. Any variation observed in ﬁee energy of activation (A3,) and b is
probably due to individual product characteristics. The lower value for the power law
index compared to pregelatinized corn ﬂour is to be expected because native potato
starch is highly shear thinning. The consistency coefﬁcient is signiﬁcantly higher than
observed for other pregelatinized ﬂours. The greater value of the consistency coefﬁcient
is most likely due to the hygroscopic nature of the potato ﬂour which causes potato ﬂour
doughs to be extremely sticky at higher moisture contents. The means of the predicted
versus observed data aresplotted in Fig. [4.4] for the capillary rheometer and twin-screw
extruder data. Note that the twin-screw exu'uder data means ﬁt with the same degree of

accuracy as the capillary rheometer data

55

6.5500 .50: 3300 .2 EMS 00.0 50030.0
000 9.3 030802.... b05000 .0. anH— .cm 03 3.00003 030.00.... 0:0..0> 0020000 .04 0.52...

mlod .350005 0020000

 

no.7: sawm— oo_o_ 2.: oh. _
0: «ma mo o . _
oz 5.3 me n

02 ”8.? mo a H d
o: No... mm» o a v3 a
02 x8 mme u o . me...
a. O

r 1.

.. 9

v02 0.
. m

S

r O

n m

. ,..A

n m

v¢o+mp _

r S

 

 

56

 

ture

Table 4.2. Summary of model parameters and comparison with values from the litera-

 

Physical

Symbol
Meaning

This
Study

Data from literature
(various food doughs at
similar moisture and
temperatures)

 

AE, Aetivation
Energy

b Moisture
coefﬁcient

11 ﬂow behavior
index

K consistency
coefﬁcient

 

8729 kcal
per g mol

8.63

0.25

34903
(Pa 5")

4967; cooked cereal
dough

8723; pregelatinized
com ﬂour

7300; soy pits

6900; defatted soy
ﬂour dough

6.7; defatted soy ﬂour
7.9; com ﬂour dough
0.19; soy pits

0.24; defatted soy
ﬂour

0.34; soy pits

0.36; pregelatinized
corn ﬂour

0.51; cooked cereal

dough

4880; cooked cereal
dough

4982; pregelatinized
corn ﬂour

16930; soy pits

28800; soy pits

 

* Harper (1981)

 

57

4.6. Conclusions

A model extending the work of Morgan et al. (1988) and Dolan et al. (1988) for
use in extrusion cooking of low moisture starch-based doughs has been presented. This
model incorporates shear rate, temperature, moisture content, time-temperature history
and strain history. The model was tested with capillary rheometry and twin screw extru-
sion of low moisture potato ﬂour doughs.

Overall, the results from the capillary rheometer and twin screw extruder are simi-
lar over a wide range of shear rates, moisture contents, temperatures, time-temperature
and strain histories. The capillary rheometer may, therefore, be used to approximate
conditions within an extruder to obtain parameters to describe shear rate, temperature,
moisture and time-temperature history.

Speciﬁcally:

l. The model was experimentally tested with potato ﬂour doughs over a'wide range
of experimental conditions: 25-95’C, 028-077 g water per g potato ﬂour (22-44%
wb), shear rate= 10-10000 sec", ut=0 to 00 and ¢=0 to w.

2. Due to the pregelatinization of potato ﬂour, time-temperature and strain history
effects were absent.

Future research must focus on assessing the kinetic relationship of time-
temperature history to starch gelatinization and strain history for ungelatinized starches,
measurement of strain history parameters, and addressing slip or friction correction for

capillary and extruder dies.

58

4.7. Nomenclature

A relative amount of viscosity increase due to gelatinization, dimensionless
b rate constant of effect of moisture content on viscosity, dimensionless
(1 rate constant of effect of strain history (it) on viscosity, 3
D capillary diameter, m

AE, ﬁee energy of activation, kcal/g mole

K power law consistency coefﬁcient, Pa s’n

L capillary length, m

MC moisture content, dry weight basis, decimal

MC reference moisture content, dry weight basis, decimal

n ﬂow behavior index, dimensionless

R universal gas constant, 1.987 cal/g mole

t time, s

T temperature, 'K

Tr reference temperature, ’K

T] apparent viscosity, Pa s

AE, Energy of gelatinization, cal/g-mol

n," predicated viscosity, Pa s

y shear rate, s‘1

(1 strain history, dimensionless

\V time-temperature history, 'Ks

AP pressure drop, Pa

59

CHAPTER 5 EXTRUSION MODELING OF CORN STARCH

5.1. Abstract

A generalized viscosity model for predicting the extrudate viscosity of low to inter-
mdiate moisture content starch based products is proposed. The model incorporates the
effects of shear rate, temperature, moisture content, time-temperature history and strain
history.

The model was tested using corn starch dough at various moisture contents. Equip-
ment used included an Instron Capillary Rheometer attached to a Model 4202 Instron
Universal Testing Machine and an APV Baker MPF 50 D/25 co-rotating twin screw
extruder. Die lengths for the capillary rheometer were 6.35 x 10" m and 2.54 x 10'2 m,
with a diameter of 3.18 x 10" m. Exu'uder dies of 6.35 x 10'3 m diameter, and 2.54 x 10’2
m and 3.18 x 10'3 m lengths were used.

Dough moistlne contents were 0.359 (26.4% wb), 0.476 (32.0% wb), and 0.572
(36.0% wb) g water per g starch for capillary rheometer tests and 0.5 (32% wb) and 0.6
(38% wb) g water per g starch for the extrusion tests. In the capillary rheometer, barrel
temperatures were maintained at 50, 55, 60, 75, 85, 95, and 110'C for cook times of 1, 2,
3, 6, 12, and 24 minutes.

Shear rate effects were characterized by the model proposed by Ofoli et al. (1988).
Viscosity was found to be a function of cook temperature and moisture content but not
cook time. Observed versus predicted viscosity gave an R2 of 0.95 after accounting for
shear rate, temperature, moisture content and time-temperature history in the capillary
rheometer. Extrusion tests indicated strain history was important for highly puffed extru-
dates (R’=0.79 before strain correction). Strain history was modelled as a function of
mechanical energy input (shaft work). After correcting for strain history effects the ﬁt of
the model improved to an R2 of 0.85.

5.2. Introduction

The major ingredient in many extruded products is starch (Harper, 1981). Over the
last ten years, many research papers have addressed the mechanisms that affect materials
during extrusion. Some have measured the effects of screw speed, temperature, moisture
content and retention time on the molecular changes seen in the structure of the starch
granule (Gomez and Aguilera, 1983; Mercier and Colonna, 1983; Colonna et al., 1984;
Doublier et al., 1986).

Others have proposed models to describe the physicochemical changes that occur
in the starch granule during extrusion (Owusu-Ansah et al., 1983; Gomez and Aguilera,
1984; Davidson et al. 1984). Owusu-Ansah et al. (1983) measured physicochemical
changes in corn starch as a function of temperature (100, 128, 170, 212, 240’C), feed
moisture (11, 13.4, 17, 20.6, 23% wb) and screw speed (50, 58, 70, 82, 90 RPM), and
reported that temperature, moisture and screw speed could signiﬁcantly affect gelatiniza-
tion. Response surface diapams indicated maximum gelatinization occrured at the low-
est temperatme (100'C) and highest feed moisture (23%), while the minimum
gelatinization occurred at the same temperature but lower feed moisture (11%) and 90
RPM. However, at lower screw speeds a minimum level of gelatinization could not be
observed except at points of high moisture and temperature. This was in contrast to
expected increases in gelatinization with increasing values of temperature and moisture.
They concluded that the anomaly was caused by a high compression screw proﬁle which
generated peater mechanical work on the starch and therefore allowed complete gelatini-
zation at lower temperatures. By using a lower compression screw proﬁle at higher tem-
peratures and moisture, peater gelatinization occurred.

Gomez and Aguilera (1984) proposed a physicochemical model for extrusion of
corn starch. This model is based on the combination of raw, gelatinized and dextrinized

61

starch. They concluded that the term "gelatinization" should not be used to describe the
starch when cooked at moisture contents less than 20% because the starch becomes dex-
ninized.

Rheological models can be used by the food technologist and process engineer to
predict product quality, and in scale-up of new products and in process control (Harper,
1981). Many rheological models for protein and starch based products have been pro-
posed. One of the earliest proposed models (Harper et al. 1971) suggested that viscosity
is a function of inverse temperature, moistlne content and shear rate. Cervone and
Harper (197 8) proposed a model for pregelatinized corn ﬂour which included tempera-
ture, moisture and shear rate effects. A model incorporating shear rate, temperature and
time-temperature history was used by Remsen and Clark (197 8) for defatted soy ﬂours.
Bhattacharya and Hanna (1986) presented an empirical model for corn gluten meal and
soy protein concentrate as a function of shear rate and moisture content: Morgan et al.
(1988) presented a model for protein dough viscosity as a function of shear rate, tempera-
ture, moisture content, time-temperature history and strain history. Of these studies, only
Morgan et al. (1988) included all of the variables Harper (1986) suggests are necessary
for process engineering analyses. While Morgan et al. (1988) have proposed a model for
extrusion cooking of protein doughs, there is no similar rheological model for use with
starch based products.

The purpose of this paper is to extend the model by Morgan et al. (1988) for pro-
tein doughs to starch based products and to test the model with capillary rheometer and

twin screw extruder data.

62

5.3. Model Development

Morgan et al. (1988) presented the following model for cooking extrusion of pro-
tein doughs.

at
1:, ' 7'(r'-17')+b(uc—uc,)
“have.” = [[7] + lit] 9

[1 + B.[As(MC)‘Cpl°[l — e“-*)“] [1 - Ba - e"')] - [5.1]
Several modiﬁcations were made to Eq. [5.1] to make it suitable for use with starch

based products. First, the shear rate characterization was changed from the Heinz-Casson
model to the generalized model of Ofoli et al. (1987):

.1 i
t . -
11=[[—;] +ll.,y" "J [52}

This generalized model allows for variable power indices, a yield stress and a high

.—

shear limiting viscosity. However, it should be pointed out that this model requires
sophisticated regression propams to obtain estimates for the parameters. In its place, any
acceptable viscosity model could be used.

The time-temperature history expression also required modiﬁcation. Morgan et al.
(1988) assumed that if the protein dough is held long enough at various temperatures,
each samme will approach the same viscosity. Kubota et al. (1979) studied the gelatini-
zation rate of rice and potato starches and found the maximum viscosity to be a function
of time and cook temperature. Similar results were found by Bakshi and Singh (1980) for
gelatinization in rice kernels. Using differential scanning calorimetry (DSC), Lund and
Wirakartusumah (1984) developed a model for starch gelatinization. By comparing

enthalpy values versus cook time and temperature, similar results to those of Bakshi and

63

Singh (1980) and Kubota et al. (1979) were obtained. Kubota et al. (1979), Bakshi and
Singh (1980) and Lund and Wirakartusumah (1984) each worked with high moisture sys-
tems.

Burros et al. (1987) used DSC to measure gelatinization of corn meal under low
moisture (25%) and high temperature (80-140’C) conditions. They found results similar
to those of Kubota et al. (1979). The order of the reaction was found to be 0.8 and it was
believed to be less than one because of the decreased moisture content. They also indi-
cated that the activation energy for gelatinization depends on moisture content, and
increased with decreasing moisture content.

Dolan et al. (1988), working with high moisture systems (about 90%), found that

viscosities at different time-temperature histories could be normalized by

'I ”a
ll“ -_ 5.
no. “0 [ 3]

It is important to note that the inﬁnite and initial viscosities are speciﬁc to the cook
temperature after either correction or normalization to the same temperature. In other
words, the inﬁnite viscosity is the viscosity after inﬁnite time at one cook temperature; if
the cook temperature is changed, then a different inﬁnite viscosity is reached.

Morgan et al. (1988) and Dolan et al. (1988) modeled the change in viscosity

caused by denaturation and gelatinization by

7] = Tlgmrc + no [5 .4]
Where 1’10 is deﬁned by:
no=n'.(1—e"")“ [5.5]

Combining Eq. [5.4] and [5.5] gives:

it = mm. +n2(1- e""')° [5.6]

As \y -> on Eq. [5.6] becomes:

“ﬁning”; [5.71
Combining Eqs. [5.6], and [5.7],

 

n,=n,mll +A(i —e"-*)“ ' [5.81

from which it follows that

A = 11. ‘ [5.9]
‘1ng

Finally, the modiﬁed Morgan et a1. (1988) model becomes

"inn.” = H: '11]. + 11.7" Faye???‘ 47‘)».wa 46')
Y 1
[1"‘(l-e4‘vlah1‘l3‘1'ed71 ~ . [5.10]

and can now be used for predicting the viscosity of low moisture starch based products.

65

5.4. Materials and Methods

Native corn starch (Melogel, National Starch and Chemical Corp., Bridgewater,
NJ) at 8% moisture content (wb) was mixed in an institutional mixer with water to give
sufﬁcient quantities for all capillary rheometer tests to be performd.

Moisture contents were 26, 32, and 36% (wb). These moisture contents were cho-
sen because less than 26% moisture caused force readings to exceed the maximum force
the capillary rheometer load cell could handle, and moisture contents peater than 36%
caused water to be squeezed out of the material giving an uneven moisture distribution in
the rheometer barrel. After mixing with distilled water, the samples were allowed to
equilibrate overnight at room temperature (24'C) and then smaller samples were placed
in polyethylene bags and stored at -10’C until capillary rheometer tests were performed.
Twenty four hours before performing the tests, each sample was thawed at 4'C overnight.
Prior to testing, each sample was allowed to come to room temperature.

An Instron Capillary Rheometer and a Model 4202 Instron Universal Testing
Machine (Instron Corp., Canton, Massachusetts) were used to measure apparent viscosity
of the doughs (Figure 5.1). Die lengths of 2.54 cm (1 in) and 6.35 x 10'1 cm (1/4 in), and
diameters of 4.90 x 102 cm (1/8 in) and 1.59 x 10'1 cm (1/16 in) were used, giving up
ratios ranging from 2 to 16. Three replicates for each plunger velocity, temperature,
moistlu'e content, cook time, and LID were performed. Force versus plunger displace-
ment curves were collected and force at the die entrance was calculated by extrapolation
of the force versus displacement curves to the die as described by Einhom and Turetzky
(1964). Barrel drag was then subtracted from the corrected force. A correction for
entrance effects was made using the technique described by Bagley (1957).

 

 

 

 

Barrel wall >

 

“ Plunger

 

 

 

 

 

 

Sample

0 O

00
00.60.00 00
00000000....nl

 

 

 

 

 

 

 

 

Capillary die
Figure 5.1. Capillary rheometer assembly.

67

Shear rate and shear stress were calculated using the Rabinowitsch equation (Whorlow,
1980) (Eq. 5.11),

(1.9..
+1"[-ﬂ] [5.11]

and the standard expression for shear stress at the wall of a capillary:

 

it. =

-APR° 512]
tw— 2L [.

 

Slip analysis was performed using the method described by Darby (1976) using dies of
same length but different diameter.

