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RHEOLOGICAL PROPERTIES OF SOY POLYSACCHARIDE DOUGH
BY
Aminta Virginia Vega-Vargas
A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Food Science and Human Nutrition
1990
mg:— 95. 5
ABSTRACT
RHEOLOGICAL PROPERTIES OF SOY POLYSACCHARIDE DOUGH
BY
Aminta Virginia Vega-Vargas
Soy polysaccharide was mixed in an APV 50mm twin screw
extruder to obtain doughs of 50, 60 and 70% moisture. Rheo-
logical properties of the dough were measured with an
Instron capillary rheometer-operated at four plunger speeds
(50, 100, 300 and 500 mm/min.) in combination with four dies
(L/D = 2, 4, 8, and 16) at ZETL Great variation in data
indicated problems in using a capillary viscometric tech-
nique with this type of material. Pseudoplastic behavior
was observed in the doughs.
An overall mathematical model was obtained for doughs at
different moisture contents (50, 56, 60, 64, 65, and 70%)
and different temperatures (25, 50, 75, and QUTU using mul-
tiple linear regression:
n = K. W" exp[“7‘(%,-%)] exptbcMC—MC.)1
where K, - 6700 Pa 3“, n = 0.26, AE = -937 cal/g-mol,
T, - 25°C and MC, - 70% w.b.
This apparent viscosity equation gave a poor representation
of the data for dough at 70% moisture, and at low shear rate
and high temperatures at other moisture contents. Sliding
and slippage are some of the possible causes for the poor
fit of the equation.
DEDICATION
I dedicate this thesis to my mother, Gladys Vargas, who
taught me that every dream and desire can be reached if you
persevere. (Esta tesis es dedicada a mi mama quien me enseno
que todos los suenos y deseos se pueden alcanzar si se per-
siste.)
iv
ACKNOWLEDGMENTS
The author wishes to express her sincere gratitude to
Dr. James F. Steffe and Dr. Robert Y. 0foli for their guid-
ance and advise during the course of this study.
Sincere appreciation is extended to the guidance commit-
tee members: Dr. Mark Uebersax and Dr. John Patridge. Also,
sincere gratitude is given to Dr. Ronnie Morgan for his
guide in the first year of the author’s program.
Special thanks are extended to Nicki Engeseth and Chit
Leong for their extensive colaboration in editing this docu-
ment.
Recognition is given to Dr. Kevin Mackey for his help
with computer analysis; and Barb, Kevin, John and Gary who
operated the extruder to obtain samples.
Thanks to Ralston Purina who donated the material for
the present work.
Also, the author expresses her gratitude to LASPAU-
Fulbright program for their financial support throughout the
program.
TABLE OF CONTENT
ABSTRACT . ..........................
DEDICATION 000.00.00.00 00000 0.0.0.00
ACKNOWLEDGMENTS ........ ........ ....
TABLE OF CONTENT ...................
LIST OF TABLES .....................
LIST OF FIGURES ... .................
NOMENCLATURE .......................
INTRODUCTION 00.00....0......0000000
LITERATURE REVIEW 000.00.... ........
2.1 Introduction ...............
Soy Polysaccharides ........
Modeling and Rheology ......
Rheology as a Modeling Tool
Rheological Model ........
2.2
2.3
2.3.1
2.3.2 Tube and Capillary Viscometers ............
2.3.3
2.3.4
Dough Rheology ...........
MODEL DEVELOPMENT ..................
Basic Equation .............
Possible Sources of Error ..
Barrel Correction ........
Plunger Friction .........
Stored Elastic Energy ....
Viscous Heating ..........
Kinetic Energy Correction
End Effect ...............
Slip .....................
Model Development ..........
Rheological Model ........
Temperature Effects ......
Moisture Effects .........
Overall Model ............
eeeeeee
\IO‘U‘IbUNi—J
uuquNNNNNNNNH
uuuuuuuuuuuuuu
eeeeeeeeeeeeee
ubUNH
MATERIALS AND METHODS ..............
4.1 Materials and Equipment ....
4.1.1 Raw Material Specifications
4.1.2
Mixing Conditions in the Extruder ........
vi
iv
....
Moisture Analysis .........................
Storage Conditions .......................
Capillary Rheometer Description ...........
Run Conditions for Capillary Rheometer .....
Experimental Design .........................
Rheological Parameters ....................
Moisture Effects ..........................
Temperature Effects .......................
Data Analysis .............. ........... ......
U'Iahu
hbbbbï¬-ï¬biflb
000000000
000
UMP
hUUUUNl-‘HP
5
C1
LTS AND DISCUSSION ..............................
Moisture Content Analysis and Density .......
Force .......................................
End Correction ..............................
Slip Correction .............................
Rheological Parameters ......................
Overall Model ...............................
010101010101
O‘UlathH
CONCLUSIONS . 0 0 0 0 . 0 . 0 0 . . 0 0 0 0 0 0 0 0 . 0 0 . 0 . 0 . 0 0 . 0 . 0 0 0 0 0 0 . 0 0
FUTURE RESEARCH 0 0 0 0 0 0 0 0 0 0 . ...... 0 . 0 . 0 0 0 . . 0 . 0 . 0 0 00000
LIST OF REFERENCES 0 . 0 0 . 0 0 0 . . 0 0 0 . 0 . 0 0 0 . 0 . 0 0 0 0 0 . 0 0 0 0 0 0
APPENDICES .......... ........ ...... ................. .
Appendix A .................................. ..... .
Schematic diagram of extruder die
Appendix B ........................................
Moisture determination
Appendix C ........................................
Calculation outline
Appendix D ........................................
Solid density based in chemical composition
Appendix E ........................................
Reynolds number and developing flow inlet length
Appendix F ........................................
Capillary viscometer raw data at 25%:
Appendixs .00..00.........0.0........000.00.......
Capillary viscometer data for the overall model
33
35
35
36
37
37
40
4O
4O
42
42
44
48
51
51
64
69
71
72
79
8O
81
82
84
86
87
92
Table
10
LIST OF TABLES
Rheological models
Proximate analysis of soy polysaccharides
Screw configuration used on APV Baker 50mm
twin screw extruder: L/D = 5
Summary of experiments
Moisture content (% wet basis) of soy
polysaccharide doughs
Density of the dough (kg/m'3)determined
using different methods
Drag force for different moisture contents
(N)
End correction force (N) at 25%:
End correction force (N) at different tem-
peratures using 3.17 mm diameter die
Power law parameters for soy polysaccharide
doughs
viii
Page
12
32
34
39
43
45
47
49
50
65
Figure
10
11
12
LIST OF FIGURES
Force balance on a capillary
Illustration of capillary extrusion pro-
cess
Typical graph from the XY recorder
Apparent viscosity versus shear rate at
25°C
Shear stress vs shear rate at 70% MC and
25°C
Means of shear stress vs shear rate at
70% MC and 25°C
Shear stress vs shear rate at 60% MC and
25°C
Means of shear stress vs shear rate at
60% MC and 25°C
Shear stress vs shear rate at 50% MC and
25°C
Means of shear stress vs shear rate at
50% MC and 25°C
Regression line for means of data at 70%
MC and 25°C
Regression line for means of data at 60%
MC and 25°C
ix
Page
18
38
46
53
54
55
56
57
58
59
61
62
13
14
15
Regression line for means of data at 50%
MC and 25°C
Effect of moisture content on doughs at
25°C
Plot of estimated and actual apparent
viscosities for the overall model
63
66
68
NOMENCLATURE
b = moisture coefficient constant, dimensionless
C1 euui C; = constants 1 and 2 for Ellis model
C3. Cg zuul C5 = constants 3, 4 and 5 for Powell Eyring
model
C6 enui C, = constants 6 and 7 for Williamson model
= diameter, m
D
F final force, N
F} = total force, N
Fd = drag force, N
Fro = entrance force at L/D = 0
K = consistency coefficient, Pa sn
KE = kinetic energy, J
L = capillary length, m
[a = required distance to develop fully flow by Darby.
MC = moisture content, % wet basis
AdC, = reference moisture content, % wet basis
[Von generalized Reynolds number
n = flow behavior index, dimensionless
r21 and n2 = power index for Ofoli model
f2 = corrected pressure drop, Pa
xi
xii
fï¬ = total pressure drop, Pa
= volumetric flow rate, m3 s"1
radius, m
universal gas molar constant, 1.987 cal/g-mol K
Q
R
R
T absolute temperature, K
T
o = absolute reference temperature, K
12= fluid velocity, m 5'1
Greek letters
a.= kinetic energy correction factor, dimensionless
F; = apparent Newtonian shear rate, 5'1
y = shear rate, 5"1
vw = shear rate at the wall, 5’1
ASE = free energy of activation of viscosity, cal/g-mol
n = viscosity, Pa 5
no apparent viscosity, Pa sn
viscosity at reference moisture content, Pa 3
n.
u = Newtonian viscosity, Pa 5
u..= Newtonian viscosity at infinity shear rate, Pa 5
o = shear stress, Pa
0 = shear stress at the wall, Pa
w
ay = yield stress, Pa
INTRODUCTION
Technologies, such as extrusion, are recently being
applied in the food industry to manufacture products such as
meat analogs, pet food and snacks. This technology had been
used extensively in the processing of thermoplastics. Math-
ematical equations for the extrusion process have been
developed for plastic materials. Harmann and Harper (1974)
showed that these equations can be applied to food materials
to a limited extent when the material viscosity is known.
There are two important reactions in foods that can take
place during extrusion cooking: protein denaturation and
polysaccharide (starch) gelatinization. The first approach
in modeling food extrusion is to use some type of material,
a "standard material", where these reactions are negligible.
In this study, soy polysaccharides were considered as model
substances because they are non-reactive. Given a complete
rheological characterization, these materials will be very
valuable in basic extrusion research.
The capillary viscometric technique has been shown to be
very useful in the study of flow properties of plastics.
The higher shear rates achieved with this viscometer are
similar to the ones obtained in an extruder. The capillary
viscometer was used to measure the rheological properties of
soy polysaccharides in an effort to obtain a non—Newtonian
model for the material.
Numerous studies (Cervone and Harper, 1978: Harper et
al., 1971; Remsen and Clark, 1978; Senouci and Smith, 1988
and others) have presented the viscosity dependency with
respect to temperature, moisture and shear rate. These fac-
tors were also considered in this current study of soy poly-
saccharide doughs.
The objectives of this study were:
(i) to determine a viscosity model for soy polysacchar-
ide doughs at three different moisture contents.
(ii) to determine if capillary viscometry is appropriate
for investigating the rheological behavior of soy polysac-
charides.
(iii) to develop an overall rheological model as a func-
tion of shear rate, moisture and temperature for soy poly-
saccharide dough.
LITERATURE REVIEW
2.1 Introduction
Knowledge of the rheological properties of any food
material is required to model fluid food processing. The
relationship between shear rate and shear stress gives some
indication of the expected material behavior during process-
ing. Different empirical models have been suggested to
express the shear rate and shear stress relationships in a
mathematical form. The selection of a rheological model for
a given material is based on: the agreement of the model
with experimental data, the accuracy of its prediction and
the convenience of its application (Clark, 1978). When the
appropriate model is determined the rheological properties
can be used in the development of many food processes.
Rao (1986) and Steffe et a1. (1983) compiled a collec-
tion of rheological parameters for various food materials
obtained from different researchers. In both references the
reader can see that rheological parameters are specific to
concentration, moisture, temperature and technique used in
their determination.
Dough rheology has been studied intensely due to its
importance in the breadmaking process. However, most of thei
rheological measurements have been carried out on instru-
ments which give parameters dependent on instrument geome-
try. Although these parameters are valuable, more food
doughs are processed by methods which require engineering
analysis, so that absolute rheological parameters with engi-
neering units are necessary. The optimal characteristics of
any dough product are intimately related to its rheology.
Determination of basic properties of dough is a chal-
lenge due to the complex nature of dough. A simplified
approach is to relate dough rheology to polymer melt
rheology. Even though there are many similarities between
them, food dough is significantly different from plastic.
The two main differences are the variability in food compo-
sition and the changes due to the cooking process. In addi-
tion, polymeric materials have a known composition and the
reactions during processing of these materials are well
defined. 0n the other hand, food materials originate from
biological sources whose composition depends on many vari-
ables. Thus, the reactions occurring during processing are
less well defined. Consequently, the knowledge of material
composition is very important for the determination of rheo-
logical properties.
2.2 Soy Polysaccharides
Traditionally, polysaccharides in foods have been used
as thickeners, stabilizers, gelling agents and emulsifiers.
The recent trend toward increased fiber intake of consumers
has created a new use for food polysaccharides as a fiber
source. New sources of food grade fiber are continually
being developed.
Soybean polysaccharides can be a source of dietary fiber
in processed foods. After the aqueous extraction ofthe
protein from the defatted flakes of soybeans, the remainder
is a product rich in polysaccharides. This by-product has
been utilized in animal feeds, but the recent claims about
the relationship between a lack of fiber in the human diet
and a number of diseases, especially those of the bowel,
have called attention to soy polysaccharides as a fiber
source. These soy polysaccharides (SPS) are composed of‘
non-cellulosic internal cell wall structural components (As-
pinall et al., 1967). Therefore, SPS are not the hull or
the bran of soybeans. SPS are obtained from dehulled and
defatted soy flakes. The non-cellulosic fraction comprises
acidic polysaccharides: arabinogalactan and arabinan chains
account for 90% of SP8. The rest is composed of cellulosic
components. The chemical structure of SPS components will
be discussed in further detail in the following section.
Acidic polysaccharides.
The fraction of acidic polysaccharides in soybean coty—
ledons consists of a range of structurally related molecular
species. Aspinall et a1. (1967) formulated the partial
structure of inner and outer chains of soybean acidic poly-
saccharides. The interior chains are composed of chains of
4-0xygen substituted asD-galacturonic acid residues
interrupted at intervals by one or two contiguous 2-0xygen
substituted L-rhamnopyranose residues:
GalA-GalA—GalA-Rha-GalA-Rha-GalA-Rha-GalA-GalA-
Rha-Rha-GalA
The exterior portions are of a variety of types, but
most include sequences of neutral polysaccharides such as:
B-D-Galp 1—[->4 B-D-Galp 1---]n
arL- Fucp 1->2 D-Xylp 1...
B-D- Galp 1->2 D—Xylp 1...
L-Araf 1...
B-D-Xylp 1...
Consequently, acidic polysaccharides of soybean cotyle-
dons consist of highly branched polymers within backbones of
D-galacturonic acid interrupted with L-rhamnose. Galactose,
Xylose and Fucose are components of side chains associated
with acidic polysaccharides. Given the backbone of
D-galacturonic acid, the characteristic structure of pectin,
these polysaccharides could be considered as belonging to
the pectic group.
Arabinogalactans.
Arabinogalactans are the principal neutral polysacchar-
ide component of soybean cotyledons (Aspinall and Cottrell,
1971). These polysaccharides are arabinose-substituted
derivatives of the linear 1->4 linked B-D-galactans in the
ratio of 1:2.0-2.5. The structure of arabinogalactan has
B-D-galactopyranose residues in 1->4 linkage with every
fourth or fifth residue linked through C-3 to a side chain
containing two L—arabinofuranose residues joined by 1->5
linkage (Aspinall et al., 1967):
...4 B-D-Galp 144 B-Galp 144 B-Galp 144 B-Galp 1-14 B-Galp l...
3
T
l
(L-Araf)
S
i
l
(L-Araf)
Arabinans.
Recognition of arabinan is very difficult due to their
presence as acid-sensitive furanosides. Arabinan usually is
bound associated with galactans and pectin from which they
are difficult to separate. Structurally, arabinan consists
of chains of arL-Ara units which are substituted mainly at
0xygen-3- but also at 0xygen-2— (Stephen, 1983):
45)-a-L-Araf (195)-a-L-Araf (145)-o-L-Araf (145)-a-L-Araf
3 2 6 3
i T
a-L-Araf a-L-Araf
Cellulose.
Cellulose is built as a linear polymer of B-1,4 glucose
units. This type of linkage favors the formation of hydro-
gen bonds between the sugar units within the chain and among
adjacent chains:
44)-f3-D-Glup-(1[-) 4)-B-D-Glup-(1->],,4)-[3-D-Glup-(1 -)
Knowing the chemical structures of the compounds present
in the working material can lead to an understanding of the
possible changes which can occur in their structure during
processing. The complex chemical structure of SP8 and any
food material needs to be considered in investigating the
mathematical model. Possible changes in the material chemi-
cal structure could explain some of the unexpected results
during rheological measurements.
2.3 Modeling and Rheology
Yankelevsky (1988) defined a model as an approximation
of a physical problem with the aid of appropriate physical
and mathematical equations. Modeling techniques can be used
in food systems to describe the effects of processing vari-
ables. One of the advantages of generating process models
is the potential for improving the existing process at low
cost without performing numerous and costly experiments.
2.3.1 Rheology as a Modeling Tool
Rheological properties used in conjunction with mass,
momentum and energy balances are very useful in modeling a
particular processing operation and predicting actual pro-
cess parameters such as pressure drop (Dervisoglu and
Kokini, 1986: Boger and Tiu, 1974). Another practical
application of rheology is as a quality parameter for raw
and processed materials (Holdsworth, 1971).
In determining rheological properties it is necessary to
use equipment with defined flow patterns where shear stress
may be related to some easily measured force and shear rate
with speed (Sigmon, 1979). Van Wazer et al. (1963), Ferry
(1970), Charm (1971), Muller (1973), Rao (1977b) and Whorlow.
(1980) reviewed viscosity equations and different flow mea-
surement techniques. Each of these techniques has advan-
tages and disadvantages. The best method for measuring
rheological properties is the one which is closest to actual
operating conditions.
2.3.2 Tube and Capillary Viscometers
Tube and capillary Viscometers are suitable for the high
shear rates which are present in mixing, extrusion or pump-
ing (Clark, 1978 and Hawkins, 1971). These instruments do
not generate a constant shear stress across the flow path,
but this problem has been avoided by measuring the shear
stress at the wall.
Capillary viscometry has proved to be very useful in
polymer processing. It is used to understand polymer struc-
ture, to establish quality parameters and to study the
effect of additives as well as to determine the flow
properties of a given polymer. Zahler and Murfitt (1963)
10
described a high shear capillary rheometer in some detail
mentioning possible applications and source of errors. They
also developed a series of calculations to find polymer melt
flow properties. An Instron capillary rheometer supplem-
ented with very fine capillaries is illustrated by Johnson
and O’Shaughnessy (1977) for measuring the apparent
viscosities of different non-Newtonian polymer thickened
multigrade oils at temperatures from 100°F (37.8°C) to 320°F
(160°C) and shear rates up to 106 5’1.
The rheological properties of carbon mixes at very low
shear rates were determined with a capillary rheometer by
Bathia (1976), who showed that yield stress is a material
property of the carbon mixes that is independent of the cap-
illary die size. Bagley (1961) used capillary viscometry
with low and high density polyethylene resins to separate
the viscous and elastic effects. Knowing the individual
effects of each can lead to the explanation of certain phe-
nomenological observations and to the determination of poly-
mer structure.
One of the later approaches in capillary rheometry has
been its use to quantify the effects on flow behavior of the
breakdown of the fibrous structure of nitrocellulose in
double base propellants (Carter and Warren, 1987). The
dough of nitrocellulose and nitroglycerine in different
strength solvents behaved as a Herschel-Bulkley fluid show-
ing a decrease in shear stress as the breakdown of the fiber
increased.
11
2.3.3 Rheological Model
After obtaining the data in engineering units, many
theoretical and empirical models can be used to express the
relationship between shear rate and shear stress. Simu-
lation and analysis by mathematical methods are possible
when a successful model is established. Some of the most
common rheological models present in the literature are
shown in Table 1.
2.3.4 Dough Rheology
Mackey et a1. (1990), Morgan (1979) and Luxenburg et al.
(1985) suggested different models for flour or protein
doughs. One of the most widely used is the power law or the
Ostwald-de-Waele model (Table 1). Holdsworth (1971) pointed
out that K and n are not completely independent properties,
but from the engineering design point of view this model
appears to give adequate results. The power law model had
been applied to fruit juices as well as fruit puree and
dough materials (Holdsworth, 1971 and Rao, 1977a). This
model has been used widely as a constitutive equation for
describing food dough rheological behavior due to its sim-
plicity and higher correlations with observed behavior over
the shear rate range of 10 to 200 5‘1.
The viscosity of the dough is a function of various
parameters such as shear rate, temperature, moisture, compo-
sition, heating and shearing time. Several models can be
found in the literature which incorporate such parameters in
m
Table 1
Rheological Modelsl.
l. Newtonian:
0=w
2. Ostwald-de-Waele
or Power Law:
3. Bin ham Plastic: _.
g 0 - 0., + MY
4. Herschel-Bulkle : '
y o = 0y + Ky"
5. Ellis: 1 .
0 = n-1(v)
Cl'+t32(3
6. Power-Eyring: 1 1 .
o = c3(y) + —sinh --Y
C4 C5
7. Williamson: 66(80/0)
0w =
c, + (Bu/D) + â€e'(8U/D)
8. CBSSOD:
9. Ofoli:
1 Ofoli, R. Y., Mor an, R. G. and Steffe, J. F.
1987. A
generalized rheo ogical model for inelastic fluid foods.
Journal of Texture Studies. 18: 213- -230.
13
The viscosity of the dough is a function of various
parameters such as shear rate, temperature, moisture, compo-
sition, heating and shearing time. Several models can be
found in the literature which incorporate such parameters in
the viscosity model for given dough materials (Cervone and
Harper, 1978; Harper et al., 1971 and Remsen and Clark,
1978). The decrease of the apparent viscosity with tempera-
ture of any material is known and has been described by
Eyring's theory (Eyring and Stearn, 1939). This theory
predicts an exponential dependence of viscosity with the
absolute inverse temperature. The effect of the dough
moisture content can be predicted by the logarithmic mixing
rule (Bird et al., 1960). Bhattacharya and Hanna (1986)
proposed a viscosity model for soy protein concentrates and
corn gluten blends as a function of moisture content and
shear rate.
Harper et al. (1971), Harper et al. (1978), Harmann and
Harper (1974), Cervone and Harper (1978), Jao et al. (1978)
and Chen et al. (1978) have used a similar empirical model
which combines the power law model with the logarithmic mix-
ing rule and Eyring kinetic theory on food dough viscosity.
The multiple linear regression technique has been used
to fit an empirical model from the experimental data. This
type of model can be useful in the prediction of viscosity
changes during processing due to shear rate, temperature and
moisture in the extrusion process (Harper et al., 1971).
14
a poor correlation at low and high shear rates. Another
disadvantage of this type of model was that the logarithmic
mixing rule assumes the same effect for free, bound or
absorbed water of the dough materials. This could not
explain the nonparallel curves of data at different mois-
tures. Brodkey (1967) suggested that deviations at high
shear rate and temperature were intrinsic in the application
of the power law model. A multiple regression analysis was
used by Jao et a1. (1978) to develop an expression with ten
empirical constants which related entrance pressure loss as
well as apparent viscosity with shear rate, temperature and
moisture content for defatted soy dough.