Temperatrues used ill this study were 50, 55, 65,75, 85, 95, and 110’C . At tem-
peratures less than or equal to 60'C, the materials were compressed in the capillary bar-
rel and allowed to equilibrate for 6 minutes. Cook times of 1, 2, 3, 6, 12 and 24 min at
75, 85, 95, and 110'C were performed on each sample after compression.

Shear rate, temperature, moisture and time-temperature history parameters were
determined as follows. Holding temperature (50'C), moisture content (32% wb) and
time-temperature history (\|I =0) constant, viscosity versus shear rate were ﬁtted to the
model of Ofoli et al. (1987), using the Marquardt compromise method in the non-linear
repession propam of SAS (SAS Institute, Cary, NC). Shear stress and shear rate values
from the capillary rheometer were then averaged for each capillary die and Instron cross-
head velocity.

Temperature correction was obtained in the following way: holding shear rate,
moisture content (32% wb) and time-temperature history constant (\[I =0), the natlu'al log
of the viscosity versus (T‘-T,“) was repessed linearly to obtain AE,/R for temperature

correction. The reference temperature, T,, was set at 323.15 'K.

68

The moisture correction parameter was determined by holding time-temperature
history constant (\|I =0) and linearly repessing the natural log of the viscosity versus
(MC-MG) with MC,=0.476 (db). Finally, the time-temperature history correction was
performed. Strain history within the capillary rheometer was assumed to be insigniﬁcant
and set to unity.

Experimental extrusion tests were conducted using an APV Baker MPF 50D (APV
Baker, Inc., Grand Rapids, MI) co-rotating twin screw exn'uder with the screw conﬁgura-
tion shown in Table 5.1. Feed rates were 1.01 x 10’2 and 1.64 x 10'2 kg/s, at 200 and 400
RPM. The die diameter was 3.17 x 10'3 m, with lengths of 6.40 x 10'3 and 2.60 x 10'2 m.
The pressure drop across the die and extrudate temperature at the die were recorded two
minutes after extruder operating conditions had been changed, to allow equilibrium con-
ditions to be attained.

Plotting pressure drop versus the two different die L/D’s with constant temperature,
moisture, and mass ﬂow rate allowed correction for end effects as described by Bagley
(1957) for capillary dies. Shear rate was calculated using the Rabinowitsch equation
(Whorlow, 1980) and shear stress was calculated using Eq. [5.4] for each die, tempera-
ture, moisture and mass ﬂow rate.

Temperature and moisture correction on the extrusion data were performed using
AE, and b estimated from the capillary rheometer. The average residence time within the
extruder was determined by adding 1 ml of Red 40 dye to the feed, timing how long it
took for the dye to appear at the exit, collecting the colored material at intervals of 20 8
(low feed rate) or 15 s (high feed rate) until no dye came out, and recording the total time
the dye remained in the extruder. The collected samples were dried, pound and Hunter

69

Lab color ’a’ values were determined for each time interval (a(t)). The mean residence
time (t) within the extruder was calculated by

_ ‘ a(t)
t- o tZadt

 

d: [5.13]

 

7O

 

Table 5.1. Screw conﬁguration for extrusion test on APV Baker 50 mm twin screw

extruder.

 

17.8 cm
8.9 cm
7.6 cm
6.4 cm
10.2 cm
8.9 cm
7.6 cm
7.6 cm

Feed Screw
Forwarding paddles 30 offset
Feed Screw
Forwarding paddles 45 offset
Single Lead
Forwarding paddles 30 offset
Feed Screw
Single Lead

Feed Inlet

Extl'uder die

 

 

71

5.5. Results and Discussion

Equilibrium moisture contents of the corn starch samples on a dry weight basis
were determined to be 0.359, 0.476, and 0.572 g water per g corn starch. Moisture con-
tents were found to be constant throughout storage.

A non-linear repession analysis of ungelatinized corn starch at 0.476 g water per g
corn starch (32% wb) and a temperature of SO'C gave the shear rate correction for all the
data:

I

0.979 573
n,=[[189;34] +69351«’y*’~‘”] [5.141

A repession coefﬁcient (R2) of 0.996 indicates a good ﬁt of the data. Shear stress

 

and shear rate values were averaged at each capillary rheometer plunger velocity for each
cook time, temperature, and moisture. When the average observed apparent viscosities
were plotted against the average predicted values for all moisture contents, temperatures
and time-temperature histories using Eq. [5.14], an R2 of 0.88 and a slope of 6.02 was
. obtained. Figure 5.2 is a plot of the observed apparent viscosity versus the predicted
apparent viscosity after accounting for shear rate effects. A plot of both predicted (cor-
rected for shear) and observed viscosities versus shear rate can be seen in Figure [5.3]. If
the shear rate correction alone were adequate, one would expect the predicted viscosity
values to match the observed viscosity values. However, both Fig. [5.2] and Fig. [5.3]
indicate that correcting for shear rate alone is not enough.

Corrections for temperature and moisture were, therefore, carried out (Table 5.2).
Both values for temperature (free energy of activation) and moisture (b) are within the
range seen in the literature for similar materials, temperature and moisture. Figure 5.4 is

the plat of the observed versus predicted apparent viscosity, corrected for temperature

72

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Table 5.2. Temperature and moisture parameters as determined by linear repession
with viscosity measured at a shear rate of 100 s-l.

 

Parameter Estimate Range from Literature

 

 

AB, 8473.14 ’K 3000-8000 'K
b -399 -15 - -0.19

 

 

75

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76

and shear rate. Compared to Fig 5.2, the ﬁt has improved (R2=0.91, slope=0.482) and all
data points appear to fall along a more deﬁned line. However, it is clear from the slope
(0.482) of the regression line that further correction is necessary.

Observed apparent viscosity versus predicted apparent viscosity corrected for tem-
perature, moisture and shear rate can be seen in Figure 5 .5 . There is further improvement
in ﬁt as measured by R2 (0.93), however, the slope of the repession line has decreased
signiﬁcantly (0.347). As can be seen in propessing from Figures 5.2 to 5.5 the data
points are becoming more alipred. The decrease in slope of the repession line is an indi-
cation that the observed viscosity is greater than the predicted viscosity. This is to be
expected since the shear, temperature, and moisture corrections were made on an
uncooked material; therefore, applying these corrections to cooked material should result
in predicted values less than those of cooked starch. When the observed viscosities cor-
rected to a shear rate of 100 s’1 are plotted versus cook time at a moisture content of 0.476
g water per g starch (32.0%) (Figure 5.6) an increase in viscosity with time is seen only
for the 7 5’C cook temperature. At the Other cook temperatures, no appreciable difference
in viscosity is observed at all cook times. By a cook time of 3 minutes, the data for the
75’C cook temperature had reached a constant viscosity. This is consistent with the
observations of Kubota et al. (1979), Bakshi and Singh (1980), Lund and Wirakartasu-
mah, (1984), Burros et al. (1987), and Dolan et al. (1988).

When an analysis of the temperature proﬁle within the capillary rheometer barrel
was made using the heat conduction equation for inﬁnite cylinders (Ozisik, 1980), the
center temperature of the starch material reached and exceeded the gelatinization temper-
ature in one minute or less. Therefore, it was assumed that the product of k. and ‘l’ was
very large, indicating very rapid gelatinization. [The term, exp(-k, 0!), therefore is zero for

all cook temperatures and cook times.

77

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79

The correction for time-temperature history then becomes:
11 = ni.T.uc[1+A1 [515]
where A’ is deﬁned as:
I n" a
A = —1=B,(Cs) [5.16]
717.131“:

 

The variable A’ is, essentially, a ratio of the maximum viscosity due to gelatiniza-
tion that can be attained (for a speciﬁc cook temperature and moisture content) to the
ungelatinized viscosity corrected to the cook temperature. It is important to note that A’
relates to a particular moisture content and cook temperature. The speciﬁcity for mois-
ture content is not due to the lubrication effects of water, but rather to the effect of mois-

ture content on the gelatinization kinetics.

Values of a and B, for Eq. 5.15 were determined by holding the temperature con-

stant and regressing In A’ versus 1n Cs for all the data. As temperature increased, a
decreased (except at llO‘C) while B, increased (Table 5.3). This was to be expected
because the difference between the viscosity of the uncooked starch and the cooked
starch also increased as the cook temperature increased. The exact cause of the high a
value at llO'C is not known. However, one possible explanation is that at the high cook
temperature, some molecular breakdown may have occurred causing more entanglement

between molecules and therefore a greater value of a.

To find a predictive equation for the constant A’, equations for at and B, as a func-

tion of temperature had to be determined. An Arrhenius relationship for both a and B,
was assumed and regression of In at or B, versus l/T was then performed. Equations

[5.15] and [5.16] are the resulting equations for a and B,.

a _ costs-3?) R2

= 0.952 [5-17]

80

 

Table 5.3. Values of constants 0t and B, as a function of temperature.

 

 

 

Temperature at B,
('C)

75 2.53 4.90
85 1.90 5.57
95 1.70 1 1.30

1 10 2.05 21.96

 

 

81

4021*)

1'

Bo = R2 = 0.947 [5-18]

Combining Eqs. [5.16], [5.17], and [5.18] yields an equation for the constant A’.
By combining Eqs. [5.10] and [5.16], the ﬁnal predictive equation for viscosity as a

function of shear rate, temperature, moisture content, and time-temperature is

JI-

‘1 . _ ; r"-r;‘ +b(Mc—Mc, a
“i,r,uc,y=l:[%] +0.3": 5‘] e ( ) 1:1 +A’(1 - 84.10] [5.19]

A plot of observed versus predicted viscosity after shear rate, temperature, mois-
ture content and time-temperature history corrections using Eq. [5 .19] is shown in Figure
[5.7]. Clearly the goodness of ﬁt has been improved (R2=0.95, slope=0.72). Further
regression analysis using forward stepwise regression (Table 5.3) indicates that the shear
rate is the most important variable. This is to be expected, since viscosity is very depen-
dent on shear rate. Moisture content is the next contributor to the model in order of
importance. Again, this is not surprising; it implies that at the moisture contents used in
this study, the lubrication effects of moisture contribute more to the viscosity than the
effects of temperature or time-temperature history. Time-temperature history was next in
importance, followed by temperature effects.

The temperature correction might have been expected to be more important
because of the large value of AEJR which indicates a high degree of temperature thin-
ning. At low moisture contents, moisture and time-temperature history should be of
greater importance compared to temperature in contributing to viscosity. This is because
moisture can have a greater effect on the friction between the material and the capillary
wall and therefore contribute to lubrication effects. While time-temperature history

effects are a function of time, temperature and moisture content are nm a function of

82

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83

 

Table 5.4. Stepwise regression of observed viscosity versus temperature, shear rate,
moisture content and time-temperature history corrections for native corn starch.

 

SUMMARY OF STEPWISE REGRESSION PROCEDURE FOR DEPENDENT

 

 

 

VARIABLE 11,,
VARIABLE PARTIAL MODEL
STEP ENTERED R2 R2 C(P) F PROB>F
1 7 0.9379 0.9379 216.1 8304.9 0.0001
2 MOIST 0.0142 0.9521 43.2 162.7 0.0001
3 A’ 0.0034 0.9555 3.1 42.13 0.0001
4 TEMP 0.0001 0.9556 4.0 1.07 0.3022

 

 

84

time. It is also important to note that while the model was developed assuming no inter-
action between terms but in actuality the order in which each term is determined may
affect the value of its parameters.

Results of extrusion tests can be seen in Table 5 .5 . The moisture content and tem-
perature ranges are similar to the conditions used in the capillary rheometer tests. Shear
rate ranges are higher than those observed for capillary rheometer tests. Average
residence times within the extruder ranged from 45 to 85 seconds. While it should be
recognized that residence time within a section is highly dependent upon the screw con-
ﬁguration, at the present time there is no accurate method to quantify actual residence
time within an extruder zone on the basis of screw geometry. Extrudates varied in
appearance from opaque and slightly swelled to translucent and very highly puffed
depending on the die length, screw RPM and mass ﬂow rate.

Figure [5.8] gives a plot of data from twin screw extrusion runs with all data cor-
rected for shear, temperature, moisture and time-temperature history using Eq. [5.19].
Some of the predicted viscosities for the extrusion data are greater than the observed
viscosities, indicating that a correction for strain history may be appropriate. Predicted
viscosities which were greater than the observed viscosities were from extrusion tests
that gave a product that was very highly puffed and translucent in appearance (compared
with an opaque, marshmellow-like, non-puffed appearance).

Vergnes and Villemaire (1987) found a semi-logarithmic relationship between the
power law consistency coefficient and work input for low moisture molten corn starch.
Therefore, the relationship between shaft work and viscosity of the extrudate may be use-
ful in attempting to quantify the effects of strain history. Use of the mechanical energy
input for characterizing the effect of strain history may also be more practical because

quantification of shear rate within each zone of the extruder is not possible

85

 

Table 5.5. Data from twin screw extrusion tests on corn starch.

 

 

 

Die Shear Shear Residence Moisture 1],, n- 11“,
Temp. Stress Ralte time Content (Pa s) (Pa 3) (Pa 3)
(Pa) (8') (8) (db)

83.9 245691 245 56.1 0.60 460 460 1004
84.4 82542 145 75.1 0.61 518 518 569
87.8 264421 220 59.6 0.67 247 247 1201
95.6 68523 215 53.1 0.60 360 360 317
96.1 55327 158 71.6 0.67 263 263 350
96.1 118835 140 84.5 0.65 387 387 849
96.1 35364 150 69.8 0.61 428 332 236
97.2 299127 231 58.8 0.45 903 903 1293
98.3 31395 239 51.0 0.58 374 290 132
100.6 104229 145 80.4 0.50 917 712 719
101.7 215059 139 75.4 0.49 967 967 1549
104.0 336694 225 64.9 0.49 672 672 1498
105.6 80833 144 71.2 0.50 878 682 561
106.7 119117 244 59.0 0.50 716 556 488
112.8 113813 143 66.8 0.49 867_ 673' 794

112.8 170817 226 45.7 0.48 698 698 757

 

 

86

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87

from currently available knowledge, except in some highly speciﬁc situations (Mohamed,
1988). Total shaft power for the APV Baker MPF SOD/25 twin screw extruder was deter-
mined using the equation

Es=4.75 x lO“(%Torque)(RPM)/Q [5 .20]
When the conected viscosity versus mechanical energy supplied by the extruder shaft
was plotted. a definite relationship is observed (Figure 5.9). N on-linear regression analy-
sis of observed viscosities corrected to 150 s", SO‘C, and 0.47 6 g/g moisture versus

mechanical energy gave

0. = 282019 e<"-°“°"E') + 4300 [5.21]

with an R2 of 0.88. Using the value of the viscosity at inﬁnite strain history (as deter-
mined from regression), and correcting for shear rate, temperature and moisture, a conec-
tion for strain history can be obtained.

The ﬁnal equation for predicting the viscosity of starch-based doughs in the twin

screw extruderis
;
1, ' .15-.“ ‘1 ;(r‘—r;‘)+b(Mc-uc,)
“mm”: '-' +9.7 7 e
7 r
[1 +A(1 .. ﬁ-Vﬂ [1 - 0(1 -e‘“)1 [5.22]

A plot of the observed versus predicted extrudate viscosities conected for shear
rate, temperature, moisture, time-temperature history and strain history using Eq. [5.22] is
seen in Fig. [5. 10]. The data appears scattered but regression analysis indicates a good ﬁt
(R2=0.85). The observed versus predicted viscosities do appear to fall along one line

88

indicating that shear, temperature, moisture, time-temperature and strain history correc-
tions may adequately be used to predict the viscosity of corn starch extrudates over the
temperatures and moisture contents used. Table 5 .6. gives the value or relationship for

each parameter in Eq. 5.22.

89

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91

 

Table 5.6. List of model parameters for Eq. 5.22.

 

 

 

 

Parameter Value or relationship

1:, 189434 Pa

ll... 69351 Pa s

11, 0.979

112 0.356

A5, 8473.14 'K

b -3.99

A’ ‘ 6070.1
(4.371 +£1.32) ( CS ),( us )

1W °°

B Dependent on T, MC, and 1]..

d and n,

-5.87 x 103

 

 

92

5.6. Conclusions

A model to predict the viscosity of extruded starch-based products was developed
using the model proposed by Morgan et al. (1988). This model incorporates shear rate,
temperature, moisture content, time-temperature history and strain history. The model is
ﬂexible enough to allow its use under a wide range of operating conditions and extrusion
equipment and yet simme enough that the parameters can be determined via capillary
rheometry and standard non-linear and linear regression techniques.

Viscosities of cooked and uncooked corn starch measured via capillary rheometry
at moisture contents of 0.359, 0.476, and 0.572 g water per g starch (26.4%, 32.0% and
36% mc wb respectively), cook times of one to 24 minutes, temperatures of 50, 75, 85,
95 and 110'C and shear rates of one to 300 s" were found to ﬁt the model with reason-
able accuracy. When capillary rheometer data was corrected for shear rate a ﬁt of the
observed versus predicted viscosity gave an R2 of 0.88 and a slope of 0.15. Subsequent
correction for temperature, moisture content, and time-temperature history improved the
ﬁt and the slope to a ﬁnal R2 of 0.95 and a slope of 0.72.

Data for capillary rheometer and twin screw extrusion tests fell along the same line
under low strain history conditions. Extrusion tests indicated that when strain history is
large, correction for strain history is necessary. Modiﬁcation of the model proposed by .
Morgan et al. (1988) for strain history to include shaft work input as proposed by
Vergnes and Villemaire (1987) yielded a ﬁnal equation that gave a reasonable ﬁt
(R2=0.85) for extrusion data.

Further research is necessary to quantify strain history effects. One problem
encountered in this research was the lack of rheological equipment to enable the indepen-

dent measurement of the effects of strain history on low moisture and, hence, high viscos-

93

ity starch doughs outside the extruder. A combination shearing and capillary rheometer
as described by Vergnes and Villemaire (1987) may be what is needed to perform this
necessary work.

Also, a redesign of the capillary rheometer so that it has a wider barrel so heat
transfer to the center of the starch dough is slower, may be necessary to quantify the
time-temperature effects at values less than inﬁnity. Further investigation into the phe-

nomena of slip and friction within the capillary die also needs to be done.

W

94

5.7. Nomenclature

A, A’, A, relative amount of viscosity increase due to gelatinization, dimensionless

b rate constant of effect of moisture content on viscosity, dimensionless

Cs starch concentration, wet basis decimal

Cp protein concentration, dry basis decimal

d rate constant of effect of strain history (0) on viscosity, s

D capillary diameter, m

AE, free energy of activation, kcal/g mole

Es mechanical energy supplied by the extruder, Jm’3

L capillary length, m

MC moisture content, dry basis decimal

MC, reference moisture content, dry basis, decimal

n,, power indices, dimensionless

R. capillary radius, m
universal gas constant, 1.987 cal/g mole

t time, s

T temperature, 'K

T, reference temperature, 'K

Q volumetric flow rate, tn3 s‘1

01 index of molecular weight effects on viscosity, dimensionless

[50, [3' material constant describing effects of temperature and moisture on
gelatinization, dimensionless

[5 material constant describing effect of strain history on viscosity at
4) = co, dimensionless

T] apparent viscosity, Pa 8

'00
'0.
TL.

“true.”

“70,1140

119

95

contribution to viscosity by gelatinization, Pa s

normalized apparent viscosity ratio, dimensionless

viscosity at \V = co, Pa 3

apparent viscosity corrected for shear rate, temperature, moisture
content, time-temperature history and strain history, Pa 8

apparent viscosity at time-temperature history \|I, Pa 3

viscosity at \y = co, Pa s
change in apparent viscosity due to gelatinization at \y = co, Pa 3

apparent viscosity before gelatinization, Pa 3

apparent viscosity at (b = no, Pa 3

€9<~

96

material exponent for describing effect of moisture content on protein dena-

turation, dimensionless

shear rate, s.,

strain history, dimensionless
time-temperature history, 'K-s

yield stress, Pa

shear stress at wall, Pa

high shear limiting viscosity (Casson), Pa 3”
high shear limiting viscosity (Ofoli), Pa 5"”

pressure drop, Pa

97

CHAPTER 6 A RHEOLOGICAL MODEL FOR NATIVE WHOLE
WHEAT FLOUR DOUGH EXTRUDATES

6.1. Abstract

A generalized viscosity model for predicting the extrudate viscosity of low to inter-
mdiate moisture content starch based products is proposed. The model incorporates the
effects of shear rate, temperature, moisture content, time-temperature history and strain
history.

The model was tested using whole wheat flour doughs at varying moisture con-
tents. Equipment used included an Instron Capillary Rheometer attached to a Model
4202 Instron Universal Testing Machine and an APV Baker MPF 50 D/25 co-rotating
twin screw extruder. Die lengths of the capillary rheometer were 6.35 x 10'3 m and 2.54
x10“2 m, with diameter of 3.18 x 10'3 m and 1.59 x103 m. Extruder dies of 6.35 x10'3 m
diameter, and 2.54 x 10'2 m and 3.18 x 10'3 m lengths were used.

Whole wheat ﬂour dough moisture contents were 0.333, 0.337, 0.385 and 0.436 g
water per g starch (25.0%, 25.2%, 27.8%, and 30.4%, wb respectively) for capillary
rheometer tests. In the capillary rheometer, barrel temperatures were maintained at 50,
55, 60, 75, 85, 95, and 110'C at cook times of 1, 2, 3, 6, 12, and 24 minutes.

Shear rate was modelled by the generalized model proposed by Ofoli et al. (1987).
Overall ﬁt of the model improved as temperature, moisture content and time-temperature
history were accounted for. The ﬁt was not as good for whole wheat flour as was
observed for corn starch and potato ﬂour (R2: 0.56). The apparent lack of ﬁt may be due
to the presence of ﬂour components such as bran, protein, and lipids which the model

does not account for and which may have altered the gelatinization kinetics of the starch.

98

6.2. Introduction

The food industry is constrained from effective use of extruders because of lack of
an adequate model which describes the effects of extrusion process variables on the
extrudate viscosity. Many researchers have proposed rheological models for extrusion
cooking of cereal products (Harper et al. 1971; Remsen and Clark, 1978; Cervone and
Harper, 1978; Bhattacharya and Hanna, 1986; Morgan et al., 1988). While all these mod-
els account for shear rate, moisture, and temperature, only Remsen and Clark (197 8) and
Morgan et al. (1988) included time-temperature history effects.

In Chapters 4 and 5, the equation below was used to model the viscosity of potato

ﬂour and corn starch:

1: i "'(r‘ 1") Marc MC)
nm=[[§°] +115!” “‘] e' ' '
r

[1 +14 ’(1 - e"-")“] [1 — 130- e‘“)] [6.1]
However, it is commonly accepted that various components of cereal doughs (protein,
lipids, and pentosans) or ingredients added to the product (sugar, salt, etc.) can greatly
affect the extent of gelatinization (Eliasson, 1983; Lund, 1984; Olkku, 1978; Ghiasi et a1.
1982). The proposed model does not account for the effects of non-starch components on
the gelatinization kinetics of starch. Since it was observed in Chapter 5 that starch gela-
tinization signiﬁcantly affects viscosity, it is reasonable to expect that the presence of
dough components such as protein, salts, or lipids may affect the changes in viscosity
during cooking extrusion. The eﬂ‘ects of these dough constituents can, therefore, be eval-
uated by applying the model to a product containing signiﬁcant levels of one or more
non-starch components. Native whole wheat flour provides an ideal material for this

exercise.

99

The objective of this study is to assess the accuracy of the model above for predict-

ing the viscosity of native whole wheat ﬂour extrudates.

100

6.3. Materials and Methods

Whole wheat flour (International Multifoods, Minneapolis, MN) containing
l4»l4.5% protein (wb) provided the feed material for the extrusion runs. Moisture con-
tents used were 0.333, 0.337, 0.385, and 0.436 g water per g ﬂour (25.0%, 25.2%, 27.8%,
and 30.4%, wb respectively). The indicated moisture contents were used because at
higher moisture contents, rapid loading of the capillary rheometer was difﬁth due to the
stickiness of the material, and at lower moisture contents damage to the Instron load cell
or capillary rheometer plunger might occur.

Flour and water were mixed in an institutional mixer and allowed to equilibrate at
room temperature (24'C) overnight before being placed in plastic freezer bags and stored
at 0'C. Prior to capillary rheometer tests, the sample was allowed to thaw for a minimum
of 12 hours. Moisture content was determined by drying overnight at 100'C. No change
in moisture content was observed during frozen storage.

An Instron Capillary Rheometer and a Model 4202 Instron Universal Testing
Machine (Instron Corp., Canton, Massachusetts) (Figure 6.1.) were used to measure
apparent viscosity of the doughs. Dies of 2.54 cm (1 in) and 0.635 cm (1/4 in) length,
and 4.90 x 102 cm (1/8 in) and 1.59 x 10'1 cm (1/16 in) diameter were used, giving up
ratios ranging from 2 to 16. Three replicates for each plunger velocity, temperature,
moisture content, cook time and MD ratio were performed.

Force versus plunger displacement data were collected and force at the die entrance
was calculated by extrapolation of the force versus displacement curves to the die as
described by Einhom and Turetzky (1964). Barrel drag was then subtracted from the cor-
rected force. A correction for entrance effects was made using the technique described
by Bagley (1957). Pressure drop through the capillary die was assumed to be the force at

the die entrance over the barrel diameter.

101

 

 

 

Barrel wall —

 

7" Plunger

 

 

 

 

 

0.0.0.000...
O.

 

Sample

 

 

 

 

 

 

 

Capillary die
Figure 6.1. Capillary rheometer assembly.

102

Shear rate and shear stress were then calculated using the Rabinowitsch equation,

0
. _3Q «15,?

and the standard expression for shear stress at the wall of a capillary:

 

_APR, [63]
1w- 2L "

 

Slip analysis was performed using the method described by Darby (1976).

Temperatures used in this study were 50, 75, 85, 95, and llO’C . At 50'C the
materials were compressed in the capillary barrel and allowed to equilibrate for 6 min-
utes. Cook times of 1, 2, 3, 6, 12 and 24 min at 75, 85, 95, and 110'C were performed at
each moisture content after compression.

Shear rate, temperature, moisture and time-temperature history parameters were
determined as follows. Holding temperature (50'C), moisture (0.333% db) and time-
temperature history constant (w=0), viscosity versus shear rate were ﬁtted to the model of
Ofoli et al. (1987), using the Marquardt compromise method in the non-linear regression
program of SAS (SAS Institute, Cary, NC). Then holding moisture content (0.333% db)
and time-temperature history (\y=0) constant, 1n 11 versus ('1‘ 1-T,.") with T,=323.15 ’K
were regressed linearly to obtain AEJR for the temperature correction. The moisture cor-
rection parameter was determined by holding time-temperature history constant (01:0)
and linearly regressing 1n 1] versus (MC-MC), with MC,=0.333 db. Finally, correction
for time-temperature was performed.

Experimental extrusion tests were conducted using a APV-Baker MPF 50 D (APV
Baker, Inc., Grand Rapids, MI) co-rotating twin screw extruder with the screw conﬁgura-
tion shown in Table 6.1. Feed rates of 1.01 x 10'2 and 1.64 x 10’2 kg/s, were used at 200
and 400 RPM. Two dies 3.17 x 10" m in diameter and 6.40 x 103 and 2.54 x 10" m in

103

length were used. Pressure drop and extrudate temperature at the die were recorded two
rrrinutes after extruder operating conditions had been changed to allow equilibrium condi-

tions to be attained.

 

104

 

Table 6.1. Screw conﬁguration for extrusion tests on APV Baker 50 mm twin screw

extruder.

 

17.8 cm
8.9 cm
7.6 cm
6.4 cm
10.2 cm
8.9 cm
7.6 cm
7.6 cm

Feed Screw
Forwarding paddles 30 offset
Feed Screw
Forwarding paddles 45 offset
Single Lead
Forwarding paddles 30 offset
Fwd Screw
Single Lead

Feed Inlet

Extruder die

 

 

105

6.4. Results and Discussion

Final equilibrium moisture content of the wheat flour samples were determined to
be 0.333, 0.335, 0.385, and 0.436 g water per g wheat ﬂour (25.0%, 25.2%, 27.8%, and
30.4%, wb respectively). No loss in water was observed during storage.

The extrudates exhibited the appearance of slip, with a " shark skin" texture on the
surface. However, analysis for slip was found to be inconclusive at all moisture contents
and temperatures. The inability to correct for slip may be due to a "slip-stic " phenome-
non where there is a combination of friction and slip occurring at the capillary wall.
Because "slip-stick" rather than pure slip occurred, Darby’s (1976) method for slip
correction did not yield meaningful results. It was either impossible to obtain a slip coef-
ﬁcient because of wide variations in the data, or a negative apparent shear rate was
obtained. Another reason for the difﬁculties encountered in slip correction may be a
varying friction coefﬁcient within the die, depending on the plunger velocity, die geome-
try or a combination of the two. Due to the non-cohesiveness of the raw material, it was
impossible to correct for this friction.

The reference moisture content was set at 0.333 g water per g (25.0% wb) ﬂow. A
yield stress of 93.8 kPa was estimated by extrapolating shear stress versus shear rate
curves to zero shear rate. After determining the yield stress, the other parameters in the
shear rate model were determined via non-linear regression.

The ﬁt of the non-linear regression parameters as measured by R2 (0.88) was not as
good as that observed in Chapters 4 and 5 for potato flour and corn starch. This poor ﬁt
may be due to the presence of bran, protein and other components in the whole wheat
flour which are not accounted for by the model. Temperature and moisture correction
terms are listed in Table 6.2. Values for both are within the ranges seen by other

researchers for similar materials.