Remsen and Clark (1978) and Morgan et a1. (1989) pro-
posed a viscosity model which includes a time-temperature
history term. The effect of different temperatures and
heating times can be condensed in this term, avoiding the
necessity to keep isothermal conditions during a process
such as in extrusion. If any reaction takes place, the
kinetics can be considered in the time-temperature history.
The semiempirical model of Remsen and Clark (1978) is a con-
tinuation of Roller's (1975) viscosity studies of epoxy
resin during the thermosetting reactions which yield a
viscosity equation as a function of shear rate, temperature
and time-temperature history. This model assumed that cook-
ing would increase the apparent viscosity. Remsen and
Clark’s (1978) model goes to infinity at large
time-temperature history which is not physically possible.
15
The viscosity model developed by Morgan (1979) combined
temperature, moisture, shear rate and time-temperature his-
tory. One important advantage of this model was that vis-
cosity approached a finite value for large values of shear
rate, temperature and time-temperature history. The Casson
(1959) model expressing shear stress-shear rate relation-
ships was preferred because the limiting value of the appar-
ent viscosity at high shear rate and the value of yield
stress at zero shear rate. However, Janssen (1985) showed
that the power law model gave a good fit for extruded dough
materials. This model, however, did not take into account
the moisture effect. A proposed model incorporating the
effects of shear rate, temperature, moisture content, time-
temperature history and stain history was developed by
Mackey et al. (1990). The latter model was created using
fundamentals of rheology, starch chemistry and polymer
kinetics, but future research is required to assess the com-
plex reaction of starch gelatinization. Dolan et al. (1989)
used a similar model for gelatinized corn starch dispersions
at various temperature-time treatments.
Most of the former models have been used for flour or
protein based dough where denaturation of protein or gela-
tinization of starch is important. This type of modeling
has not been used with fibrous materials such as SPS. Soy
polysaccharides are long chains of carbohydrates in which
the two reactions are not expected. Therefore, a basic
knowledge of this inert material and effects of shear rate,
16
temperature and moisture can be useful, not only for the
quality of the final product, but also as a modeling tool
for non-Newtonian materials in extrusion processing.
MODEL DEVELOPMENT
In this section, the basic equations for the capillary
viscometer will be presented. Also included is the equation
which incorporates moisture and temperature effects in a
generalized viscosity model.
3.1 Basic Equations
The relationship between flow rate and pressure drop for
capillary flow were developed by Poiseuille (Van Wazer et
al., 1966). The Hagen-Poiseuille law was developed by Wied-
ermand and Hagenbach, who applied Newton’s law of viscosity
to Poiseuille’s experiments (White, 1986).
Consider a steady downward flow of fluid in a vertical
cylindrical tube of constant radius R similar to the one
shown in Figure 1 (Van Wazer et al., 1966). Poiseuille
stated that the applied pressure is equilibrated by the vis-
cous loss under ideal conditions inside the tube or capil-
lary viscometer. An ideal tube viscometer has to satisfy
the following assumptions (Whorlow, 1980 and Van Wazer et
al., 1966):
a) the flow is steady, laminar and parallel to the
axis.
b) the velocity of any fluid element is a function of
radius r, given axial symmetry.
17
18
‘—
n
'1
" 7N
W)
W
Force
Applied
anZ Direction
of
Flow
-——>
Q——>
. Q
l
Shear
Force
0 (21cRL)
L___-________________.
l
l
l
l
_+____________________
\
\
‘\
1.-
\
l
i
I
/
/.
R
P——2R——->l
Figure 1 Force balance on a capillary
c3)
d)
e)
f)
9)
h)
i)
19
the fluid properties are independent of time.
the fluid velocity is zero at the wall.
the fluid is incompressible.
the normal stress is isotropic.
the fluid viscosity is not influenced by pressure.
the measurement is conducted under isothermal con-
ditions.
a unique function y=f(o) relates the rate of shear
to the shear stress.
In those conditions, if a cylinder of fluid with radius
r measured from the center and length L is used, the rela-
tionship between the shear stress and the respective pres-
sure to force the fluid through the capillary tube is
obtained by balancing the forces on the cross section of the
tube. The force required to move the fluid downstream is
Pnr2 where P is the pressure differential in the tube. The
shear force, or o,(2nr£), is the force retarding this move-
ment on the wall of the cylinder:
Therefore,
dr(2an)=Prtr2 (1)
_Pr
0’ _—
r 2L
(2)
which gives the shear stress at any r where r 5 R.
The shear stress at the wall is
20
PR
= —— 3
Combining the previous two equations gives
F
Or — 0'w E (4)
The latter expression indicates that shear stress has a lin-
ear distribution from zero at the center of the tube to a
maximum value 0,, at the wall (r=R).
The shear rate changes with the radius, but the mode of
variation depends on the velocity distribution, which is
determined by the nature of the fluid. Since both shear
stress and shear rate vary with the radius, the flow curves
have to be constructed using the same reference point in the
capillary tube. For convention this point is the capillary
or tube wall (Clark, 1978).
The expression for shear rate is
-212
dr
Rabinowitsch (1929) and Mooney (1931) derived the
Y = (5)
expression for a true shear rate at the wall for non-
Newtonian fluids. The derivation can be found in detail in
Skelland (1967), and is based on ideal capillary flow. The
Rabinowitsch-Mooney equation (Skelland, 1967) begins with an
expression for volumetric flow rate:
21
Q = j: 2nrv(r)dr (6)
where v(r) is the fluid velocity as a function of r.
Therefore, the shear rate at the wall may be written as
Q
3Q ‘15.?
3+Ow
HR dow
1.. = f(%) = (7)
where the derivative is evaluated at each particular value
of ow.
This equation is commonly referred to as the
Rabinowitsch-Mooney equation, and expresses the shear rate
at the wall in terms of flow rate, shear stress and tube
geometry.
3.2 Possible Sources of Error
Any condition which violates any of the assumptions men-
tioned in Section 3.1 would be a possible source of error in
determining rheological properties with a capillary
rheometer. Some common sources of error are described
below.
3.2.1 Barrel Correction
Some researchers (McLuckie and Rogers, 1969b: Einhorn
and Turetzky, 1964) showed that a possible source of error
may be the amount of material present in the barrel or res-
ervoir located before the capillary. This source of error
increases the total force due to the height of material
22
acting as a hydrostatic head. The additional pressure can
be neglected if the height of the barrel is not significant
and the capillary L/D is greater than or equal to 100.
‘McLuckie and Rogers (1969b) found less than i 1 % change in
the pressure along the barrel at different initial material
height. Metzger and Knox (1965) illustrated some of the
problems created if the barrel corrections for the amount of
material present in the barrel are neglected.
3.2.2 Plunger Friction
An additional pressure may be generated if the plunger
does not move freely in the barrel. The pressure is caused
by friction between the plunger surface and reservoir wall.
This frictional force cannot be taken into account as the
effective force throughout the capillary. Whorlow (1980)
suggested placing a pressure transducer near the capillary
entrance to avoid this problem. Van Wazer et al. (1966)
recommended the use of a thin plate with a hole of the same
diameter as the capillary, to correct for friction and end
effects.
3.2.3 Stored Elastic Energy
When a viscoelastic fluid is sheared, it acquires elas-
tic potential energy at the entrance to the capillary. This
energy is lost in transit through the capillary, reducing
the effective driving pressure. Thus, the rheological prop-
erties could be overestimated or underestimated. Philippoff
and Gaskins (1958) developed an equation which measures the
23
elastic energy per unit volume by the product of the shear-
ing stress and recoverable shear. They stated the need for
using another type of viscometer in combination with the
capillary viscometer to distinguish between end correction
and recoverable shear stress.
McLuckie and Rogers (1969b) suggested that this loss of
energy can affect the linearity in the plot of pressure ver-
sus capillary length to diameter ratio. Their experiments
showed the presence of relaxation during transit of the
material through the capillary. This effect is very impor-
tant when viscoelastic materials are being studied.
3.2.4 Viscous Heating
One of the advantages of capillary Viscometers is their
capability to achieve high shear stresses. When a fluid is
subjected to high shear stress, internal friction causes an
increase in temperature. The shear stress at a given shear
rate may then be overestimated because of decreases in vis-
cosity due to temperature effects (Van Wazer et al., 1966).
This effect is significant in high viscosity fluids at high
shear rates.
3.2.5 Kinetic Energy Correction
The capillary extrudate emerges with some kinetic energy
which originated from the work done by the driving pressure
in a tube viscometer. This kinetic energy in the issuing
stream causes a loss of effective pressure in the capillary
2’.
flow (Van Wazer et al., 1966). The equation for calculating
the kinetic energy, KE} generated per second for a fluid of
density p is (Whorlow, 1980)
2
K15 = deU (8)
where: Q = volumetric flow rate, m3 5'1.
density, kg m‘â€3
D
II
Li= mean velocity of the fluid, m s"1
0,: kinetic energy correction factor which depends
on the velocity profile, dimensionless
The effective pressure or the real pressure through the
capillary (P) to use in determining rheological properties
is (Whorlow, 1980)
_, 2
P — P,-ozpv (9)
where: in = total measured pressure, Pa
P = pressure in equilibrium inside the capillary, Pa
If the pressure is not corrected for kinetic energy
losses, the rheological parameters present higher values.
The a factor is a function of the material properties for
which some correlations and equations are presented in the
literature (Osorio and Steffe, 1984: McCabe et al., 1985 and
Van Wazer et al., 1966). McLuckie and Rogers (1969b) found
less than 0.1% pressure loss due to kinetic energy even at
the highest crosshead speed. Therefore, this effect can be
neglected if pv2 is small compared to the total pressure
25
drop.
3.2.6 End Effect
Couette was the first to recognize that Poiseuille flow
needs to be corrected for entrance effects (Van Wazer et
al., 1966). This is due to fluid flow from a wide tube
(barrel) to a narrow cylinder (capillary) and the sudden
changes in velocity profile associated with it (Van Wazer et
al., 1966 and Whorlow, 1980). Therefore, there is a section
before the capillary entrance and after entering the capil-
lary where the velocity profile is not fully developed.
This section, which is required to obtain a fully developed
flow pattern, is called the entrance length. The pressure
drop per unit of length in this section is greater than when
the velocity profile is completely developed. The pressure
drop term in the shear stress equation is for fully devel-
oped flow. Therefore, the pressure has to be measured after
the flow is completely developed, or the appropriate
correction must be made.
To study end effects, some research has been done using
visual observations of polymers with markers flowing through
a transparent tube viscometer (Singleterry and Stone, 1951;
Tordella, 1957 and Bagley and Birks, 1960). These studies
showed that the different patterns of flow in the entrance
region depend on the material properties. Bagley (1957)
~ rhod to determine the entrance pressure drop
using capillaries Wlth the ;ame :g; ' *’ 4"‘°rent
26
lengths. The correction term is determined by extrapolating
to zero pressure on a linear plot of pressure versus length-
to-diameter ratio (g) at each shear rate. In this tech-
nique, the entrance effect is assumed to be a function of
the capillary dimensions, shear rate and the fluid. Data
from different capillaries are compared in one master curve.
3.2.7 Slip
One of the basic assumptions in the analysis of capil-
lary and tube viscometers is the absence of slip at the
wall. In the derivation of the Rabinowitsch-Mooney equation
(Skelland, 1967), the fluid is assumed to adhere to the tube
wall. Therefore, its velocity at the wall is zero. In some
cases the fluid may slip at the capillary wall presenting a
finite slip velocity at the boundary or its immediate vicin-
ity (Nubar, 1971). In other conditions a lubricating layer
of low viscosity fluid is built near the wall due to the
alignment of molecules resulting in sliding of the adjacent
layers.
Mooney (1931) and Oldroyd (1956) developed a method to
determine shear rate and shear stress in the presence of
wall slip. This procedure requires the use of capillaries
with different diameters and the same length (Darby, 1976).
The presence of wall slip has been associated with sev-
eral extrudate surface distortions such as melt fracture
(Ramamurthy, 1986). The extrudate distortion results from
the failure of adhesion of the fluid to the die wall.
27
Kalika and Denn (1987) experimented with low density
polyethylene and showed four flow transition regions as the
throughput is increased. Each transition region can be
related to different extrudate surface appearances: stable,
sharkskin, slip-stick and wavy. These surface distortions
are associated with changes in the slope of the pressure and
flow rate curves. Therefore, these data cannot be used to
determine rheological properties.
3.3 Model Development
An overall viscosity model was developed as a function
of shear rate, temperature and moisture as explained in this
section.
3.3.1 Rheological Model
The Ostwald-de-Waele (or power law) model was chosen to
predict the steady shear rate effects. The power law model
has been successfully used to model dough and polymeric melt
viscosities (Cervone and Harper, 1978: Crater and Cuculo,
1984; Culioli and Sale, 1981; Harmann and Harper, 1974:
Holdsworth, 1971; Janssen, 1985: Jao et al., 1978; Remsen
and Clark, 1978; Senouci and Smith, 1988 and Vergner and
Villemaire, 1987). Although this model has some limita-
tions, the fact that it contains only two parameters makes
it easier to manipulate:
0=Kyn (10)
28
where: o = shear stress, Pa
K = consistency coefficient, Pa sn
n flow behavior index, dimensionless
y = shear rate, s'1
The apparent viscosity is given by
6Ԡ(11)
n. = -
Yw
Therefore, for a power law fluid:
n. = W“) (12)
3.3.2 Temperature Effects
The viscosity of a fluid generally decreases when it is
heated at constant pressure. This reduction of viscosity is
a consequence of the combination of two basic factors: the
.thermal energy of the molecules and the intermolecular dis-
tance between the molecules (Holdsworth, 1971). Glasstone,
et al. (1941) stated that the temperature effect on
viscosity for a Newtonian fluid can be represented by an
Arrhenius expression:
AE‘
= ——— 13
u H... eXp RT ( )
where: :15 = free energy of activation, cal/ g-mol
R
molar gas constant, 1.987 cal/ g-mol K
T absolute temperature, K
A5 is the energy required for a molecule to move from
one equilibrium position to the next molecular site (Remsen
and Clark, 1978).
Carter and Warren (1987), Metzner (1959), Remsen and
Clark (1978) and Senouci and Smith (1988) applied a similar
expression to the power law model:
0 AE
= K "'1 —
(14)
3.3.3 Moisture Effects
Moisture content was the other variable considered in
the development of this model. Bhattacharya and Hanna
(1986), Harper et al. (1971), Morgan et al. (1978 and 1989)
and Senouci and Smith (1988) suggested an exponential rela-
tionship between viscosity and moisture content for dough
n = no exp(bMC) (15)
where: b = coefficient of the moisture effect, dimension-
less
AdC = moisture content, % mass of water/total mass
no = viscosity at reference moisture content, Pa 5
Harper (1981) argued that this type of equation does not
take into account the interaction between moisture and other
molecules and, therefore, is not suitable for extrapolation
to 100% moisture. However, the exponential relationship is
satisfactory over a small range of moisture contents.
30
3.3.4 Overall model
The viscosity data for soy polysaccharides (SPS) was
fitted to an overall model to account for shear rate, tem-
perature and moisture content:
- K '"“ , 95 —1-—-1- ex [b(\/IC-MC
n. .v exp R 7} .T p I .)]
(16)
To obtain the necessary four parameters K. IL .AE'and b,
a multiple linear regression technique was used. iMC; and
7} were the moisture content and temperature used as refer-
ence (70% MC and 2513. Cervone and Harper (1978), Chen et
al. (1978), Harper et al. (1971), and Senouci and Smith
(1988) applied this type of model to dough material and
obtained a good fit for the experimental data.
MATERIALS AND METHODS
This section will introduce and describe the materials
and equipment used for the experiments. As well as a sum—
mary of the experiments performed and the range of variables
investigated.
4.1 Materials and Equipment
4.1.1 Raw material Specifications
In the present work soy polysaccharide (SPS) was chosen
as "standard material" for non-Newtonian fluids since pro-
tein denaturation and starch gelatinization reactions are
minimal. It was donated on two occasions by the Protein
Technology Division of Ralston Purina Company (St. Louis,
MO). Analysis of each batch was obtained from Ralston
Purina and are presented in Table 2.
Fibrim Soy Fiber, the tradename of SP5, is a product of
Ralston Purina's Protein Division which has been shown to be
a viable marketing speciality fiber. Fibrim is a bland,
odorless source of dietary fiber which can be added to dif-
ferent food systems. The material is available in three
types (Fibrim 1000, 1450 and 2000) based on particle size,
and are made to fit specific applications. Fibrim 2000 was
used in the present study. The SPS was mixed with water
31
32
Table 2
Proximate Analysis of Boy Polysaccharides
(Ralston Purina Company, St. Louis, MO)
Batch 1 Batch 2 “
Properties 2/12/87 3/04/87
Moisture, wet basis (%) 5.2 NA
Protein, dry basis (%) N x 14.5 NA
6.25
pH 7.0 7.1
Particle size (%) NA NA
+ 100 mesh NA 0.5
+ 325 mesh 27.0 18.5
Ash (%) 4.0 NA
Density (g/cc) 0.28 NA
Water absorption (%) 705 NA
33
to prepare dough with different moisture contents.
4.1.2 Mixing Conditions in the Extruder
A Baker Perkins 50mm twin screw extruder (TSE) (APV
Baker Inc., Grand Rapids, MI.) was used as the mixer. The
TSE was chosen because of the need to obtain a uniform prod-
uct. The screw configuration used in the TSE is shown in
Table 3.
A die with a 0.63 cm (1/4") diameter hole and a half
flange was used. Appendix A shows the schematic diagram of
the die. The screw speed was 250 rpm and the flow rate was
approximately 45.45 kg/hr (100 lb/hr). Different moisture
contents of the dough were obtained by changing the powder
feed and water pump rates.
4.1.3 Moisture Analysis
Moisture contents were determined for each bag of Fibrim
(SPS) fed to the extruder and for each extrudate. Also, the
moisture content of each stored bag was measured in the
beginning and end before each experimental condition to
detect any change in the moisture content. Moisture con-
tents were determined by oven drying the material at 100%:
for 24 hours (ASAE standard 8358, Appendix B) and expressed
on a wet basis. The samples were placed in small aluminum
weighing dishes and dried with a Central Scientific Co. oven
(Cat. #95100A). Triplicate samples were taken for analysis.
34
Table 3
Screw configuration used on Baker Perkins 50mm Twin Screw
Extruder: L/D = 5.
Feed inlet
Extruder die
76.2 cm (30.0") spaces
38.1 cm (15.0") feed screw
6.35 cm (2.5") forwarding paddles
45° offset
5.08 cm (2.0") feed screw
0.63 cm (0.25")
35
4.1.4 Storage conditions
Extrudates were taken from the extruder, stored in
Ziploc bags, and allowed to equilibrate at 7°C overnight.
One hour before running the capillary rheometer, the samples
were taken from the refrigerator to let them equilibrate to
room temperature. One bag of dough material was used for
each temperature and die in the capillary rheometer to pro-
vide uniformity of analysis. Samples were used within three
days after preparation to avoid product degradation.
4.1.5 Capillary Rheometer Description
An Instron Capillary Rheometer model 3210 (Instron Corp.
Canton, MA) consists of an extrusion assembly equipped with
a plunger and a temperature control system. The plunger can
be driven at preselected speeds by the moving crosshead of
the Instron 1120 Series Universal Testing machine. The
range of operation are as follows:
Shear rate range 10 - 106 s'1
Shear stress range 500 -106 Pa
Temperature control 10° C above ambient to 340°C
The unit is placed on a special fitting underneath the
crosshead of an Instron Universal Testing Machine model
4202. The sample is loaded into the barrel, allowed to
equilibrate to a the target temperature and forced out with
a plunger through a capillary die located at the end of the
barrel. The equilibration time was 3 minutes after loading.
36
The crosshead of the testing machine holds a compres-
sion, 10 kN load cell. This cell measures the required load
on the plunger to force the fluid through the capillary die.
The force is recorded on an XY chart recorder and is con-
verted to pressure when it is divided by the plunger area.
Different crosshead speeds (plunger speeds) give a variation
in volumetric flow rate at the capillary die. Shear rate
and shear stress are obtained by mathematical calculations
involving the geometry of the capillary rheometer, plunger
speeds and force data.
4.2 Run Conditions for Capillary Rheometer
There are two possible sources of error in using a cap-
illary rheometer, and both relate to the equipment assembly
itself. One of the sources of error is the misalignment of
the plunger and barrel. To correct or eliminate this prob-
lem the alignment rod was inserted every time the assembly
was put together. Drag or friction between the plunger and
the barrel walls is the second possible source of error and
needs to be minimized. To account for this, high speeds
were run when the barrel was full and additional measure-
ments were made with the reservoir empty to determine the
drag force. This force was eliminated from the total force
obtained from the XY recorder.
The capillary rheometer was loaded as rapidly as possi-
ble by feeding extruded SPS dough into the rheometer reser-
voir and tamping it with a rod until the barrel was full.
37
This method may be a possible source of error since the
material density may change during the process. The mate-
rial was compressed with the plunger until the extrudate
exited through the capillary (Figure 2). At this point the
plunger was immediately stopped and the parameters such as
plunger speed and time were set. The experimental run was
started and the plunger force was recorded by the XY chart
recorder.
4.3 Experimental Design
The variables of concern in the flow experiments were
shear rate, moisture (SO-70%) and temperature (ZS-90%â€.
Experiments were designed using at least three levels of
each variable. Data collection was divided into two series,
the temperature and moisture effects were grouped together
and analyzed by multiple linear regression. A summary of
the experiments is presented in Table 4.
4.3.1 Rheological Parameters
The flow experiments (Series A, Table 4) were designed
to obtain power law parameters for the different doughs
using the capillary rheometer at room temperature (25%â€.
To accomplish this the samples were extrudated at four dif-
ferent plunger speeds (50, 100, 300 and 500 mm/min) using
four dies (L/D = 2, 4, 8 and 16).
PLUNGER ROD
CONED TEFLON
PLUG
-———4ME CAP
W/é ///////// 7//////
m//////%ssm
.....
IIIIIIIII
V/////////////////. ..
EXTRUDER
BARREL—
DOUGH
[NE
EXTRUDATE
of capillary extrusion
2 Illustration
process
Figure
39
Table 4
Summary of Experiments.
Series A.
Moisture, % w.b. : 50, 60, 70
Temperature, °C: 25
Plunger speed, mm/min: 50, 100, 300, 500
m/s x 104: 8.3, 16.7, 50.0, 83.3
Volumetric flow, m3/s x 10'8: 5.94, 11.98, 35.63, 59,38
Capillary length, mm (in): 6.35 (1/4), 25.4 (1)
Capillary diameter, mm (in): 1.59 (1/16), 3.17 (1/8)
Capillary, L/D: 2, 8, 4, 16
Series B.