106

 

Table 16.2. Temperature and moisture correction parameters for whole wheat flour at
100 s'

 

 

Parameter Estimate Range of previous values .
Temperature (A5,) 5354.38 2000-5000 ’K
Moisture (b) -7.91 ~15.0 - -0.19

 

 

 

N0te: All estimates are signiﬁcant at the 95% level.

107

Comparison of average observed versus predicted viscosities at all shear rates,
temperatures, moisture contents, and time-temperature histories conected for shear rate
only can be seen in Figure 6.2. Regression analysis (R2=0.56, slope=1.86) of observed
versus predicted values indicate that shear rate- correction alone is inadequate to describe
the viscosity of whole wheat ﬂour.

Figrne 6.3 shows observed versus predicted Viscosities corrected for shear rate and
temperature at all moisture contents and time-temperature histories. Temperature correc-
tion improves the fit of the line (R”0.635) and the slope approaches unity (slope=0.83).
While the correction for temperature improves the ﬁt, the data still appears to be
somewhat scattered as seen in Figure 6.3.

Correcting the predicted viscosities for moisture content gives ﬁn'ther improvement
in the ﬁt (Rz=0. 638) of the average observed versus predicted viscosities. A plot of
observed versus predicted viscosity can be seen in Figure 6.4. The slope of the line has
decreased to 0.76 indicating that predicted viscosities corrected for moisture, temperature
and shear rate are less than observed viscosities. These predicted viscosities are lower
because most of the observed viscosities were either fully or partially cooked and there-
fore the starch and protein molecules had undergone gelatinization or denaturation,
respectively. It is commonly accepted that viscosity increases as starch gelatinizes and
protein denatures, therefore the predictive model must incorporate a term to quantify the
effects of gelatinization on viscosity.

Comparison of the observed and predicted viscosities of wheat ﬂour cooked at
75'C and 85'C at a moisture content of 0.337 g water per gram solids (25.2% wb) and
75'C with a moisture content of 0.385 g water per gram solids (27.8% wb) indicated that

no increase in viscosity occurred at varying cook times and therefore the

108

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Lo 80.. .0030 00.. 0808.60 0036033 0020020 m:80> 080680 .m.0 839...

m on. 5.60005 0050000

 

 

mo+mo.. mo+mo.. 21.00.. odwo. 3%: 0.0.
330: Rm... 6 .
330.2 003 a no 00.
330.... 8.8 a d
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8
Dr
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r¢o+mo. o
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$050.. moo
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x4007...»

 

100+m0._

109

050300 So: 300;; 0653
.o. 00:30:. 8380080705: 0:0 03:03:00 8306:. :0 30 0.380083
0:0 030. .0050 .o. 00308.60 00280.03 00>.0mno 0:0.0> 003208.”. .00 0.30.1.

0 00 0300005 0050000

 

 

9:00.. 0300.. 2:00.. 0.000. 0.00. 0.0.
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110

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x050...» 00030..

5 od ‘ArlsooslA perolpeld

111

time-temperature history variable was set to zero (01:0). The lack of differences between

the predicted and observed viscosities may be caused by the low moisture contents and
lower cook temperatures.

Lund (1984) observed that the transition temperature on a differential scanning
thermogram increased slightly as the moisture content decreased. This transition temper-
ature is indicative of the onset of gelatinization. Presence of gluten, lipids and solutes
can also compete with the starch for water and thus aﬂ'ect the onset of gelatinization. The
combination of low moisture contents and the presence of gluten in the whole wheat ﬂour
most likely caused the gelatinization temperature to shift higher, leading to the lack of
noticeable differences between the observed and predicted viscosities corrected for shear,
temperature, and moisture content.

Using observed and predicted viscosities at a 24 minute cook time and at each tem-
perature where a noticeable difference between the observed and predicted viscosity
occurred, In A’ versus ln(Cs) were regressed for each cook temperature. A relationship
between a and B, and the inverse temperature was then determined. An Arrhenius rela-
tionship between inverse temperature and B, was observed. This is similar to what was
observed for corn starch (Chapter 5.). However, unlike cornstarch, an Arrhenius
relationship was not observed between or and the inverse temperature. The equations for

orandB,are

 

[6.4]

B. = Ami?) 16.51

112

Viscosity was observed to be a function of cook time and therefore time-
temperature history parameters were calculated according to the procedure described by
Morgan et al. (1988) and Dolan et al. (1988). The parameter AE‘ was found to be
unaffected by moisture content. This is in agreement with Dolan’s (1988) ﬁndings that
there is little difference between AE, values for high moisture corn starch solutions of
varying starch concentrations. Burros et al. (1987) estimated activation energies for corn
starch. Over the moisture content ranges used in their study, no signiﬁcant difference
between activation energies was observed. The moisture content range for this study is

within the range studied by Burros et al. (1987).
In this study, the activation energy (A5,) was found to be 25100 cal/g-mole. The

constant kI was found to be slightly affected by moisture content, however, this may be
due to normal sample variations and not because of any moisture content dependency.
Values for k, were 2.5 for 0.436 g water per g solids (30.4% wb) and 1.1 for 0.385 and
0.337 g water per g (27.8% and 25.2% wb, respectively) solids.

Figure 6.5 is a plot of observed viscosity versus predicted viscosity corrected for
shear rate, temperature, moisture content and time-temperature history. The ﬁt of the
data improved (R2=0.687) when compared to the ﬁt after correcting for shear rate, tem-
perature, and moisture content alone; the slope was also slightly improved (0.815). This
improvement is not as dramatic as that observed for native corn starch (Chapter 5).
Reasons for this may include a) "slip-Stick" phenomena or friction effects may have had a
greater effect on the viscosity of whole wheat flour than observed for native corn starch,
b) the presence of protein, bran and other flour components that were not accounted for in
the model may have had an effect on the time-temperature parameters, and c) the low
moisture content used in this study may have ampliﬁed either of these effects or made it

very difﬁcult for the capillary rheometer to measure the effects.

113

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x..0.0.0n>

 

114

Another possibility is the likely presence of an elastic component due to gluten in
the whole wheat flour. Gluten is developed by mixing flour and water together and then
kneading (mixing) the dough. The shear rate term in the model does not account for
energy losses due to elasticity of the dough and therefore this may be why the overall fit
of the model is less for whole wheat flour than for corn starch.

It should be recognized that gluten development is probably the major contributor
to viscosity below starch gelatinization temperatures. In the capillary rheometer it may
be assumd that gluten development was negligible because very little mixing occm's in
the instrument. Therefore, gluten development occurred during sample preparation and
not during capillary rheometer tests.

Stepwise regression after log-log transformation gave results similar to those for
native cornstarch where the order of importance for each model parameter was shear rate,
temperature, time-temperature history and moisture content. Table 6.4 lists the stepwise
results for whole wheat flour.

Extrusion test results after correction for shear rate, temperature, moisture content
and time temperature history are plotted in Fig. [6.6]. Extrudate properties varied from
unpuffed and unswelled material to a highly puffed bread-like material which did not
hold its puffed appearance upon cooling. Unlike the case for corn starch, strain history
does not appear to affect wheat flour during extrusion. A relationship between observed
viscosity and shaft work input, as was seen for native corn starch, could not be deter-
mined and therefore the strain history correction term was set to unity. Regression
through the origin for observed versus predicted viscosity corrected for shear rate,
temperature, moisture content and time-temperature history indicates a better ﬁt
(R’=0.788) than the data from the capillary rheometer when one compares R2 values
(0.788 versus 0.687).

115

 

Table 6.3. Results of stepwise regression for whole wheat flour doughs.

 

SUMMARY OF STEPWISE REGRESSION PROCEDURE FOR DEPENDENT

 

 

 

VARIABLE n...
VARIABLE PARTIAL MODEL
ENTERED 19.2 1?.2 C(P) F PROB>F
«’1 0.4953 0.4953 669.14 1026.39 0.0001
TEMP 0.1391 0.6344 198.65 397.65 0.0001
A’ 0.0538 0.6882 17.79 180.31 0.0001
MOIST 0.0046 0.6929 4.00 15.79 0.0001

 

 

116

050300 .00: .0002. 06:2. .0.
00.0 .00:..x0 5 E302 0.30.00E00I0E: 0:0 0.30.0... 0.30.0000.
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0.000. .000. 0.0.
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0
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00:78.

 

117

Inability to correct for strain history for whole wheat ﬂour compared to corn starch
may be attributed to the differences in the general make-up of the two materials. Corn
starch is nearly 100% starch, whereas the whole wheat ﬂour consists of starch, bran,
wheat protein and some lipids. ‘ The inclusion of water and the mixing in the extruder
most likely caused development of the gluten which may have contributed to increase in
viscosity that was not counteracted by a lowering of the viscosity by mechanical break-
down of starch.

A list of the parameter values or the relationship used in Eq. 6.1 are given in Table
6.5. It is important to note that the order in which values were determined may affect the
ﬁnal results. Also, some of the values depend on either temperature or moisture content
or both.

118

 

Table 6.5. List of parameter values for Eq. 6.1.

 

 

 

Parameter Value or relationship

1:0 93.8 kPa

p,_ 105000 Pa s

n1 1.0

n2 0.40

AE, 5354.4 'K

b -7 .91

A e(—59.99+2“r—‘5)(Cs)(-143.6+-’°$’-)
AEx 25100 cal/g-mole.

k, 2.5 s"-'K at 0.436 g/g db

[1 - [3(1 -e‘“)]

1.1 s"-'K at 0.337 & 0.385 g/g db
1.0

 

 

119

6.5. Conclusions

Capillary rheometer tests were performed on whole wheat ﬂour at moisture con-
tents of 0.333 to 0.436 g water per g solids (25.0% to 30.4% wb), cook times of one to 24
minutes, temperatru'es of 50, 55, 60, 75, 85, and 110'C and shear rates of one to 1000 s“
to obtain the variables needed use Eq. 6.1. Overall ﬁt (R2=0.687) of the observed versus
predicted viscosities for whole wheat flour was less than was observed for native corn
starch (R2=0.950). This may be due to the effects of flour components (bran, protein, fat)
which were not present in the corn starch and are not accounted for by the general model.

No differences due to time-temperature history were observed for samples contain-
ing 0.337 g water per g solids (25.2% wb) and cooked at 75'C and 85'C, but at the other
moisture contents and cook temperatures, viscosity did change with cook time. The
presence of ﬂour components competing for water probably aﬁ‘ected the gelatinization
kinetics at the low moisture content and lower cook temperatures, causing no measurable
change in viscosity at different time-temperature histories. '

Use of the parameters obtained from the capillary rheometer in Eq. 6.1 gave good
agreement between observed and predicted viscosity (R2=0.788) for whole wheat extru-
dates. Different strain histories did not appear to affect the twin screw extrusion data and
therefore the strain history term was set to unity for all extrusion tests. Again the
presence of the different ﬂour components may have had an effect on the ability to cor-
rect for strain history.

Future research should include the effects of flour constituents (e. g. bran, protein,
fat) or other additives (salt or sugar for example) on the model. Speciﬁcally, the effects
of flour constituents on the time-temperature history and strain history correction should

be determined. Further research into quantiﬁcation of strain history within the extruder is

120

also necessary. The question of whether an accurate measurement of shear rate in each
extruder zone is necessary to quantify strain history or if measurement of work input
alone is adequate must be answered.

121

6.6. Nomenclature

A,

t" coca
.3. ”.63 ..

E

C,

wpogsa

9:1—1"

"a:

relative amount of viscosity increase due to gelatinization, dimensionless
rate constant of effect of strain history (<b) on viscosity, s

rate constant of effect of moisture content on viscosity, dimensionless
starch concentration, wet basis decimal

capillary diameter, m

free energy of activation, kcal/g mole

energy of gelatinization, cal mole‘l

reaction transmission coefﬁcient, 'K“ s'1
capillary length, m

moisture content, dry basis, decimal
reference moisture content, dry basis, decimal

power indices, dimensionless

pressure drop, Pa

volumetric ﬂow rate, m3 s'1

capillary radius, m

universal gas constant, 1.987 cal/g mole

time, 8

temperature, ‘K

reference temperature, 'K

index of molecular weight effects on viscosity, dimensionless

material constant describing effect of strain history on viscosity at q: = co,

dimensionless

material constant describing effects of temperature on gelatinization, dimensionless

122

apparent viscosity, Pa s

predicted apparent viscosity, Pa 3
shear rate, s"

high shear limiting viscosity, Pa sm“
strain history, dimensionless

time-temperature history, 8 'K

123

CHAPTER 7 SUMMARY AND CONCLUSIONS

7.1. Overall Summary
A generalized viscosity model based on the work of Morgan et al. (1988) for the

cooking extrusion of low to intermediate moisture content starch based products was
developed. The model describes the effects of shear rate, temperature, moisture content,
time-temperature history, and strain history on the viscosity of the extrudate, assuming no
interaction among the various effects.

The model is ﬂexible enough to allow its use under a wide range of operating con-
ditions and extrusion equipment. This is demonstrated by its ability'to accru'ately ﬁt data
from both a capillary rheometer and an extruder. As a result, model parameters for shear
rate, temperature, moisture content and time-temperature history can be determined by
using capillary rheometry, thus saving time and material by not having to perform all
tests on an extruder. The simplicity and ﬂexibility of the model when compared to other
proposed models is also evident when data analysis is performed. This is because a stan-
dard statistical package with the ability to perform both non-linear and linear regression
is all that is required to determine the model parameters.

Overall, results ﬂoor the capillary rheometer and twin screw extruder were similar
over a wide range of shear rates, moisture contents, temperatures, time-temperature and
strain histories.

Tests were conducted using pctato ﬂour at temperatures of 25-95'C, moisture con-
tents of 0.28 to 0.77 g water per g potato flour (22 to 44% wb), and shear rates from
10-10000 8". Shear rate effects were found to be best described by the power law model.
Correction for moisture content and temperature improved the ﬁt of the observed versus
predicted viscosities to give an R2 of 0.951. Since the starch in potato ﬂour is gelatinized
in the process of making the flour, no differences were observed between samples cooked

124

at different temperatures and cook times. Therefore, the time-temperature history portion
of the model was set to unity. Extrusion tests over different strain histories did not affect
the viscosity of the potato flour doughs, either, and so the strain history term was set to
unity. Lack of measurable strain history effects may also have been due to the pregelati-
nization of the starch.

Cooking extrusion of native corn starch were simulated in a capillary rheometer at
moisture contents of 0.359 to 0.572 g water per g starch (26.4% to 36.4% wb). Tempera-
tures of 50, 55, 60, 75, 85, 9S, and 110'C at cook times of one to 24 minutes after com-
pression within the capillary rheometer were used to determine the effects of temperature
and time-temperature history. Shear rates within the capillary rheometer dies ranged
from one to 300 s“.

Shear rate effects were best described by the model proposed by Ofoli et al. (1987).
A ﬁt of the observed versus predicted viscosity yielded an R2 of 0.877 when all the data
were modelled as a function of shear rate only. Subsequent correction for temperature,
moisture content, and time-temperature history improved the ﬁt, with a ﬁnal R2 of 0.950.