Moisture, % w.b.: 50, 56, 60, 64, 65, 70
Temperature, °C: 25, 50, 75, 90
Plunger speed, mm/min: 50, 100, 300
m/s x 104: 8.33, 16.7, 50.0
Volumetric flow, m3/s x 10‘3: 5.94, 11.88, 35.63
Capillary length, mm (in): 6.35 (1/4), 25.4 (1)
Capillary diameter, mm (in): 3.17 (1/8)
Capillary, L/D: 2, 8
40
4.3.2 Moisture Effects
Each moisture content was considered as a different
material and the samples were run independently at four dif-
ferent plunger speeds, using four dies as explained above.
4.3.3 Temperature Effects
For the runs at temperatures higher than room tempera-
ture (Series B, Table 4) a preheated period of 30 to 60
minutes before testing was required to reach a constant
temperature in the barrel. After reaching a constant tem-
perature, the barrel was filled and the material compressed
to avoid air pockets. Two or three minutes of heating time
was needed to bring the material center temperature to
within 1°C of the wall temperature (Morgan, 1979 and How-
kins, 1987). At this time, the sample was extruded at a
given plunger speed and the force recorded.
4.4 Data Analysis
The total force required for the extrusion of SPS dough
was determined using the technique of Einhorn and Turetzky
(1964) for each volumetric flow rate.
The shear stress and the apparent shear rate at the wall
were obtained with the following equations:
_ PCR _ P, 17
Ow " 2L ' 4L/D ( )
fl
H
4Q (18)
a nR3
41
where F3 is the pressure drop corrected for the end effect
using Bagley's (1957) technique. The slip correction was
done with the procedure suggested by Darby (1976) using cap-
illaries with the same length and different radii.
The Rabinowitsch-Mooney correction (Skelland, 1967) for
non-Newtonian fluids was applied to obtain the true shear
rate at the wall:
Q
30 d5?
3+Ow
HR dew
v... = (7)
where the derivative is evaluated at each particular value
of ow.
The parameters for the power law model, Kfand n, were
established using the true shear rate and shear stress val-
ues and nonlinear least squares regression analysis using
the Marquardt method. In the Series B of experiments the
remaining parameters for the overall model
— K '"“ AE —1—-—1- b MC-MC
n. .v eXp R T. T expl ( 0)]
(16)
were obtained by multiple linear regression after the appar-
ent viscosities were found at each temperature and moisture
content. The model was adjusted by a stepwise technique
adding one variable at a time. The complete outline for
-ca1culations is presented in Appendix C.
RESULTS AND DISCUSSION
The flow behavior of soy polysaccharides at 25°C and
different moisture contents was determined using the Instron
capillary viscometer. In this series of experiments, four
dies and four plunger speeds were used to obtain the rheo-
logical model of SPS doughs. A second series of experiments
was made at three temperatures and different moisture
contents to obtain an overall model with moisture and tem-
perature effects.
5.1 Moisture Content Analysis and Density
The samples obtained from the extruder were analyzed for
moisture content of the final product. This analysis showed
a very close value to the target for the product coming out
of the extruder. Moisture content was determined from the
product fed into the capillary viscometer after the equilib-
rium time. The latter data showed, in general, 3% moisture
loss. Table 5 shows the mean moisture analysis data from
both sets of analyses.
The different moisture contents gave extrudates with
different appearances. The product surface varied from
shark-skin type to a glossy rope material (70%-50%). These
changes in the extruded products showed an instability in
42
Moisture Content (% wet basis) of Soy Polysaccharides doughs
43
Table 5
Nominal Extruder Viscometer “
(% w.b.) (% w.b.) (% w.b.) i
70.0 70.9 67.6
60.0 61.3 58.1
50.0 51.4 46.1
65.0 65.0 64.9
64.0 64.0 64.1
(% w.b.) = percent of moisture in wet basis
44
the flow during mixing in the extruder. As the moisture
level decreased to 50%, a concentric coil formation was
observed.
The densities of these doughs were determined by two
empirical methods. One approach was by weighing a die of
known volume full of the material. The second method was an
approximate value based on the chemical composition of the
dough (Lewis, 1986). The latter method and calculations are
presented in Appendix D. Both approaches gave similar val-
ues (Table 6).
These densities were used to calculate Reynolds numbers
for checking laminar flow criteria.
5.2 Force
The force required to make the material flow was deter-
mined at the entrance of the die as Einhorn and Turetzky
(1964) suggested to avoid the barrel height correction. A
typical graph is presented in Figure 3. The drag force
obtained by running the plunger with an empty barrel was
subtracted from the total force to obtain the force required
for the material to flow. Table 7 is a presentation of the
values for the drag force which increased as the volumetric
flow increased. As the moisture content decreased, this
force decreased. The sample with the highest moisture con-
tent adhered more to the wall. As a result, the frictional
forces between the plunger and barrel were greater.
45
Table 6
Density of the Dough (kg/m3) Determined Using Different
Methods
Moisture content Die Chemical Assumed
(% w.b.) weight composition density
70.0 1109 1098 1100
60.0 1152 1135 1150
50.0 1198 1170 1200
46
Force
I
W
l
i I
I i
I
H—A'pl’i
~4 X,.u,_
---1
—---_-—-
I
X30â€)
Time
X, a distance run a it.
Figure 3 Typical graph from the XY recorder
47
Table 7
Drag Force at Different Moisture Contents (N)
Moisture L/D Speed
(% w.b.) (mm/min)
50 100 300 500
50 2 29 42 67 84
4 27 45 80 91
8 37 46 80 90
16 30 40 87 80
60 2 41 40 58 71
4 36 43 62 60
8 37 40 60 72
16 40 50 55 64
70 2 83 82 89 110
4 74 76 91 104
8 50 58 65 78
16 68 70 89 78
48
5.3 End Correction
The entrance corrections were determined by Bagley’s
technique (1961) for each capillary diameter (1.59 and 3.17
mm [1/8 and 1/16 inches]) and plunger speed using two
lengths (6.53 and 25.4 mm [1/4 and 1 inches]). The results
are presented in Tables 8 and 9. The least square method
was used to calculate the regression line to fit the data
for each speed or volumetric flow rate and both lengths to
obtain the end correction. The data of the smaller diameter
die gave the best coefficient of determination (r2) showing
a linear relationship between force and L/D.
In general, the value of entrance pressure drop
increased with increased shear rate. These results were
similar to the ones obtained by Jasberg et al. (1981) and
Onogi et a1. (1973) using polyethylene. Soy dough at 160%:
and low shear rate showed the same behavior in entrance
pressure drop as was observed by Jao et al. (1978). As the
moisture content increased, the end corrections decreased.
Therefore, the water acted as a lubricant providing less
resistance to flow. The magnitude of the end corrections
decreased as the temperature increased, too. The linearity
at the higher temperature was very poor as indicated by the
value of coefficient of determination.
The large diameter die and the high moisture content
sample data presented negative values with the same trend.
These negative values of the entrance pressure drop were a
49
Table 8
End Correction Force (N) at 25°C
MC D Speed
% mm mm/min
w.b.
50 100 300 500
70 3.17 -6.8 0.52 -14.0 0.72 -26.4 0.80 -4.8 0.20
1.59 -33.0 0.72 -42.3 0.92 -10.2 0.85 -64.0 0.92
60 3.17 -38.0 0.87 -11.3 0.87 105.1 0.49 45.3 0.81
1.59 89.5 0.77 93.4 0.84 272.9 0.93 139.5 0.98
50 3.17 -33.7 0.91 -81.7 0.79 56.9 0.81 180.3 0.52
1.59 410.0 0.93 438.4 0.93 190.2 0.94 -36.4 0.97
Fx=o = Force when L/D = 0
r2 = coefficient of determination for regression line of
F versus L/D
50
Table 9
End Correction Force (N) at Different Temperatures using
3.17 mm Diameter Die
Moisture Temp Speed
L % w.b. °C mm/min
50 100 300
EX: r2 Fx=o r2 Fx=o r2
50 25 -64.3 0.93 69.6 0.90 340.3 0.29
50 -16.2 0.73 55.8 0.67 223.2 0.75
75 31.1 0.32 48.9 0.63 160.9 0.88
90 -22.7 0.77 -26.2 0.97 73.7 0.64
56 25 -26.4 0.85 -21.3 0.91 149.6 0.86
50 -36.0 0.72 -14.7 0.68 51.3 0.90
75 -10.0 0.59 8.2 0.60 78.2 0.77
90 -3.6 0.59 2.7 0.83 62.7 0.81
60 25 -29.6 0.91 -25.3 0.94 93.3 0.91
50 -18.7 0.85 -9.3 0.97 57.8 0.96
75 -11.1 0.84 -2.7 0.85 49.6 0.96
90 4.9 0.91 -11.2 0.92 25.3 0.93
64 25 -10.9 0.68 -0.8 0.73 105.3 0.66
50 -9.8 0.52 -12.0 0.75 66.7 0.64
75 -3.6 0.51 -16.7 0.97 -23.3 0.92
90 -6.3 0.77 -18.3 0.99 -23.8 0.93
65 25 -12.4 0.86 -10.4 0.88 50.2 0.90
50 11.2 0.95 27.0 0.97 63.9 0.98
75 9.2 0.61 13.1 0.76 46.6 0.85
90 -3.1 0.45 -0.6 0.63 31.6 0.7
70 25 -9.4 0.75 -15.9 0.87 7.8 0.91
50 N.An N.A. 4.7 0.57 22.7 0.64
75 N.A. N.A. N.A. N.A. 45.6 0.10
90 N.A. N.A. N.A. N.A. -4.0 0.14
51
consequence of the large pressure drops with the short die.
White (1973) found similar negative results which cannot be
explained physically. Jasberg et al. (1981) attributed this
behavior to the short transit time in the die which did not
allow equilibrium or compressibility of the material. Onogi
et al. (1973) also found that for one type of polyethylene,
the end correction only appeared at the higher shear rates.
Therefore, in the calculations of the current work where
negative values were obtained, zero values were assumed.
5.4 Slip correction
The other possible source of error in the capillary vis-
cometer is the presence of slip at the wall. Darby’s tech-
nique (1976) was used to approach this type of problem. The
correction term to be subtracted from the volumetric flow
rate was greater than the average volumetric flow rate of
the material through the die. These results suggested the
presence of another type of phenomenon, such as sliding.
The difference between sliding and slippage is the presence
of a low viscosity layer next to the wall. The mathematical
approach to this problem requires determination of the fric-
tion coefficient and thickness of the low viscosity layer.
This analysis is beyond the scope of the present study.
5.5 Rheological Parameters
Shear stresses were obtained with the correct pressure
drop using Eq. 3. To calculate the true shear rate at the
52
wall the Rabinowitsch-Mooney correction (Eq. 7) was applied.
Apparent viscosities were calculated from the shear stress
and shear rate values using Eq. 11.
Data on different doughs in the literature suggested the
power law and the Herschel-Bulkley models as possible models
for the experimental data. Pseudoplastic behavior was pres-
ent when the viscosity values were plotted versus shear rate
at the wall (Figure 4). The decrease in viscosity as the
shear rate increased suggested a greater breakdown in the
structure of the 50% moisture content dough compared with
the one at 70% dough. The presence of concentric coiled
structure could be observed visually in the 50% dough.
The parameters for these rheological models were
obtained by nonlinear least square using the Marquardt
method. This method was applied to all data and to the mean
of each volumetric flow rate. The power law model fitted
better to the mean of the data for the entire moisture con-
tent range.
Presented in Figures 5 to 10 are the shear stress and
shear rate data and means for 50, 60 and 70% moisture con—
tents. The greater standard deviation of the data for each
volumetric flow rate suggested a possible problem in the
capillary viscometer technique for this type of material.
The extrudate was loaded into the barrel and packed
using a brass rod, hence a possible source of error in the
53
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during mixing could give the material different characteris-
tics.
The regression lines for the data means and standard
deviations for the three moisture contents are presented in
Figures 11-13. A short length die was used by Morgan
(1979). However, greater deviations were observed by the
shorter dies in the present study. This problem could be a
result of the short transit time, since the material never
reached fully developed flow in the capillary. To ensure
fully developed laminar flow, Darby (1976) calculated the
minimum inlet length of die required to obtain fully devel-
oped flow as a function of the Reynolds number.
For the power law fluids the following estimation can be
made:
L s 0.06 NH9 (19)
e
where the generalized Reynolds number (NGRe) for a power law
fluid is defined as
pUZ-nDn
NGRe 8n-1K(3:;l)n (20)
The Reynolds number and the inlet length for each mois-
ture content, die diameter and plunger velocity are pres-
ented in Appendix E. The Reynolds numbers were small and
decreased as moisture content decreased.
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The parameters for the power law model are summarized in
Table 10. Values of K increased when moisture content
decreased. The flow behavior index decreased with decrease
in moisture content, indicating a greater pseudoplasticity
for the sample at 50% moisture. Holdsworth (1971) stated
that a decrease in the value of flow behavior index is
expected as solid content increases. The regression lines
for the three moisture contents are plotted in Figure 14.
To evaluate the fit of the models, the residuals were
plotted against the shear rate and the predicted shear
stresses. Both residual graphs showed a normal distribu-
tion.
5.6 Overall Model
For the overall model shear stress and shear rate at 50,
56, 60, 64, 65, and 70% moisture contents and 25, 50, 75 and
90°C were obtained. The constants for the proposed viscos-
ity model were obtained by multiple linear regression using
the stepwise method. The raw data and ANOVA tables for
multiple linear regression are presented in Appendices G.
A correlation matrix of the independent variables was
used to select the order to add these variables to the model
equation based on their significance. In the present study,
the moisture content had the highest correlation with vis-
cosity and temperature had the lowest. All three variables
were highly significant at a = 0.05.
65
Table 10
Power Law Parameters for Boy Polysaccharide Doughs
Moisture Content K n r2
(% w.b.) Pa sn
70.0 6700 0.26 0.97
60.0 25365 0.29 0.98
50.0 168320 0.16 0.97
66
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The overall viscosity equation obtained by the present
study is:
- , :937 __1___1. _
na — 67OOY exp — exp[ 13.82(MC-MCO)]
(21)
where:lz== flow behavior index, 0.26 dimensionless
n = viscosity, Pa 5
y = shear rate, 5"1
R = universal gas constant, 1.987 cal/g-mol K
T = absolute temperature, K
T} = absolute reference temperature, 298K
AdC = moisture content, % wet basis
A4C0== reference moisture content, 70% w.b.
The values obtained for the flow index (0.26) and the
activation energy (937 cal /g-mol) for soy polysaccharide
doughs were similar to those obtained for potaton powder
with a capillary by Senouci and Smith (1988). Estimated
values of viscosity were plotted against the experimental
values to visually inspect the fit of the model (Figure 15).
In general, this graph showed a reasonable correlation
between both sets of data. Some deviations were present in
the dough at 70% moisture, and also at combinations of low
shear rates and high temperatures at the other moisture
contents.
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CONCLUSIONS
Although there was great variation in experimental data,
the following conclusions can be drawn from the present
study:
1.)The sharkskin appearance of the product after
mixing is a consequence of the flow instability pres-
ent in the extruder. This results in material with
different characteristics.
2.)In the cases where the end corrections for soy
polysaccharides could be calculated, a decrease was
observed as the moisture content increased. This
behavior was very similar to those observed on poly-
meric materials such as polyethylene.
3.)Three levels of moisture (50, 60, and 70%) of soy
polysaccharide doughs demonstrated a pseudoplastic
behavior. The degree of pseudoplasticity decreased as
moisture level increased.
4.)The negative values obtained for the end correction
and slip suggested that an alternative mechanism, such
as sliding friction may be required to explain rheo-
logical behavior.
69
70
5.)The great variability of data obtained in the
capillary rheometer imposed large uncertainties on the
values of viscosity and shear rates calculated.
Therefore, this type of rheological technique is not
appropriate for SP8 dough material. The method of
loading the barrel and compacting the material may be
the principal cause of this problem. It was not pos-
sible to ensure the same degree of compression in
filling the barrel.
1.)
2.)
3.)
FUTURE RESEARCH
Investigate the presence of sliding. One approach is to
measure the friction coefficient of the doughs.
Analyze the structure of the material entering and leav-
ing the capillary rheometer. This assessment can detect
any breakdown of the material and compressibility of the
dough.
Use a modified capillary rheometer, such as the one used
by Senouci and Smith (1987) with a preshearing chamber
to avoid inconsistencies in loading the barrel.
71
LIST OF REFERENCBB
Aspinall, G.O., Begbie, R. and McKay, J.E. 1967. Polysac-
charide components of soybeans. Cereal Science Today,
12:223-228,260—261.
Aspinall, 6.0. and Cottrell, I.W. 1971. Polysaccharides of
soybeans. VI. Neutral polysaccharides from cotyledon
meal. Canadian Journal of Chemistry, 49:1019-1022.
Bagley, E.B. 1957. End corrections in the capillary flow
of polyethylene. Journal of Applied Physics,
28(5):624-625.
Bagley, E.B. 1961. The separation of elastic and viscous
effects in polymer flow. Transactions of the Society
of Rheology, V:355-368.
Bagley, E.B. 1960. Flow of polyethylene into a capillary.
Journal of Applied Physics, 31(3):556-561
Bhatia, G. 1976. Rheological properties of carbon mixes at
very low shear rates using a capillary rheometer III.
Carbon, 14:315-317.
Bhattacharya, M. and Hanna, M. 1986. Modeling textural
properties of extruded starch. Paper 86-6524 presented
at the Winter Meeting of American Society of Agricul-
tural Engineers. Chicago, IL. December 16-19.
Bird, B.R., Stewart, W.E. and Lightfoot, E.N. 1960. Vis-
cosity and the mechanism of momentum transport. Chap-
ter 1. In "Transport Phenomena." p. 3-33. John Wiley
& Sons. New York, NY.
Boger, D.V. and Tiu, C. 1974. Rheological properties of
food products and their use in the design of flow sys-
tem. Food Technology Australia, 26:325-335.
Brodkey, R.S. 1967. Non-Newtonian phenomena. Chapter 15.
In "The Phenomena of Fluid Motions." 3rd printing with
revision. p. 365-455. Addison-Wesley. Boston, MA.
Carter, R.E. and Warren, R.C. 1987. Extrusion stresses,
die swell, and viscous heating effects in double-base
propellants. Journal of Rheology, 31:151-173.
Casson, N. 1959. A flow equation for pigment-oil suspen-
sions of the printing ink type. Chapter 5. In "Rheol-
ogy of Disperse System." Mill, C.C. (Ed.) p. 82-104.
Pergamon Press. New York, NY.
Cervone, N.W. and Harper, J.M. 1978. Viscosity of an
intermediate moisture dough. Journal of Food Process-
ing Engineering, 2:83-95.
Charm, S.E. 1971. Flow of fluid foods. Chapter 3. In
"The Fundamentals of Food Engineering." 2nd. Edition.
p. 54-93. AVI Publishing Co. Westport, CT.
Chen, A.H., Jao, Y.C., Larkin, J.W. and Goldstein, W.E.
1978. Rheological model of soy dough in extrusion.
Journal of Food Processing Engineering, 2:337-342.
Clark, J.P. 1978. Dough rheology in extrusion cooking.
Food Technology, 32:73-76,82.
Crater, D.H. and Cuculo, J.A. 1984. Flow characteristics
of polyethylene terephthalate deduced from pressure
drop measurements. Journal of Polymer Science: Polymer
Physics, 22(1):1-19.
Culioli, J. and Sale, P. 1981. Spinning of fababean pro-
tein 1. Flow properties of fababean protein dopes by
capillary extrusion viscometry. Journal of Texture
Studies, 12:335-350.
Darby, R. 1976. "Viscoelastic Fluids: An Introduction to
their Properties and Behavior." Marcel Dekker, Inc.
p. 283-296. New York, NY.
Dervisoglu, M. and Kokini, J.L. 1986. The steady shear
rheology and fluid mechanics of four semi-solid foods.
Journal of Food Science, 51:541-546.
Dolan, K.D., Steffe, J.F. and Morgan, R.C. 1989. Back
extrusion and simulation of viscosity development dur-
ing starch gelatinization. Journal of Food Process
Engineering, 11:79-101.
Einhorn, S.C. and Turetzky, S.E. 1964. Rheological proper-
ties of SBS polymers by capillary extrusion. Journal
of Applied Polymer Science, 8:1257-1273.
Eyring, H. and Stearn, A.E. 1939. The application of the
theory of absolute reaction rates to proteins. Chemi—
cal Reviews, 24:253-270.
Ferry, J.D. 1970. "Viscoelastic Properties of Polymers."
2nd. ed. John Wiley and Sons Inc. New York, NY.
74
Glasstone, S., Laidler, K.J. and Eyring, H. 1941. Viscos-
ity and Diffusion. Chapter IX. In "The Theory of Rate
Processes." lst. Edition. p. 477-551. McGraw-Hill.
New York, NY.
Harmann, D.V. and Harper, J.M. 1974. Modeling a forming
foods extruder. Journal of Food Science, 39:1099-1101.
Harper, J.M. 1981. Dough rheology. Chapter 3. In "Extru-
sion of Foods." Vol. 1. p. 21-46. CRC Press, Inc.
Boca Raton, Fla.
Harper, J.M., Rhodes, T.P. and Wanninger, L.A. Jr. 1971.
Viscosity model for cooked cereal doughs. Chemical
Engineering Progress Symposium Series, 67(108):40-43.
Harper, J.P., Suter, D.A., Dill, C.W. and Jones, E.R. 1978.
Effect of heat treatment and protein concentration on
the rheology of bovine plasma protein suspensions.
Journal of Food Science, 43:1204-1209.
Hawkins, A.E. 1971. Non-Newtonian technology associated
with some food products. The Chemical Engineer,
245:19-23.
Holdsworth, S.D. 1971. Applicability of rheological models
to the interpretation of flow and processing behavior
of fluid food products. Journal of Texture Studies,
2:393-418.
Howkins, M.D. 1987. A predictive model for pressure drop
in food extruder dies. M.S. Thesis, Agricultural Engi-
neering. Michigan State University. East Lansing, MI.
Janssen, L.P.B.M. 1985. Models for cooking extrusion.
Chapter 9. In "Food Engineering and Process Applica-
tions." Vol. 2: Unit Operations. Le Manuer, M. and
Jelen, P. (Ed.) p. 115-129. Elsevier Applied Science
Publishers. New York, NY.
Jao, Y.C., Chen, A.H., Lewandowski, D. and Irwin, W.E.
1978. Engineering analysis of soy dough rheology in
extrusion. Journal of Food Process Engineering,
2:97-112.
Jasberg, B.K., Mustakas, G.C. and Bagley, E.B. 1981.
Effect of extruder retention time on capillary flow of
soy dough. Journal of Food Process Engineering,
5:43-56.
Johnson, T.W. and O-Shaughnessy, M.T. 1977. Measurement of
temporary and permanent shear with the Instron Capil-
lary Rheometer. ASAE SP 416 and ASTM STP 621. Rela-
tionship between Engine Oil Viscosity and Engine
Performance, p. 57-69.