Cook temperature and moisture content were found to be important for predicting
the viscosity of cooked corn starch. Due to the small barrel diameter of the capillary
rheometer, cook time was not a factor when effects of time-temperature history were
modelled. This is because the center temperature of the starch material within the rheom-
eter barrel reached the barrel wall temperature in three minutes or less. However, mois-
ture content and cook temperature were found to be very important factors when
modelling the effects of gelatinization on the viscosity of cooked starch.

Data from capillary rheometry and twin screw extrusion tests were identical under .
low strain history conditions. Extrusion tests indicated that when strain history is large,
correction for strain history is necessary. Estimation of shear rate, within each zone of

the extruder is extremely difﬁcult and therefore was not done. However, modiﬁcation of

125

the strain history term to include shaft work input (mechanical energy) as proposed by
Vergnes and Villemaire (1987) yielded a ﬁnal equation that gave a reasonable ﬁt
(R2=0. 846) for the extrusion data. With the present knowledge on estimating the shear
rate within each extruder zone, the use of shaft work input (mechanical work input) may
be a viable alternative to describing strain history.

Capillary rheometer tests for whole wheat ﬂour doughs with moisture contents of
0.333 to 0.436 g water per g solids (25% to 30.4% wb) were cooked from one to 24 min-
utes at the same temperatures as those for corn starch. Shear rates ranged from one to
1000 s". Shear rate effects were modelled using the generalized model proposed by
Ofoli et al. (1987); the generalized model reduced to the Herschel-Bulkley model. Vari-
ables determined for moisture content and temperature effects were similar to those found
in the literature for similar materials. Viscosity was found to be a function of moisture
content and cook temperature or moisture content, cook time and cook temperature
depending on the moisture content and cook temperature of the whole wheat ﬂour dough.
Low moisture content (0.337 g water/g solids) and lower cook temperatures (75 and
85'C) were observed to produce no differences in viscosity with changing cook times. At
other moisture contents and cook temperatures, viscosity changed with cook time.

Presence of flour components competing for water probably affected the gelatiniza-
tion kinetics at the low moisture content and lower cook temperatures, causing no mea-
surable change in viscosity at different time-temperature histories. The overall ﬁt
(R’=0.687) of the observed versus predicted viscosities for the capillary rheometer tests
was not as good as was seen for corn starch (R2=O.950) and potato flour (R’=0.951). This
apparent lack of ﬁt may be due to the presence of whole wheat ﬂour components such as

bran, protein and some lipids whose presence were not accounted for in the model.

126

Different strain histories did not appear to affect the twin screw extrusion viscosi-
ties and therefore the strain history term was set to unity for all extrusion tests. The pres-
ence of the different ﬂour components may also have had an effect on the ability to
correct for main history. This may be especially true if development of the gluten was
occurring within the extruder. Gluten development may have counteracted any degrada-
tion of the starch molecule due to the strain history, therefore giving the inconclusive

results.

7.2. Conclusions

A generalized model has been developed to describe the effects of shear rate, tem-
perature, moisture content, time-temperature history and strain history on the viscosity of
low moisture starch based products.

The model was evaluated for corn starch, potato flour and whole wheat flour extru-
dates. It was found to be less accurate in modeling the viscosity of whole wheat ﬂour, in
' comparison to the other two materials .' The presence of bran, protein and some lipids in
the whole wheat ﬂour accounted for the lack of accuracy. In particular, gluten develop.
ment may have contributed elastic effects which contributed to the drOp in accuracy.

Capillary rheometer and twin screw extrusion data overlapped each other at small
strain histories. Therefore, capillary rheometer can be used to determine shear rate, tem—
perature, time-temperature and moisture content parameters for use in twin screw extru-
sion. However, use of the capillary rheometer to quantify strain history parameters is not
practical because of the very small strain histories that occur in the rheometer.

Starch gelatinization affects the ﬁnal viscosity of the extrudate. The extent of the
effect depends on moisture content, cook temperature and, for some materials, cook time.
Non-starch components such as bran, protein, and lipids affect starch gelatinization kinet-

ics and therefore inﬂuence the ﬁnal viscosity.

127

CHAPTER 8 SUGGESTIONS FOR FUTURE RESEARCH

The four primary activities for future research are to:

1). determine the effects of ingredients such as protein, bran, lipids, salt and sugar
on the viscosity of the extrudates;

2). develop or modify a technique which will enable one to determine the effect of
cook time at varying cook temperatures on time-temperature history and, therefore, vis-
cosity; .

3). develop equipment to measure strain history parameters outside the extruder;
and

4). investigate the phenomena of slip or "slip-stic " and sliding ﬁiction in the
extruder and capillary dies.

8.1. Effects of non-starch ingredients.

In determining the effects of non-starch ingredients on the viscosity, it is important
that these effects are examined before and after gelatinization. This is because the pres-
ence of bran, proteins, fats, simple sugars and salts are known to have an effect on the
gelatinization kinetics, even though the mechanism is not known. It is important that
every attempt be made to keep the modiﬁed model as simple as possible.

Some possible methods for evaluating these effects include:

1. Starting with starch-water mixtures, adding different quantiﬁes of protein to the
mixture and measuring the effects on the viscosity of both cooked and uncooked mix-
tures. Repeat these experiments, replacing the protein with bran, lipids, sugar and salt.

2. To measure the effects of these non-starch constituents on the gelatinization
kinetics, gelatinization could be characterized by means other than viscosity such as dif-
ferential scanning calorimetry and thermomechanical analysis, or by measuring starch

gelatinization via enzymatic methods.

128

3. Finally, once the effects of each individual ingredient are known some attempt

should be made to quantify their effects on gelatinization.

8.2. Development of methods to quantify time-temperature history
effects.

Measuring the effects of time-temperature history in the Instron Capillary Rheome-
ter is difﬁcult because the center temperature of the starch dough reaches the gelatiniza-
tion temperature in a very short time (three minutes or less). This can be further
compounded by loading difﬁculties due to the small diameter of the rheometer barrel. If
sample loading is impeded, the time before compression of the sample may not be consis-
tent across all tests. Therefore, some alternative method is needed to determine time-
temperature history parameters.

Modiﬁcation of the capillary rheometer barrel is necessary to achieve both
improvement of sample loading and better quantiﬁcation of time-temperature history
parameters. The easiest way to achieve this would be to increase the diameter of the bar-
rel. By increasing the barrel diameter, the heat transfer to the center of the starch dough
cylinder may be slowed enough to have a mixture of gelatinized, partially gelatinized and
ungelatinized starch across the radius. It is also important to have strict temperature con-
trol of the barrel wall.

Use of thermal analysis methods such as differential scanning calorimetry (DSC)
or thermomechanical analysis (TMA) may also be useful to determine the time-
temperature constants. Burros et al. (1987) and Lund and Wirakartusumah (1984)
describe methods to determine starch gelatinization kinetics and the effects of moisture
content on the kinetics. Care must be taken, however, that the parameters obtained by
DSC or TMA actually describe the same effects of time-temperature history on viscosity
as observed in either test. Use of DSC or TMA would be easier than redesigning the cap-

129

illary rheometer and would also reduce the size of the starch-water sample needed.

8.3. Development of equipment for measuring strain history.

Measurement of strain history outside the extruder is difﬁcult for low to intermedi-
ate moisture products, because most rheological equipment cannot handle the high torque
requirements of these products. Therefore, it is necessary to design new equipment for
the measurement of strain history parameters as an alternative to the extruder. Strain his-
tory within the capillary rheometer is negligible in comparison to an extruder and there-
fore unacceptable for strain history measurement.

Elements of the new equipment should include the ability to:

1) measure shear rate accurately,

2) vary shear rate,

3) measure torque and subsequently shear stress,

4) control temperature and moisture, and

5) quantify mechanical energy input.

8.4. Investigation of slip or friction within the capillary die.

Examination of slip phenomena in the capillary die is also necessary. Attempts to
quantify slip using the techniques described by Darby (1976) did not produce useful
results. In addition, due to the non-cohesive nature of the product, a friction coefficient
could not be determined using uniaxial compression. At the present time possible solu-

tions to this problem are not obvious to this author.

LITERATURE CITED

130

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APPENDICES

138
Temperature, moisture content, cook time, shear

, shear ra e, and observed viscosity of potato flour

doughs.

1.

Appendix
8 ress

Y

Ogserve-
Viscosrt
(Pa s)

ear

Rate
(s-l)

ear
Stress
(Pa)

00
Time
(min)

'013 ure

Content
(g solids

empera ure

(°C)

766008323669821474285805310373310149161413229
255684855887910218251765588011.3232768686396363
2003117495525261541358811 5121 1 4 2 225424
133133218118 3 11 62

l l 66

966922221001090066097666600849904085151599538
388322661771232588531557766815521286464588534

477422 6666040277245227722354435338383933945
ll 11 33 6 69119 229999 411242 11113 3 6
2 2 22 2 2 l 1 1

522466938227672062066768360645628239090701657
600098972664900034512712708119496709030491503
88875697000890879081000550058991l405000590705
255884797225911205690841974923794885525228104
944988874880546676573995433153165510303921926
455433335555313322321111122 l l l

555500000000555555555555555222222224444444466

77777777777777777777777777777777777777777
222233333333333333333333333333333333333333333
222233333333333333333333333333333333333333333

000000000000000000000000000000000000000000000

000055555555000000005555555555555555555555555
555522222222555555556666666999999999999999999

139

(cont'd).

Appendix 1.

Y

Ogserve-
Viscosrt
(Pa-s)

ear

R t
(3'?)

ear
Stress
(Pa)

'ors ure 00
Time
(min)

Content
(db)

(°C)

empera ure

260280368548899544722882020264304652599
910130133412344310836755318753348327534
112 7 2 15 21166131 3 5
l

8484.86289920000000776633773558800000000
656543967797699766669999005111189198017
757555988899677922441122552881151655167
41416 019901 55155 2288221333335812402

1 3 3 11 24 23

44 11

660520050696811544345994184841900698071
628482984581077960817022201660824952590
806985205432533297025001506436234956599
3872270474.35577694265313717714333238300
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591401698855424167622366758385334083137985485
913776025011436140273753965183486887443659098
450184985700406759755513888223007987029302862
672129039000016942433311550014454245023975724

12121 16 133111 6311111 45 l 4 21
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097153773600390009792466473094612594100800008

510506194233037595943024880735327490387924459

5475010121116514081613 13343499005111856 1132
111 111. l 1222 1212

424950410044908890543084463296815019235169752

254027537300878253949301781151971414445813551

206753141722762057720305496956492400544911247

730630978500943759563397037753887056574344945

055690058099298394645255113791718677599597092

91812112123365244259781466434435940461762 174
1 1111111 1

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000000000044444444444444444444444442222266666
222222222222222222222222211111

000000000055555555555555555555555555555555555
555555555577777777777777777777777777777777777

999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000

(Cont'd). 141

Appendix 2.

0270733700406 117426

ooooooooooooo 788200708 0 o o o o 009357990014179320428232

0135144690671 ooooooooo 774187 ooooooooooooooooooooooo

877540017697694331623422852933556643618158766151544

626096652651534891566266583452501536389889470772128

75243331592l193967677766532330537622567634613222315
75311157632322255011158741323482864523322220
2 1 6 2 46

l

377723369165064626175311715970711199569685318842349
ooooooooooooooooooooooooooooooooooooooooooooooooooo

07097440360974.1159207244134571454710138308779133741

5100777 222956287541 23127818950 4 4617713580
111111 1 1222 l 12 1 11222

241258808652332012322711472277495572186836087563170
024362218282692090013777962179357874690951485720541
342842295947185239268411493626953045649421570152931
609488825199217022923822995489954595082883676169955
826492261452167364298733712146394535970783369372781
362466612223353442666522134215641336632335413456411

222222288888888888888822222222222222288888888888822

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

(Cont'd). 142

Appendix 2.

283l49272469664538724002895753034947874470124075341
56952491486924519554288278868959919383351251635419l
585594840819366059954556719399596469191788854153887
71l731081010649222993003962426061916865244842458282
324124546382226639642334464342220007774443235442806
211 l 1111 1111 222111 11 1 l

4.154966450037314134.14900000004.544548786666568561173858
...................................................

638114007054104870656000677333010131696210168519574.4

3014443354376611.1323555000666111.535007003231701114.264
11111 111.. 111111 111212

166073391998563517248661807373235353535965660474077

957775476494046476932449226967377477777508122840264

648143402435041053532333623830607772324434292974.2139

467899618110242762548332282126366866268957990991020

657439980426201730742666300603532626269183013588308

82623511316344.32171566645775722253566655575721 5272
ll

222222888888882222222222222228888888888888882222222

666666666666663333333333333333333333333333332222222

555555555555555555555555555555555555555555555555555
777777777777777777777777 7777777777777777777777777777

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

(Cont'd). 143

Appendix 2.

600671066498566297126582910367465430778762846232996

724095546422912961753870705723361227283898148960350

965489324629652551507l1349261334647990304889789680l

831686543619210512092652190006655443021283302284983

708773243536211235541 l1296664442221256545845331112
1 11 11111 11

693207247220704937413193319882536598781896687611207
471813072549899779016552592213965904017112665720681
145340932 1112227884441 13436752126122244455001666

l 12 . 111 11112 111111

598290979564014332232712404108243260097997419534230
039778538516486087912443812804572792342493961116282
332841692418480413583741382628397882952515550987736
568133875152914095676918408912851180036339024370933
191928204853212551098823699599652993416102939596207
144233267 1223334431 21 11212323222411122322331333

222222222888888888888882222222222222288888888888888

444444444444444444444442222222222222222222222222222
222222222222222222222221111111111111111111111111111

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888888888888888888

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

(Cont'd) . 144

Appendix 2.

086658672910794734893305731026440215778461906513496
041155983999808504074993194718663724468769123730454
8487999836919810573124lll15049222888788025972696957
996853814688483460848719991014554853123737784380103
122778665331226787664452222225003138992441334338557
1111. 111 655111 2182

76478558446196396795556T942644990483798874129723566

528415557404920877222706725121330706377556621048443

11334754236791 345886576191 24.234481041444111. 15
11111 111212 1112

652369204866500124318728582628330489425594887923566
8044302333101781404406139964895565053331132945807l7
833312057698948416368506743441?78324049577935790355
663748245509456546939115176859996680040455168333869

1222353245245111223343454434 112523442542811133333

222222222222228888888888888882222222222222288888888

666666666666666666666666666663333333333333333333333

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888 888888888

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

145

(Cont'd).

Appendix 2.

0045311..195544211389004466640700384

3788954499466640783 ................................

................... 64736332291135218991800112806464

99551977830011280643511.00032377885008746003004223035

3333007990183004223061572880862228565095699005576361

652266225799005576328875443222229420014.620053332221200
46223988848533322212 2 2 222

22

416618444879446848783872332473330908996279446848783
996685775917443347872687881452275839774917443347872
25440211426511777 3237994102221 12386511777

111 11111 111222 11111

571180552399991987778960779464417446038499991987778
997703770787776686468601444992277108111287776686468
347707333403339345353259112899992583593003339345353
O6778944.6043334946563881228284488879986843334946563
3822944484544413778762907722700141 7132354441377876
4333321131533364411122244443255512 2 12253336441112

888882222222222228888888888888882222222222222228888

33333222222222222222222222222222ll11.1111122222222222

555555555555555555555555555555555555555555555555555
88888888888888888.8888888888888888888888888888888888

999999999999999999999999999999999999999999999999999.
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

146

(Cont 'd) .

Appendix 2.

531119554421138900494400442731432792377205671768873
736332291135218991805911009797582140551208724256265
110003237788500874621351998711258019707324975073425
572880862228565095676495770241805028530089551694754
875443222229428146211117448425 11211056341934898394
2 2 8 1805671 1
1 151

8723324733309089962591834‘40857002790516425924959593

687881452275839774975981226421464468829555587272491

237994102221 12389443222233 0003531 1111777156222
111222 111 111111

960779464417446038483214660369541151325642668597892

6014449922771081l1288108002629486315440960582797943

259112899992583593076689333866818668610622435956684

881228284488879986875409770884524900599655791930140

2907722700141 7132363175001471816696427181872373984

2244443255512 2 122122211121 3 11212020891423255 25
212 11

888888888882222222222228888888888888888888888222222

22222222222111.11llll1111111111111111144444444

422222
22222222211111

12

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888999999999999999

555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

147

(Cont'd).

Appendix 2.

861376666314872691639728454915224973535395005836203

685620310363818206404617460213056596105053335655130

444466360201828708652447267152948497665700994 96517

40455952445433513216443 331255343213211822552 61376
12 l 412 77
22

602812506845330420667652634166063233785405442545273
005006579141979545919350605143697744922084118562290
43155370833344400012 229824444355411677213 8854112
1 1 111 111 11111 11

206326878223876325672213437526734860246463006557078
266597899612612964242402997482434022702502335810140
841717298440128130809170007058051680978770666526406
2l7784075373958810242497844042462123876737881 93943
63322342311111213321435 2423221221242221 332 32311

20080088888800888888822222222228888888888822222222220000

222222222666666666444444444444444444444222222222222
111111111 222222222222222222222111111111111

000000000000000000000000000000000
111111111111111llllllllllllllllll
111111111111111111111111111111111

95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

14
(Cont'd). 8

Appendix 2.

872830827443844438891903758915784948118393219628947
16162318778441?782277185988893960560441060876792309
641810456127418885575397960462231795224070307097060
365130294635293393333643638277220207442848209688582
7051432 1215765511121125156416302421669070511 3342
215 11 1 1 1 1 1

262845489710717743327668885065647593911707047ng?552

884406671631070012246279909582922334445464882996486

1 0671541 232553990569 131433234805 111218882223
1 111 1111 . 11

787712941081683335591988591064035632998454526104522
6247634071161944366763075470811.074369337060638480429
301347922710421148876366637225668051336282788144859
4.83409018057273324472532357188515761662141853403589
29326265013128?762241695362961938517225525406580837
2121222122 12122 112224 131 2 3 322 111121 1 l

888888888222222222222228888882222222888888888882222

222222222666666666666666666663333333333333333332222
111111111

000000000000000000000000000000000000000000000000000
lll111111111llllllllllllllllllllllllllllllllllll111
1111111111111111lllllllllllllll11111111111111111111

999999999999999999999999999999999999999999999999999
555555555555555555555555555555555555555555555555555
333333333333333333333333333333333333333333333333333

...................................................

000000000000000000000000000000000000000000000000000

(Cont'd). 149

Appendix 2.

0132239874202523213388004393625858351452134.008 2231.0

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 2 O O O o O
415589210600691412233366131868985198262493804 046559
982384641923886982363392068837933698126—[96170407853

17282403335196793825 4.2600006100317371.6387700402011013
1.72 31509211. 024. 6556530099955544500675151554
25 1 11111111. 5 3

4.7129
1072005115464163607039989316942274.00522784.702304 . . .Qnrnw
oooooooooooooooooooooooooooooooooooooooooooooo 121
54.1867261016642371648898693065704930251.2940151019001
4306054 18551205621222433333367666836788576901 1

1.111. 11231.. 1 11 11 111.11 .I.

888339956896365206546645327868767042355348346 17739
451786486562817132687785072592521726050436476101325
853412109507109277239936279340841470835642716077271
34601834846919909094 43302508867325125008034774397
56245212867857314526 63023158912523483727539719650
2213221 2223 232 665554676669788854444153445

. 5

222222888888882222228888228882228882228822888222888

222222222222221111111ll1666666666666666666666666666

00000000000000000000000000000000000000005
11111111111111111111111155555555555555555
llllllllllllllllllllllll

999999999999999999999999666666666666666666666666666
555555555555555555555555777777777777777777777777777
333333333333333333333333444444444444444444444444444

000000000000000000000000000000000000000000000000000

(Cont'd). 150

Appendix 2.

555922918830790118546288488986598413062382827379375

966097413383750895324674067685713611566876575079593

433441710084909835029461542361521579601716393531275

455577605523643922222518064436244038921786034715516

322222343348261121134543355757832222232130912234361
2 1 21

37723266779607643468596183448263774.0244662534264795
63338344776225?763114611822015358872187443606687845
4333900100844509235222332444433999999333 1150865644
1222121 11 1 31 33 l l

722253686645293598164781549636038076831262763211208
16.10625624458041792271369434291005237686905374823609
866622542282175307124375813644201089390485321126025
422252497725367228305918790048768305029190909759270
099945847775852921270431833026723036727604475315474
5555553333333343344 1111 2232223222221 111 2222222

222888228822882228822288822288822288822288828882228

666666666666666666644444444444444444

422222
22222222222222222211111

12

22222222
11111111

000000000000055555555555555555555555555555555
6666666666666777777777777777777777777777777

55

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777???
44444444444444.4444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

151
(Cont'd).

Appendix 2.

081390738265000667666653137720165867038505454306913
600707690464297658343995079237872281522751236786108
654079527607572437047970191170675549688137755146504
55492265963111.08721222043176308191612304111203766915
1153456544544422222243553445434231222345333236222ll

506516483956921253993772532418342532145426831949643
05078363838894.96315300600581780849468980166736800113
772111.1144555611.02251122114434511912312222233355699
11. 11111.1 11 1.1.1

247484860262510167445136111333842913119839741362146
544208171780974726428326703299348679314132123877935
93231933193580?13245072306381106718796732403054.6754
612871960404826914758137870155305693861924181135104
671677074014463136747510489555447549259088962633804
221 1 223222332223 11 12112331223 1|. 1211111

882228882228882228882228882228822288822288822288822

226666666666666666663333333333333333322222222222222
ll

75
75

5 555555555555555555555555555555555555555555555555
7 777777777777777777777777777777777777777777777777

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44.44444444444444444.44444444444444444.444444444444444

ooooooooooooooooooooooooooooooooooooooooooooooooooo

000000000000000000000000000000000000000000000000000

(Cont'd). 152

Appendix 2.

038117178569923923131619125261398989595317411266469
564708342929964415454701474197531905684717054463139
960576748215560615957297965273785773133810339460000
64670965284558632 4 8698469703898882034732806659092
31112412114111312 4 24344111232 200444214222 1 l
2 21
1

850533456296608581117695195719531309717264124072021

341069188187710524243590201654711393094968832696669

9123324335 99959712131132356443900666 2125725529599
111 111 111

025363005155541491715861769412777695614540518522920
083753053086631048682256632802591789401484903635656
582314385762280307178223157779772618675978871112128
67495597936229301 9 6298910439794372939148231867679
4.6927469491556836 9 9774950194085444.790912494477571
3112 1 2111111 1 11 11 1111 l 111 11 1111

288822888222228882228882228882228882228882228882228

2222111111111111144444444444444444

4.2222222222222222
2222222222222222221111111111111111

555555555555555555555555555555555555555555555555555
777777777777777778888888888888888888888888888888888

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
4.44444444444444444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

(Cont'd). 152

Appendix 2.

038117178569923923131619125261398989595317411266469
564708342929964415454701474197531905684717054463139
960576748215560615957297965273785773133810339460000
64.670965284558632 4 8698469703898882034732806659092
31112412114111312 4 24344111232 200444214222 1 1
2 21
1

850533456296608581117695195719531309717264124072021
341069188187710524243590201654711393094968832696669
111 111 l

02536300515554.1491?15861769412777695614540518522920
08375305308663l048682256632802591789401484903635656
582314385762280307178223157779772618675978871112128
67495597936229301 9 6298910439794372939148231867679
4.6927469491556836 9 97749501940854447909124944775?1
3112 1 2111111 1 11 11 1111 l 111 11 1111

288822888222228882228882228882228882228882228882228

222211111111111114444444444444444442222222222222222
2222222222222222221111111111111111

55555555555555555555555555555
88888888888888888888888888888

75
75
75
75
75
75
75

5

5

5

5

5

5
75
75
75
75
85
85
85
85
85

666666666666666666666666666666666666666666666666666
444444444444.444444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

153

(Cont'd) .

Appendix 2.

857728749101188055259165603744010353222657684075205

172215989801487368050887949211692167933388556607177

667765496352658741098704460695706712411155687340716

339929779140462680091891292893415429766469491643064

1144327521322121 11 4.282219933631112 111333315922221
11

597758950520698460174039451336075569555615752239507
230060735985291985575734457856264683011645303291704
532214 1323641298677 14445332474871922211143257889
ll 1 111 1 l

5822816526374120175238948780301248996888149762706711.
007774075767296267062783400746216720144639328543569
710086948593097390185564941997916216377973347989129
733330083311528648566086993708555745844011701345198
0800526703330376767779199884464822?0533956487146803
2111 l l 111 21 111 1 11111 21111 1211121

882228882228882228882228882228822288822288822288222

11

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888888888888888888

66666666666r0666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
444.44.444.44444.44444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

(Cont'd). 154

Appendix 2.

025390440189944110091167617473990197108921697326434
179317443773402507780021270598337494417614119684626
700313023978428400692947664643771313320058429223464
233797219123635754888839127865229005089624599037727
1.113983243551111. 11 16190133344111111 443122371 1
05 l -
l

910740439781405326293583094582227599513411489326535
980015945498156127793676386552667827845488834516848
135 12515117077865384 41 4.654033571971122 623215727
111 l 1111 _ 1 ll 1

013192705936701745863539998417775853853290453391303
67868887703011.039715114956519030080711.003461193279656
453991234966560038273813438983666213276441446531595
2064ll458447781335650791910239440150174298594628868
589783917709132523325849198504551815800112060789555
111 l l 11 111 12111 1 221111 11 2111 1 l 1

888222888222888222888222888222888222888222822288222

22211111111111111ll11444444444444444444222222222222
222222222222222222111111111111

55555555555555555555555
88888888888888888888899

95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95
95

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
444444444444444444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

(Cont'd). 155

Appendix 2.

033820451902074671194352848782533156622969024573738

89115301239636949166439791618811.1155120152071774135

927452857121081030914832778636844622821292630030323

16467l799286465936102020110673388277728829344972647

1 1222111211111 111118172221211 3 324222 111 l
11

95023782316451?426516320127393211444.344413798024772
685332344544565011222 122272548874.5212212332340826
1 111111 11 ll 1 ll

016313052327920231845998637269366141532073642576074
647928162215954804164542408l41644225528014252901437
153897997210480478171652085866500500414325663217492
3645270024351.738405037462787192833952734987851735519
8178956881877089585255274452775551018 96468915725001.
1. 1.. 1 11.111. 11. 11 .I. 11..

888222888222888222888222888228822288222888222882228

222666666666666666666333333333333333222222222222222
111

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
444444444444444444444444444444444444444444444444444

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

0000000000000000O0000000000000000000000000000000000

(Cont'd). 156

Appendix 2.

l78518574373643156852910100944940088004949402733442
321078653171500526465131955300063192292422289295558
776670234191685603462011166066619501113865614642229
13284121 1 015 2211 1141111211111 11 l 115

1 11 l

473636062616909005011728211495301067357052586585883
583213742323593544855203266141018243746196952645883
666231 7351581 21 188601122333334669892026432233
ll 2 ll . 1 2 111

186349777555514320856218299380341288220481849732881
38807061731305961.8163342544816016193541012193394006
074467123737l79599169250655205816498341382866994665
122169918979250898438607866600861881528706073266882
22088090750529451 41181 32284543144771278587623 445
111 l 1 2 1 l l l

888882288222882282288228822288822288822288822882228

221111111111114444444444422222222222222222266666666
22222222222111111111111111111

555555555555550000000000000000000000000000000000000
999999999999991111111111111111lllllllllllllllllllll
1111111111111111111111111111111111-1111

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
444444444444444444444444444444.444444.444444444444444

000000000000000000000000000000000000000000000000000

1
(Cont'd). 57

Appendix 2.

494455859277625200968873392071087430975640191657593
847718552085260499942371589112696436495305172818479
47660457467309453806799596475935024893967.7432250129
3755864709831632024453594649286224.440231269455331 3
330421 1111289 11111 928222313111 1

11 12

058884128384286437155778931319717760393776926426884
033333917814602877112001540547923859583078019505137
54446781 2228874453 75316345877110 1321321366887

11 1 111 l

348852460952110732340331364573106530221969235135039

279943060590921899397769816943442640217657150709740

465516619310821314060422680416672320092497841147333

731l17021167868891276129337951085013891629109415928
l . l l 1

882288822222222288822288822288222888222888222888222

666666633333333333322222222222222222l11111111111111

000000000000000000000000000000000000000000000000000
111111111111111111111111111111111111111111111111111
llllllllllllllllll111111111llllllllllllllllllllllll

666666666666666666666666666666666666666666666666666
777777777777777777777777777777777777777777777777777
444444444444444444444444444444444444444444444444444

...................................................

0000000000000000000000000O0000000000000000000000000

(Cont'd). 158

Appendix 2.

546
.rnw5023633999011.81.475756575573363300552198323366981.
19 000000000000000000000000000000000000000000000000
040849214461162693590598158872164488455628565799363
767088222203386297225056058816152244161829010788057
417545511102218232467576666202244.857210989899241
309074443337765644433356665655533342277555444333
11 1

1.74
o o 0984443376610086887920482263739922349063959122310
196 000000000000000000000000000000000000000000000000
592893699988849743563939555529155533309976606611241
1 1355484497797798966644345576788844489935777899565
111222 111222 111111 111

039406891145531267129649050005276655228285646422894
010166213389932585782367835527818888998429646044284
07320107449557935932961.42599230499885768968987008002
64.919300355522736706258084388025188336324793939440079
06820286771770?589929493266689434499424569505155867
.l. 565466688895554.57670090023343444444585423444444454

888222222222228888888888822222222222222288888888888

ll1000000000000000000000066666666666666666666666666

000000000000000000000000055555555555555555555555555
ll1555555555555555555555555555555555555555555555555
111

666222222222222222222222222222222222222222222222222
7777777777777 77777777777777?777777777777777777777777

000000000000000000000000000000000000000000000000000

159

(Cont'd).