Kalika, D.S. and Denn, M.M. 1987. Wall slip and extrudate
distortion in linear low density polyethylene. Journal
of Rheology, 31(8):815-834.
Lewis, M.J. 1987. Density and specific gravity. Chapter
2. In "Physical Properties of Foods and Food Process-
ing Systems." p. 51-68. Ellis Horwood. Chichester,
England.
Lund, D.B. 1983. Considerations in modeling food pro-
cesses. Food Technology, 37:92-94.
Luxenburg, L.A., Baird, D.G. and Joseph, E.G. 1985. Back-
ground studies in the modeling of extrusion cooking
processed for soy flour doughs. Biotechnology Progress,
1:33-38.
Mackey, K.L., Ofoli, R.Y., Morgan, R.C. and Steffe, J.F.
1990. Rheological modeling of potato flour during
extrusion cooking. Journal of Food Process Engineer-
ing. 12:1-11.
McCabe, W.L., Smith, J.C. and Harriott, P. 1985. Basic
Equation of Fluid Flow. Chapter 4. In "Unit Opera-
tions of Chemical Engineering." Fourth Edition. p.
56-72. McGraw-Hill Book Company. New York, NY.
McLuckie, C. and Rogers, M.G. 1969a. Influence of elastic
effects on capillary flow of molten polymers. Journal
of Applied Polymer Science, 13(5):1049-1063.
McLuckie, C. and Rogers, M.G. 1969b. Reliability of capil-
lary rheometer measurement of polymer melts. Journal
of Applied Polymer Science, 13(5):1069-1072.
Metzner, A.B. 1959. Flow behavior of thermoplastic. In
"Processing of Thermoplastic materials. (E.G. Bern-
hardt, ed.). Van Nostrand Reinhold, Co. New York, NY.
Metzger, A.P. and Knox, J.R. 1965. The effect of pressure
losses in the barrel on capillary flow measurements.
Transactions of the Society of Rheology, 9(1):13-25.
Mooney, M. 1931. Explicit formulas for slip and fluidity.
Journal of Rheology, 2:210-222.
76
Morgan, R.G. 1979. Modeling the effects of temperature-
time history, temperature, shear rate and moisture on
viscosity of defatted soy flour dough. Ph.D.
Dissertation, Agricultural Engineering. Texas A&M Uni-
versity. College Station, TX.
Morgan, R.G., Steffe, J.F. and Ofoli, R.Y. 1989. A gener-
alized viscosity model for extrusion of protein doughs.
Journal of Food Process Engineering, 11:55-78.
Morgan, R.G., Suter, D.A. and Sweat, V.E. 1978. Design and
modeling of capillary food extruder. Journal of Food
Process Engineering, 2:65-81.
Muller, H.G. 1973. "An Introduction to Food Rheology."
Crane, Russak & Co. Inc. New York, NY.
Nubar, Y. 1971. Blood flow, slip and viscometry. Biophys-
ical Journal, 11:252-264.
Ofoli, R.Y., Morgan, R.S. and Steffe, J.F. 1987. A gener-
alized rheological model for inelastic fluid foods.
Journal of Texture Studies, 18:213-230.
Oldroyd, J.G. 1956. Non-Newtonian flow of liquids and sol-
ids. Chapter 16. In "Rheology: Theory and Applica-
tions." Vol. 1. Eirich, F.R. (Ed.) p. 662-666.
Academic Press, Inc. New York, NY. '
Onogi, S., Masuda, T., Shiga, I. and Costaschuk, F.M. 1973.
Rheological properties of anionic polystyrenes. IV.
Non-Newtonian flow of monodisperse polystyrene and
their blends. Applied Polymer Symposia. No. 20. p.
37-48. John Wiley & Sons, Inc.
Osorio, F.A. and Steffe, J.F. 1984. Kinetic energy calcu-
lations for non-Newtonian fluids in circular tubes.
Journal of Food Science, 49:1295-1296,1315.
Philippoff, W. and Gaskins, F.H. 1958. The capillary
experiment in rheology. Transactions of the Society of
Rheology, 2:263-284.
Rabinotwich, B. 1929. Uber die viskositat und elastizitat
von solen. Zeitschrift far Physikalische Chemie, A
145:1-26.
Ramamurthy, A.V. 1986. Wall slip in viscous fluids and
influence of materials of construction. Journal of
Rheology, 30(2):337-357.
Rao, M.A. 1977a. Rheology of liquid foods - a review.
Journal of Texture Studies, 8:135-168.
Rao, M.A. 1977b. Measurement of flow properties of fluid
foods - developments, limitations, and interpretation
of phenomena. Journal of Texture Studies, 8:257-282.
Rao, M.A. 1986. Rheological properties of fluid foods.
Chapter 1. In "Engineering Properties of Foods." Rao,
M.A. and Rizvi, S.S.H. (Ed.) p. 1-47. Markel Dekker,
Inc. New York, NY.
Remsen, C.H. and Clark, P.J. 1978. A viscosity model for a
cooking dough. Journal of Food Process Engineering,
2:39-64.
Roller, M.B. 1975. Characterization of the time-
temperature viscosity behavior of curing b-staged epoxy
resins. Polymer Engineering and Science, 15:406-414.
Rossen, J.L. and Miller, R.C. 1973. Food extrusion. Food
Technology, 27(8):46-52.
Senouci, A. and Smith, A.C. 1988. An experimental study of
food melt rheology. I. Shear viscosity using a slit
die viscometer and a capillary rheometer. Rheologica
Acta, 27(5):546-554.
Sigmon, 8.6. 1979. "Capillary Rheology of Soy Isolated
Doughs." M.S. Thesis, Chemical Engineering. Virginia
Polytechnic Institute and State University. Black-
sburg, VA.
Singleterry, C.R. and Stone, E.E. 1951. Rheological prop-
erties of a lubricating grease. Journal of Colloid
Science, 6:171-189.
Skelland, A.H.P. 1967. Determination of flow properties.
Chapter 2. In "Non-Newtonian Flow and Heat Transfer."
p. 27-67. John Wiley & Sons, Inc. Notredame, IN.
Steffe, J.F., Mohamed, 1.0. and Ford, E.W. 1986. Rheologi-
cal properties of fluid foods: data compilation. In
"Physical and Chemical Properties of Foods." Okos,
M.R. (Ed.) ASAE. St. Joseph, MI.
Stephen, A.M. 1983. Other plant polysaccharides. Chapter
3. In "The Polysaccharides." Aspinall, G.O. (Ed.).
Volume 2. p. 97-193. Academic Press, Inc. New York,
NY.
Theander, O. and Aman, P. 1979. The chemistry, morphology
and analysis of dietary fiber components. In "Dietary
Fiber: Chemistry and Nutrition." Inglett, G.E. and Fal-
kehag, S.I. (Ed.). p.215-244. Academic Press, Inc.
New York, NY.
78
Tordella, J.P. 1969. Unstable flow of molten polymers.
Chapter 2. In Rheology: Theory and Application. Vol
V. Eirich, F.R. (Ed.) p. 57-92. Academic Press. New
York, NY.
Van Wazer, J.R., Lyons, J.W., Kim, K.Y. and Colwell, R.E.
1966. "Viscosity and Flow Measurement. A Laboratory
Handbook of Rheology." 2nd. Printing. Interscience
Publishers. New York, NY.
Vergnes, B. and Villemaire, J.P. 1987. Rheological beha-
viour of low moisture molten maize starch. Rheological
Acta, 26:570-576.
White, F. 1986. Flow in a circular pipe. Chapter 6. In
"Fluid Mechanics." p. 302-316. McGraw-Hill. New York,
NY.
White, J.L. 1973. Critique on flow patterns in polymer
fluids at the entrance of a die and instabilities lead-
ing to extrudate distortion. Applied Polymer Symposia.
No. 20. p. 155-174. John Wiley & Sons, Inc.
Whorlow, R.W. 1980. Tube viscometers. Chapter 2. In
"Rheological Techniques." p. 60-111. Ellis Horwood
Limited. New York, NY.
Yankelevsky, D. 1988. Engineering models and computer
codes. Journal of Professional Issues in Engineering.
Vol. 114(2):218-230.
Zahler, G.C. and Morfitt, G.R. 1963. High shear capillary
rheometer. British Plastics (Europlastics),
36:698-701.
APPENDICES
APPendix A
Schematic Diagram of Extruder die
Q
7
5' 1
I
90 ""-"""-------nun-£5131â€
VL- 1 [
I~+———
0.1476
81
Appendix B
Moisture Determination
The procedure utilized for the moisture content determi-
nation on the different product were the standard developed
by ASAE for moisture measurement on forage (ASAE standard:
ASAE 8358.1) with small modifications.
Procedure
Weigh the aluminum dish.
Place a representative sample in the aluminum dish at
least 5 g.
Weigh the dish plus sample.
Place the aluminum dish plus sample in the drying oven.
Dry the sample in the oven at 100°C for 24 hours.
Remove samples from the oven, place in a desiccator and
allow to cool to ambient temperature.
Weigh the aluminum dish plus dried samples.
Record loss in weight as moisture.
Calculate moisture content as follows:
(Wt. of wet sample -I/t. of dried sample)x100
Wt. of the wet sample
MCwm
where Nflzwx = moisture content wet basis, percent.
82
Appendix C
Calculation Outline
1- Read from the graph total force Ft(N)
2- Read from the graph drag force Fd(N)
3- Calculate final force F = Ft - Fd (N)
4- Calculate the end correction:
4.1 Calculate FX=OI force when L/D = 0, via linear
regression using two dies with the same diameter, but
different length.
4.2 Calculate correct force Fc = F - FX=0
C
5- Obtain correct pressure drop, Pc = 2—
p
PCRC
6- Calculate shear stress at the wall, 0w HIRE
7- Calculate the slip correction:
Q
nRso
7.1 Plot against.ow for each radius.
7.2 Plot —%—-against.% for each ow.
R a
n a
7.3 Calculate the slope (B) for each ow.
7.4 Plot B versus ow to find B as function of 0w.
7.5 Calculate Qc == Q - Bowan.
0. ,
8- Calculate Eï¬ias function of ow.
83
10- Calculate yw:
L
. 3Q nR3
= + O
11- Construct a rheogram for ow and V,
12- Find the parameters for rheological model (K and n)
using nonlinear least square regression (Marquardt
method) using Series A data.
13- The remaining parameters (AE‘ and C» for the model
were obtained by multiple linear regression (stepwise
method) applied to Series B data.
14- Find a value of K assuming 70% Mc as reference,
using a fixed value of n = (126.
7)
Kay‘n"
15- Calculate n’
16- Plot ln.n"versus moisture content to find the value
of b.
n
K09“ ‘ exp[b(MC-MCO)]
17- Calculate n"
1 1 ,
18- Plot 1n n†versus (ï¬'fl to obtain A75-
where: nu
Appendix D
Solid Density based in Chemical Composition
The density of solid constituent disregarding any inter-
nal pores, have been summarized by Peleg and are shown in
the next table ( Lewis, 1987).