Appendix 2.

451534410751015523255668480578404483460125203850375

218570305310805812284611675953050162579285068331251

97235015941353194221746032697762489758509964809263?

594689408406269774634584093059679438978749802595702

22242535138181... 4 3123312 11 1 1112222 11 11222231
71 .

823886293370300983529302965503623843240539605146637
1533259963453578658827824?1.042122953420417495447652
241 258418383840 121444009665 2125550116662334440
222 2 l 134 11 111 111111 1

76817503416282?15221576518416?497266383111646325046
929615324670400904719858679728703804719210269075429
86798958991626?444001622553465073290008871677500865
487627419681|.517626346753300684133903065467162530870
72189205087070123 02068419278 4265648966473802233
5752233242232333 1 11112 21 111 11111 11111

888222222888888822222222222228888888888888882222222

666666666666666644444444444444444444444444442222222
22222222222222222222222222221111111

55
55
55

000000000000055555555555555555555555555555555555
6666666666666777777777777777777777777777777

000000000000000000000000000000000000O00000000000000

(Cont'd). 160

Appendix 2.

897574.6951883476000012?1574904352562133506339498558

910651844820510421667423303357730697Gal-8437251615474

386373601695432294771855493253279047248930624205806

7068763325359713109915149818069562058 3354633040705

11 1182481 21 11 121 1 322 11 5212121111 1
1

35390217670564481600246809945314674.6143375891325474

541801087906387958009740391902189766312270877641031

9065622 32289634368805204121444999455 121735203079
1111 111 1 121 111 111211

47594253071017289755716814274606481310284406534001l
328355296691312044880676969066511038267833291288218
7059155218414806040003698770742479635 3418466117727
5362447935748648118828304746310687305 637944098235
61.032325836388546?7724493121212561592 652663708139
11111 1 111 ll 1 111 l 111 ll 1 1 1111211

222228888888888882222222288888888888822222222222228

222222222222222226666666666666666666633333333333333
lllllllllllllllll

555555555555555555555555555555555555555555555555555
77777777777777777777777777777777777777777777777

000000000000000000000000000000000000000000000000000

(Cont'd). 161

Appendix 2.

834853032000361830530047771520011015989557758613521
375346123722333961251143303962217514771737732714328
216150429244168052698813388454084453907750437523276
353 90919188894116519919947769997771170272 52543531
1 2 1211 l 3333 11 1222111 84421 1 1111163
1 8

1

504199281188893468466688882529369976589354178371018

146487161122460559059975539362649520040026975211603

1116474l72204425718558111678102224 61477332 333423
111222 1 111 111222 «I. 111

337564084988517554710070024400926276051798798762196
924994159699145698696666667409408726794955321698857
528160272855583845525524413673827234948767614294009
678 46840277650859226696643826521821391944687041086
1 3 39361988684774705504432240927681569856 6 544720

1 111111111 1 11112 1111 111112 2 l 11

888888888888822222222228888888888882222222228888888

333333333333322222222222222222222221l11111111111111

555555555555555555555555555555555555555555555555555
77777777777777777777777777777777777777777777777

2222222222222222222222222222222222222222
7777777777777777777777777777777777777777
555555555555555555555555555555555555555555555555555

000000000000000000000000000000000000000000000000000

72
72
72
72
72
72
72
72
72
72
72

162
(Cont'd).

Appendix 2.

941841665091101013259694415703027551031675382260363
055305888704438774280284595838174.332360098907797143
767391334720092072421000351937443553480556166666024
532536331103371249565430392628857338812008959929004
124 221 2111112 111111111 33 l 221 21221

2592567794111498412095428490200?4229930172051152606

91869266656991.5497441095897117629446290425718813469

76355511213445007566 322444908565 12265100688 2224
111 11 111 1 111 111111

035527223399909737626970153702267555663099787749373
531579444302246973177458027049812555666865873317904
345328008700014472009842281673101000149843359956176
45632399023442966593 285568443197444251091801135921
246869333 7669129480 4.326955263811114 31199988 4457
111 1111 l 1111 l 111 ll

888888222222222222228888888888888222222222222288888

l1|.ll11444444444444444444444444444222222222222222222
222222222222222222222222222ll1111111111111111

555555555555555555555555555555555555555555555555555
777777888888888888888888888888888888888888888888888

000000000000000000000000000000000000000000000000000

1
(Cont'd). 63

Appendix 2.

26896646850409980949624559084397?298777040573928702

159319695336994025653901165865131148999617778082592

656944542546898185559516609802330907888537165146101

447786660560512995758403338995554341666453775074088

11 161311 4 717111 2111111 1 226
221

8379969698064.16999395740041512145609222767099264635
378319795490136108780001155121816527444462124904174
56124232212344993434 444868973204 3335551108823 0

111222 111 111222 11111 1....

06979292952761562020062004l846608769333649643765947
7958646442398324275772433.48023236297888471476082381
693341115868775707874248831844719491777666665301659
871899696673517342323565596040400077777962968150394
7999145429496528580811 5557670979891555787785936648
1111 1 l 1 ll

888888882222222222228888888888888882222222222228888

222222226666666666666666666666666663333333333333333
11111111

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888888888888888888

2222222222222222222
7777777777777777777
5555555555555555555

000000000000000000000000000000000000000000000000000

572
572
572
572
572
572
572
572

164
(Cont'd).

Appendix 2.

76729124845415840856907878410522712.152533000008512?

394497853944534254330820549216442378127693116518620

05453336305793669785690Ion/2695227207021123669168313

l 442 111111122 33422221211 711211
9

8
164377828889108248385943181442999164930496552060689

289968224069537728023569367233220424966659220096046
76241421156272141 133344809656 1223435128669 43285
21222 2 122 1 111 11 111

646326929504851762658722011571006814982672880324886

798020702902387202367435150052773754201897448533057

394475400172837824938468845739335880758016992429643

402143674660119345803173098102991366041539994007854

740889856037743521155740772049 5549042362998386497
l 1 1 11 11 11 V 1 111 1

8008000000002222222228888888888888822222222222222200000080000

333333322222222222222222222222111111111111111111111

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888

85

222222222222222222222222222222222222222222222222222
777777777777777777777777777777777777777777777777777
555555555555555555555555555555555555555555555555555

000000000000000000000000000000000000000000000000000

1
(Cont'd). 65

Appendix 2.

348097637216356392593253703324883995922450903249438
14.—[057242058246716518748697790624552323315569651404
174799978879944992701281108262645118623334446964677
166644446194144437855565214144101116653332228816423
1 832 1 3 11 1111 131

13 3

517998023410207399792724069627285550699667538759032

797723931222701546529306624986920224075243811205601

8485637 55773 1134223323 465459211459435644 22133
111222 1 l 111 11 111222

547516938919630363078125824.537951883658535142506893

131004260961384159785796016708422556?40141046715191

256843455139874687969466818456586990516226135085417

701506784485472n].56916003751851663330318414191542781

90203135414315 2366721 8278629211335445665 64 1
111111 11

888888822222228888888822222222228888888888882222222

111111144444444444444422222222222222222222226666666
7.2222222222222211111111111111111..11111..

555555500000000000000000000000000000000000000000000
88888881111lllllllllllllll1111111111111111111111111
11111111111111111111111111111111111111111111

000000000000000000000000000000000000000000000000000

(Cont'd). 166

Appendix 2.

325972307069833680955950019116120109598078552287524
348909571846299119809387701127063252758231744023225
85588818667 777422333429991714478012862269434083197
82325 90128 544221222824450171744405021968355323975
611 1311111 1 111 11

1675548165219885354661611270538830796853428458709l4

70333401739481163504325661l147004921133523290752530

399574 32121333998303 22345384086 343545012667112
111 222 1111 111111

65689412513846682904849224657432643670100644151.2353

9370286711795222925420544863984213375

70557867065 2223600199900517582009793

23340253235 25530157537999294248972 4

323401 33 2 211221545 133445210486 3
l «I.

47

4891
57087535067031
53524366545321

222222888888888888888222222222222288888888888888222

666666666666666666666333333333333333333333333333222

000000000000000000000000000000000000000000000000000
111111111111lllllllllllllllllllllllllllllllllllllll
111111111111111111111111111111111111111111111111111

222222222222222222222222222222222222222222222222222
777777777777777777777777777777777777777777777777777
555555555555555555555555555555555555555555555555555

000000000000000000000000000000000000000000000000000

17
(Cont'd). 6

Appendix 2.

496326008955579636774699243527531916758857112047029
5l1662891083836696559156108918605541733397957234925
798715274650769716843921403041039972363189985587124
50877334535736344234320495714877060532 913261319337
1 111 3313 81 2 1 11211111 13

445179410901429837897155950437184393881587459447916
ooooooooooooooooooooooooooooooooooooooooooooooooooo
006103112714676040799292053834670718070761865861248
2541164121223432108972 616721 272741953334874446651
1111 111111 13 11 l 1

3.0436338723321174.234491676850587116706287840764.5501

1598589964186348242101924.97517005898229324849952693

709227739479736598410686978027587796423879780381974

150697763616314776291288223481462341454139483540298

15400750013 .I.l13154278672843513445454661 749125656878
1 1 l1.

222222288888888888888222222228888888888222228888888

22222222222222222222211111ll11111111111444444444444
222222222222

000000000000000000000000000000000000000555555555555
11111111111111llllllllllllllllllllll111999999999999
11111111111111lllllllllllllllllll111111

000000000000000000000000000000000000000000000000000

(Cont'd). 168

Appendix 2.

716758121413320229946780640472879
280672971568606177616119104898341
333674272779309914695828352564959
829505525126968146400553738011017
6211 1111 42 11111 531 11111....
9

9
856989190612312614839531809207744

679826830586248726961280928334566
l 137783455122325234640 250778813
1 11 ll 1 11 2 ll

512654876830255133715746166065130
159074530981988718114614777551005
283940539201466254454856221432740
767086930541400553805269102757348
945679946678111 14.556857177789930

111 2 l l 11

822222288888822228888882222888888

46666666666662222222222lll1111111

.................................

000000000000000000000000000000000

169
Temperature, moisture content, cook time, shear

, shear ra e, observed viscosity of whole wheat flour

Appendix 3.
s ress
doughs.

Ooserveo
e Viscosity
(3' ) (Pa 8)

. ear ear
Time Stress Rat

(min)

00
(Pa)

'01s ure
Content
(db)

empera ure
(°C)

07078817876649494081806518965350164150188644

1.l913660570815738976944926502790584495420494
0683759262732296851.1368890163054219615753126
7430353512950018164.4.51190523409832222320067792
9628665416923499955544307.5916355888666333464
1.11 653111 1.11 1.. 3

67496886406525239176129232707072641751927015

28674614347085137820853921033727248080449314
533686396230123453910343666533515
111222 11 111

3541197
11111....

40385371549068895366200943525594042075782233

85550600644247903498844663253289862929252123

77255621067839472997355326941912074319120024

06970559632381538335492314873802846035001082

53983638020320065548471987700767661837092503

6617707223655676708998124362365233343645242
l l l

66666666666666666666666666666666666666666666

33333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333

000000000000000000000005
555555555555555555555555

55

170

(Cont'd).

Appendix 3.

14782838983842150045128460967626770471247451798380

1809053430558235188912852276002123?4.549813945724392
17270043512986212073502176585040311268621560770311
67287800602274069701039219324372775616511... 68908426
6582223824959176060765221 l 7 7 6111 03110131
2 0941 211 12 l
1

87128306878430853197299001606005423018951688190153

03617504263954602562449745121617282252206294523006
5751000139113902134171795929512701329252651 001249
1111 l 23 1113495 3 325 112 12
. .3

420805406417174491001474.4755 900500055053009650730

50623210512002519642096524853322760187707748076970

98930422570706416643207064233166558652909281965742

55001549271077207524492184968755101882264305770805

32629900581557525870501013226111247395838911014235

34432234335870412548061115 l 2111 1 11121221 11
111112 1 11.111

66666666666666666666666666111122222222222233333333

3333333333777777777777777777777???7777777777777777
33333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333

00000000000000000000000000000000000000000000000000

00000000005555550000000000555555555555555555555555
66666666662222225555555555777777777777777777777777

171

(Cont'd).

Appendix 3.

60932489762688690508565208761375961376033995554801
04880443406755930948442324736627321745486092730748
96036841228267773221414271221469763111252242265423
74411 1 1511 761271 721 2 54211

1

91827733746730405147071082266564867761760623609196
57505119521429409634708186221753389325989622774151
l2406121851351641464367511165 48524194589813649618
1111491 1112481 2 1348 124753 121 11234

1 1 1 11 ll

44.900704703223388446911073010069738994540864957214
22110506273211168727677910593419163221274061987413
99465375016072048744282214516687712145796984820988
55785458487369135175521053667594330440391866303453
11112 1 2211 211 122231...

31304463549278
21132 11221 1

2
22444444444444
1

144
511 31 11111
66666666666666666666222222222222222
lllllllllllllll 1222222222222

77777777777777777777777777777777777777777777777777
33333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333

172

(Cont'd).

Appendix 3.

071878931513764128908546553643589726116802166014l3

52849732441234613127430347049357557873712150710625
81286852517401551380721238252714673591191789722298
16940343323963341522186686522895177422221712443144

74211 532111 621 4211 78121 421

40652457183157023289409021763052105356647233679556

22403626618008155745107346704739678257770969068641

71361198710236401481814169769136445089012505598484

8 1223518 1212648 11 219 1113632 11158 1
1 11 l 11

56474875853255758989000382144002248716929018505781
80913141099170115455534185638717340087309712093075
31430376049391373471939590440960308668798736915863
11001024489999178133884366458277046837267425114100
69752032039105992399262836492890711309626030758911
l 1113112221111211123 111 122 1111122211122 22122

4111111-11111111111111122222222222222222233333333333
2

77777777777777777777777777777777777777777777777777
33333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333

00000000000000000000000000000000000000000000000000

55555555555555555555555555555555555555555555555555
78888888888888888888888888888888888888888888888888

173

(Cont'd).

Appendix 3.

35854607220868421876756547734439526088917312341128

36884175383747766353379638773726929645918598100294
78643115497097050327856106586260161561232943507227
24211656705311006642110009743229358375322258888222
1 m361 1 51 251 432 1 60224

2 l

9205676990100687077680541748625154567827607804.0280

...................................................

98182556267841539887811956852039461896183099851402

6715 117032704 93280969273996361352262343215836200

289 113728 123840 1112611 1113632 2475
l 11 12 11 ll 1

859011066210773392064855020103582538338586635l7340
85986124541768116552658902246490366924309904640196
93985652434424892949253374317017545385270598881279
85708617697947384450549752040753449498812579097497
83195502748332498462728473544509149726018206562983

122 11 112231 11223111111223 2121212 31

123
2222444444444
1111222222222

12 1
12 l

11
33336666666666666666666222222222222
1111111111

77777777777777777777777777777777777777777777777777
33333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333

00000000000000000000000000000000000000000000000000

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888

174

(Cont'd).

Appendix 3.

57752081640151451421090093681673814041018269473906

05930855270193515462021657085208666259337614385284

070340743631597668517000047657237874.414408141990875

627733321509613222231233556718321l114372213255811
4 5

414619172063884.7230?966495188813627686221879187248

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

63321786578755550206229779052496633247298721553760

483809333 17338370609231471011.764301758191395 311
1255605 13157046678 222273 1112282 1 933
11 l 1 1 11.1

25503984000501600524205090910105870578305891990605
43869591280223176238962340337188846336188880040278
43024171564420925626456287192429525192429528897329
32870494311972540965209695754704l1.0754709197836446
1720783502507623415404156716387845416387642 481531

222211222433211212211122111121 12 11121 12 232

44444444411111111111111l12222222222222222223333333
222222222

7777777777777777777777777777777777777777777777777?
33333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333

...................................................

00000000000000000000000000000000000000000000000000

55555555500000000000000000000000000000000000000000
88888888811lllllllllllllllllllllllllllllllllllllll
111111111111111111111111lllllllllllllllll

175

(Cont'd).

Appendix 3.

10678672484222609332505458644.653077272490942490050

60395439746632625831749418398887108275235739438015

16204271025765040265164976339073377508642120608764
B9843521 $8532511 5432211 84321 64321

660374144807018186626555366814.132688910492734777594

2410095710039032495522470827873850651927266612566079

5.19 240656084 366259447 340650422 34.216162135100565

64.9 11 2485 12 3509 11 23003 123612 11134
1.. 11 1.. 12

08876559504097764950409692205810569220817579643588
20654966513505496651350279315191627931197936028510
49229520519152952051915715693313671569316426901338
58490475639159047563915025315616102531611802281566
04308701993770870199377557500270155750279973035020
12212355256691235525669 112412234 11242223 1223122

333666666666666666666661111111ll111111111122222222

77755555555555555555555555555555555555555555555555
33388888888888888888888888888888888888888888888888
33333333333333333333333333333333333333333333333333

...................................................

00000000000000000000000000000000000000000000000000

00000000000000000000000555555555555555555555555555
11155555555555555555555777777777777777777777777777
111

176

(Cont'd).

Appendix 3.

65209004629744127984109690766395092641476898068835
48652414036995155967979188725998662429716591025083
29839715421473107532229401542144284074229719426522
533116 742 1 432211 043112 343111
1 2

27364824909174347180827685143838810368738613321131

1140317581241909726712064?824161564547722072722872
413620110091304052581350693532 464157852 464190627
4 12 4510 1112382 11 3428 12 2509 12 3507
l 12 l 11 ll 11

57964358835594802154659440215458239941285123994128
83602851088573010563257391056339145505013514550501
02690133850315611101731541110132613107753161310775
502281566555275553630527955363674.3439807634343980?
5730350205505511991550557199156817019891691701989.1—
3 122312223112 11133 112111133 122311224 122311224

22222222222333333333333333333366666666666666666666

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888
33333333333333333333333333333333333333333333333333

177

(Cont'd).

Appendix 3.

51693093202628661820602863255348834848997657969699

...................................................

35918735210377697165712325526008227911075293934771

20949447038255333474334969272700705717221787493602

92037642215799553215436356522927068652267821086324

44221 743113 654221 653211 443311 2
1

19608004556763454535758470671739210038990906395485

42958461616979845239300130631358112935149409086777

3507805931351038949 351679121 35446932522575045154
11 4707 12 4929 11 3696 12 3696 112382
11 11 l l 1

76040657338604965733643101910364320191001108568760
81214375848121737583915019684391501968417629511531
74277454197427745414356311868435631186815622343441
72099150117209515012382651314238265131456207526015
62305630586230363056819817256681981725613138022061
122412333 122412333 122312323 12231232311221122321

22222222222222222224444444444444444444411111111111
llllllllllllllllll122222222222222222222

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888
33333333333333333333333333333333333333333333333333

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

00000000000000000000000000000000000000000000000000

5555555555
8888888888

75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
85

178

(Cont'd).

Appendix 3.

536602796655811561465682341987977608705307826882999

569365085179941713704008205341490495130066606934150

196454705016637379305143573289848555805379451542280

372004321700895421368864311226805432162076432123736

21212 052 631 1 06421 462 54321
1 l 2

004524425943960523411892395889756021630678244949054
961919080320618966393544023849218276660158906937542
570—,51138141432907252579265 239531205 3329140613517
11 5646 1113415 11 4672 124515 1114537 11

1.1le2232122111233122112233 112111122112 11122 1222

111111...ll1222222222222222222333333333333333333366666

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888888888888888888
333333333333333333333333333333333333333333333333333

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

000000000000000000000000000000000000000000000000000

555555555555555555555555555555555555555555555555555

,888888888888888888888888888888888888888888888888888

 

179

(Cont'd).

Appendix 3.

50976736090046114894539398477213822376226461723378

77193973878053094445620180849067934545762445346407
94.823643434916805?50866036329753168026177937639118
33227196115321827044542255239754217668375321755518.
764211 443211 9321 2 743112 23211
8 1

41555417379372089093056551730403088440395521159757

37903893453790568951297756895129777832954597
8442696496844.272967615587296741558785165087?
93881221489388732290674973229867496706230874
954537839495458678974.80886789548082774859379277
58827827725882448231100544823210055691209643569120

1123 122111123 112212233 1 233 112211123 11221

12212
66666666666666222222222222222222224444444444444444
111111111111111111112222222222222222

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888
33333333333333333333333333333333333333333333333333

00000000000000000000000000000000000000000000000000

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888

180

(Cont'd).

Appendix 3.

754709864138024646523803484093835984000153544678101
579743036314735288191356199917038964530647790010945
072891400352368301257473922157747906328571380896533
532173311745327019153211471583721 589137411 7284642
37432 08522 354328 37432 64332

l 1 1:. l

513526026137108200195178212899846851.691380281921735

3408390379821491412790285209008286963461620876701ll

9380124283865323332796981241910908113332715423527l3

3408 11 1383 1212306 11 1183 1211205 1124
ll 1 ll 1 11

112312133 12332134 1 1221145 1121145 1111244 1

444411111llllll111—lll11ll222222222222222222223333333
2222

555555555555555555555555555555555555555555555555555
888888888888888888888888888888888888888888888888888
333333333333333333333333333333333333333333333333333

000000000000000000000000000000000000000000000000000

555500000000000000000000000000000000000000000000000
88881111111111111111l1|.11111111lllllllllllllllllllll
11111llllllllllllllllllllllllllllllllllllllllll

 

181

(Cont'd).

Appendix 3.

03017032205974867878542422208342103581731943695386

25007629452312851510169897199450392792515722472248

57172784756913497210636671970519717547514720165840
2162421 9097994211085792621 37391153112629243211
B7532 47321 26321 4 2 11 3 1 1

1 l

01558498570240203304673111174293591286114058.430709

23398349595000461814813810054607813654264813781440
0224222721.1434096255143304166111406001501140572125
5 123654 12 1373 1241275 1112398 1123408
1 11 . 1 2 1|. 11

15277483917920800941792080094147090491754469019175
48146195546410009397641000939725140156752924035675
02895164103804060185380406018586162910298176221029
876053113844.92856436449285643663531237806203103780
70681590172818997783281899778341199211404159931140

31245 11 22133 122133 1

12 2

1 111112 11111
3333333333666666666666666666662222222222222222222
11.111111111111111qu

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888
33333333333333333333333333333333333333333333333333

00000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000
1111111111111111111111111111llllllllllllllllllllll
111111111111llllllllllllllllllllllllllllllllllllll

182

(Cont'd).

Appendix 3.

41391873450266833063223196184479242610763998653442

89265939270683641507208586553836142628541955159578

333040051l5107338902455225534811515798088435882299

21226431159355741 087.65756491439185327062954322404

5 1 52 0653221 963211 2211 321
1

51019563196746799830347735985287189072419773881115

48416842014862151450220664638104846805465960505259
128877994 29724470 3528148613007604611374739436137
112494 1 387 111275 12114730 1123619

1

1 1 ll 1

020455824626715834777316697?4485628142673468948703
90113323371144323375589146942362727357317116797979
09551120994278120968473050057169474222919788482250
639844081 3195408124062865376344392552886067621139
7 1111556 2382155650046171133563921194628727422471

211111 11111 234433571234313452 11111232 1

4444444444444444446666666666666666666ll11111111111
222222222222222222

55555555555555555566666666666666666666666666666666
88888888888888888833333333333333333333333333333333
33333333333333333344444444444444444444444444444444

00000000000000000000000000000000000000000000000000

00000000000000000000000000000000000005555555555555
111111111111ll111155555555555555555557777777777777
llllllllllllllllll

183

(Cont'd).

Appendix 3.

22032307585033879686488660403760586954593050089420
5305842543222458650324481489801042113460310144.7027
20609827558182282596888786962425849087310907863181
77531120300743217350614211926006432266602952l17811

22311 3211 1 22111 22111 2221

93381580708760371420057573037071111557157533264708

78672961592945012654728961476002467283441423189410

222526145232511413960830751374642261 4734014231302

213763 1113730 12 3862 1113605 1113853 11
11 11 ll 11 11

85580254315896459264631503745618727440712753183155
6345339972243406986581104.6446?14518328025621720564
227343311.997308951634272542958623061399295535960549
5021127565321156551417454514454274.1526150368903704
69832538834973994857496200482469511021237052725923
l 1232 111 1221 111 1232 111 1233 111111222 21

lll11122222222222222222222333333333333333333336666

66666666666666666666666666666666666666666666666666
33333333333333333333333333333333333333333333333333
4.4444444444444444444444444.444444444444444444444444

184
(Cont'd).

Appendix 3.

06323876303874053648194817117525277433798579610566
46190258404305070720797011782030438595396031196899
44045259570920254358120028917614117255543354929568
54422802908532140876453218905515321847152532188137
221 11 241 11 1 532211 5221

85971609143614374543247068685633293109804982733849

75739234138883043254579922941557627197629630462377

522782475446786228177718074164063261234094483 3540

13608 11 2759 1123869 12113858 12 3746 12
1 ll 11 11 11

51759366305680074907597241491846754420584622829609
45017342184967602228870562194121392858631461384832
8306574224145128658679014.2087625746311301900015609l
552723874379955041684.92904969178253404632438363614
84562689458542369581195336914819623600112865139106

1222 11 1232 111232 11 11233 113311233 121

1
66666666666666622222222222222222222444444444444444
11111111111111111111222222222222222

66666666666666666666666666666666666666666666666666
33333333333333333333333333333333333333333333333333
4444444444444444444444444444444444444444444444.4444

185

(Cont'd).

Appendix 3.

943144240476603495932552790884863065454678372247587
301510418579884595229495151521300797531676709257973
5109—I1547439797901591.6386?5379595640034190352577836
653110360973111756074321172729632113549994211278118
4211 3211 2211 421 42111

628919078673489495323053749795283668812061158223397

ooooooooooooooooooooooooooooooooooooooooooooooooooo

911324976789438339435844169852289140596190500583927

10160311.476753848148616814413748467801389796887138440

14873 1112419 1223820 1113742 11 3754 111
ll 1 11 ll 11

37850607901.0510208068923847127902449726299272957359

10532512761982751476l493648388949484828594839605769
12232 11111 21 111111121 111 1121 111 1121 1111

444441111111111111111111122222222222222222222333333
22222

1066666666666666666666666666666666666666666666666666
333333333333333333333333333333333333333333333333333
444444444444444444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

555555555555555555555555555555555555555555555555555
777778888888888888888888888888888888888888888888888

 

186
(Cont'd).

Appendix 3.

77468738104874147429421213219035900409866737707734
5228437ll486876848l7842921833135536050926094560683
423957357021867991201550236971.254433560007476411.527
32146498753215952754.322613864432251760543226761974
221 4211 321 33111 4211

30580520483646650572166508266871174376225156507560

73732384473492945847368576318352626478522189683305

08724000768291365473360.1497Ion/3331363595235 388828

737 12213741 1113610 . 1223619 1113619 1112
11 11 ll 1 1

86331523879185190687553240122378035845245703534265
23247000540115173544058963955403273047077407664994
59433518432935706605652069368652281292578108980579
475912534578677306171646980683590441789106940445?4
40351597385025100093095592549508341126949034040783
232 111111232 1121 1222 111 1222 1121 1132 1121

1|.
33333333333336666666666666666666622222222222222222
1.1111111111111111

66666666666666666666666666666666666666666666666666
33333333333333333333333333333333333333333333333333
44.444444444444444444444444444444444444444444444444

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

00000000000000000000000000000000000000000000000000

55555555555555555555555555555555555555555555555555
88888888888888888888888888888888888888888888888888

187

(Cont'd).

Appendix 3.

1|.13818269709091582378468297037336814006795061584566
216500280301281332026826713189471898833464579474605
229195953835508178141671328280416759090160709124303
32156031842123—[295543134481432217267733211101565321
32211 3211 522 l 42 421

185626076636337236456118114272792109255944708366617
175816016071963624604392579769696429473706106384766
988 34160382 352953737 2496547051239654682123938278
627 112425 1113493 123483 134415 11263

11 11 1|.- 1 11 4'.

962l4058017614058101765977520736991.7130736113557761

285389587093389588709345170030957527143095444480738
223 111222 11 1222 1 211111 1111.111 1 11

22244444444444444444441lll1111111111111111222222222
1112222222222222222222

F066666666666666666666666666666666666666666666666666
333333333333333333333333333333333333333333333333333
444444444444444444444444444444444444444444444444444

000000000000000000000000000000000000000000000000000

555555555555555555555500000000000000000000000000000
888888888888888888888811111llllllllllllllllllllllll
11111111111111111111111141.1111

 

188

(Cont'd).

Appendix 3.

331019354688842711935223129362?49838068160734.1150?
68813188722315387239904423829779610313377248667768
58308298603250094584545161053564529786718222065708
4384352111383752211054334321143211 5 1221111424331
21 l 211 l

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0966420337001775803333784019492598053874823979594900
9569060017227506952245470514605729771.001406299776204.
1340071911 402173072223266493181677.36294004200396075
1.213517 1122610 12136200113516 11340034. 1237
11 1.1 11.. 11 11

63333282476099294539208128283861207177760470395544
78567465551692369284990657078734207371471530148182
770979840627119586184582.2073569044.9259292782492444
69936141751875836779958963475288936959331251556632
443479918733380856943346713955678444 1579069127714

111 l 111 1112 11 111

12 1

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2222222222333333333333333333366666666666666622222
111111.

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00000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000
111111111lllllllllllllllllllllllllllllllllllllllll
11111111111111111111111111111111111111111111111111

189

(Cont'd).

Appendix 3.

70128511823540837843153132

22428476557697630735370696

86987732766937707548813146

8432111517254321 45744321
54 42

98372684663964358410780112

948960340930055?4105065191
93170704116244936112817663
5 124859 1123723 11350
1 1 11 1

29300681130401833589393554
12304356158336201677159356
30492910355880999765272183
208631699185578955443854ll
33501501584371441746647147

11121 1112 111

1
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