Constituent Density (kg m-B)
Glucose 1560
Sucrose 1590
Starch 1500
Cellulose 1270 - 1610 ( mean 1440)
Protein 1400
Fat 900 - 950
Salt 2160
Water 100
In theory, if the composition of the food is known, the
density can be estimated from
m1 m2 mn
—+—+--°+—
p1 p2 9n
to nznare the mass fraction of constituents 1
to n.
pl to on are the densities of constituents 1 to n
85
Given soy polysaccharide composition:
Constituent % in sample Density (kg m‘3)
Dietary fiber 75 1440
Moisture 6 100
Protein 12 1400
Ash 4.5 2160
Fat 0.2 900
the densities for the doughs are:
Moisture content (%) Calculated density (kg m'3)
70.0 1098
60.0 1136
50.0 1176
Appendix E
Reynolds number and developing flow inlet length
Using the generalized form of Reynolds number (NGRe) for
a power law fluid the following values were obtained.
p UZ-nDn
NGRe n-l 3n+1 n
8 K( 4.. )
Moisture Die diame- Plunger NGRe L
ter Speed
% w.b. mm mm/min
70.0 3.17 50 3.02 x 10'5 5.74 x 10’9
100 1.01 x 10'4 1.92 x 10‘8
300 6.85 x 10'4 1.30 x 1077
500 1.67 x 10'3 3.18 x 10'7
1.59 50 2.83 x 10"4 2.69 x 10"8
100 9.46 x 10'4 9.01 x 10'8
300 6.41 x 1073 6.11 x 1077
500 1.56 x 10'2 1.49 x 10‘6
60.0 3.17 50 7.48 x 10'6 1.43 x 10'9
100 2.44 x 1075 4.65 x 10'9
300 1.59 x 10'4 3.03 x 10‘8
500 3.80 x 10"4 7.24 x 10'8
1.59 50 6.49 x 10'5 6.18 x 10'9
100 2.12 x 10'4 2.02 x 10"8
300 1.38 x 10'3 1.31 x 10'7
500 3.30 x 10'3 3.14 x 10‘7
50.0 3.17 50 1.76 x 10'6 3.36 x 10'10
100 6.31 x 10'6 1.20 x 1079
300 4.77 x 10"5 9.09 x 10'9
500 1.22 x 10"4 2.33 x 10'8
1.59 50 2.03 x 10'5 1.93 x 10'9
100 7.26 x 10'5 6.92 x 10‘9
300 5.49 x 10'4 5.23 x 10'8
500 1.41 x 1073 1.34 x 1077
87
Appendix F
Capillary viscometer raw data at 25%:
Symbols used in data presentation
MC = nominal moisture content, % wet basis
L/D = lenght - diameter ratio, dimensionless
v = plunger speed, mm minâ€1
PC = Corrected pressure drop, Pa
Q = volumetric flow, m3 5'1
0w = shear stress at the wall, Pa
V = shear rate at the wall, 5’1
n = apparent viscosity, Pa sn
L/D
mmmmmmmmmmmm bbbb-bububbb-bbb NNNNNNNNNNNN
1.128+05
5.618+04
1.688+05
l.OlE+06
5.SlE+05
1.12E+05
5.618+05
1.962+05
9.54E+05
3.658+05
4.498+05
8.4ZE+05
l.7lE+05
8.988+05
6.17B+05
6.74E+05
l.12£+06
1.57E+06
2.198+06
1.57E+06
2.362+06
2.4IE+06
l.68£+06
2.64E+06
2.692+06
2.75E+06
3.37E+06
2.3OE+06
3.37E+06
1.198-07
1.198-07
3.553'07
3.563-07
5.943-08
5.943-03
5.943-08
1.198-07
1.193’07
1.193-07
3.563-07
3.553-07
5.943-08
5.948-08
5.945-08
5.948-08
1.198-07
1 o 193'07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
3.568-07
3.568-07
3.568-07
9.088+03
l.84£+04
3.6OE+04
1.93E+04
2.17E+04
3.14B+04
4.3OE+04
22.90
40.91
88.26
156.03
275.80
449.82
957.59
396.5
451.0
408.1
123.9
78.8
69.8
45.0
MC
70
70
70
70
mmmmmmmmmmmm bahbhhbbbahbaéhhb NNNNNNNNNNNNNNN
Speed P
300
500
500
500
500
50
5O
50
100
100
100
100
300
300
300
300
500
500
500
2.13E+06
3.37E+06
2.923+06
2.028+06
2.47E+06
5.618+04
l.12£+05
5.058+05
7.3OE+05
6.17E+05
7.868+05
1.508+06
7.138+05
9.108+05
4.33E+05
6.55E+05
1.168+06
2.623+05
2.068+06
2.782+06
l.55£+06
2.73E+06
7.108+05
3.298+06
4.64E+06
3.07E+06
2.188+06
5.4BE+05
4.03E+06
2.63E+06
4.258+06
4.44E+06
2.258+06
3.94E+06
3.438+06
2.398+06
1.74E+06
1.182+06
2.47E+06
2.818+06
4.07E+06
9.94E+05
3.918+06
6.24E+06
3.07E+06
l.95£+06
2.968+06
89
Q
3.568-07
5.948-07
5.948-07
5.942-07
5.948-07
5.948-08
1.198-07
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
3.568-07
5.948-07
5.948-07
5.948-07
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
3.568-07
3.568-07
5.948-07
5.948-07
5.948-07
5.948-07
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.562-07
3.568-07
5.948-07
5.948-07
4.223+04
1.05E+04
8.262+04
1.llE+05
8.67E+04
1.338+05
1.818+05
1.718+05
2.208+05
5.53E+04
9.758+04
1.118+05
8.67E+o4
1405.29
16.07
38.38
93.58
149.75
167.87
359.67
800.18
1306.85
22.24
36.85
88.19
150.11
30.0
656.1
2151.7
1189.2
578.8
794.3
502.7
213.3
168.4
2488.1
2646.0_
1261.8
577.4
MC
60
60
60
60
60
60
6O
60
60
60
60
60
60
“GOGQ bbbbhbï¬bbbébb-ï¬b NNNNNNNNNNNNNN
Speed P
500
50
50
50
100
100
100
300
300
300
300
500
500
500
3.4IE+06
1.188+07
7.72E+06
6.04E+06
1.47E+07
9.07£+06
1.IOE+07
1.153+07
1.122+07
9.788+06
1.125+07
1.42E+07
1.3BE+07
1.4ZE+07
1.688+06
3.03E+06
2.928+06
2.253+06
3.14E+06
2.398+06
l.45£+06
4.652+05
1.03E+06
2.855+06
6.59E+06
4.87E+05
4.87E+05
7.83E+06
5.3OE+06
6.7lE+06
2.898+06
4.7SE+06
7.77E+06
7.3BE+06
7.54E+06
1.ZBE+O7
5.53£+06
9.57E+06
8.4SE+06
9.218+06
1.298+07
6.623+06
1.433+07
1.10£+07
9.54E+06
9.0SE+06
l.52£+07
90
Q
5.948-07
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
3.568-07
5.948-07
5.948-07
5.948-07
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.198-07
3.568-07
3.563-07
3.568-07
3.568-07
5.948-07
5.948-07
5.942-07
5.948-08
5.948-08
5.948-08
5.948-08
1.198-07
1u198-07
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
5.948-07
5.943-07
5.948-07
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.33E+05
l.82£+05
1.7lE+05
2.208+05
3.72E+05
3.24E+05
1.818+05
3.168+05
3.568+05
5.058+05
4.918+05
G.OOE+05
4.328+05
384.41
601.04
1027.08
1587.61
5.62
14.55
69.65
187.58
253.76
376.02
835.26
1276.12
11.09
346.9
302.1
166.2
138.6
66283.7
22306.2
2601.1
1682.9
1402.1
1342.0
588.1
470.0
.38972.9
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
t‘
\
U
anonmcomoocnoo
Speed P
100
100
300
300
300
500
500
500
‘1.192+07
1.91E+07
7.518+06
4.7OE+06
5.158+06
9.158+06
3.87E+06
9.03E+06
.293+07
.822+07
.625+07
.36E+07
.565+07
.998+07
.688+07
.4OE+07
3.508+07
2.93E+07
2.823+07
3.662+07
3.623+07
3.993+07
4.358+o7
wwNNNNO-‘N
91
Q
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
5.948-07
5.948-07
5.948-07
5.948-08
5.948-08
5.948-08
5.948-08
1.198-07
1.198-07
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
5.948-07
5.948-07
5.948-07
1.818+05
2.308+05
3.568+05
5.058+05
4.9IE+05
6.24E+05
61.86
117.05
231.92
718.03
1125.45
2040.33
2928.4
1965.1
1534.1
702.8
436.4
305.7
92
Appendix G
Capillary viscometer data for the overall model
Symbols used in data presentation
Temp. = temperature, 3:
MC = nominal moisture content, % wet basis
L/D = lenght - diameter ratio, dimensionless
in = Corrected pressure drop, Pa
Q = volumetric flow, m3 s"1
ow = shear stress at the wall, Pa
V = shear rate at the wall, 5"1
n = apparent viscosity, Pa sn
50.2
50.2
75.2
75.2
75.2
75.2
75.2
75.2
75.2
75.2
mmmmmmmm NNNNNNNNQNNNWNQQN NNNNNNNNNN â€mmmmmmmmmmmm
P.
1.BOE+06
1.578+06
1.603+06
1.24E+06
5.612+05
6.74E+05
7.86£+05
1.118+06
3.37E+05
2.258+05
3.93E+05
6.3ZE+05
2.83E+05
3.67E+05
2.558+05
6.4BE+05
1.128+05
3.27E+05
5.BOE+05
5.5ZE+05
2.53E+05
3.0QE+05
2.818+04
5.618+04
2.298+05
2.298+05
5.828+05
2.3lE+05
2.038+05
8.768+05
3.85£+05
93
Q 0..
3.568-07 4.863+04
3.568-07
3.568-07
3.568-07
1.198-07 2.45E+04
1.193707
1.198-07
1.193-07
5.943-08 1.24E+04
5.948‘08
5.943-08
5.948-08
3.565-07 4.863+04
3.568-07
3.568-07
3.568-07
1.198-07
3.558-07 1.528+04
3.558-07
3.563-07
1.193-07 6.15E+03
1.198-07
5.948-08
3.568-07
3.568-07
3.568-07 1.188+04
3.568-07
3 0 568-07
3.568-07
3.558-07
120.24
41.31
19.43
87.28
110.29
36.10
71.75
404.3
592.8
638.6
556.9
138.1
170.3
165.0
Temp.
{q
0|
NNNNNN
MC
t‘
\
U
NNNNNNQNWQQ m N ‘
Q Q†N NNNNNNNQQmmmmmmmmmm mmmmm nummmmmmmmm
P.
3.15E+05
4.63E+05
2.113+05
2.815+04
1.40£+05
9.04E+04
1.18£+06
5.335+05
1.128+06
3.938+05
3.37£+05
1.122+05
5.61£+04
2.258+05
1.54E+06
1.43E+06
1.BZE+06
1.38E+06
1.04E+06
8.14E+05
7.3OE+05
4.4SE+05
3.93£+05
5.868+05
8.118+04
5.3OE+05
1.128+05
l.96£+05
l.68£+05
1.298+06
1.48E+06
1.4SE+06
9.68£+05
8.568+05
1.04£+06
5.7ZE+05
7.27E+05
6.858+05
3.668+05
3.388+05
2.67E+05
2.112+05
1.23£+05
2.07E+05
94
Q
2.388-07
1.195-07
1.192-07
1.198-07
1.198-07
3.5sal07
3.568-07
3.568-07
3.568-07
1.198-07
1.198-07
1.198-07
5.948-08
5.948-08
3.568-07
3.568-07
3.568-07
1.198-07
1.198-07
1.198-07
5.948-08
5.948-08
5.942-08
3.568-07
3.568-07
3.562-07
1.198-07
1.198-07
1.198-07
3.568-07
3.568-07
3.568-07
1.198-07
1.198-07
1.198-07
5.948-08
5.948-08
5.948-08
3.568-07
3.568-07
1.198-07
1.198-07
5.948-08
5.948-08
OW
5.498+03
2.968+04
8.798+03
4.398+03
5.00E+04
3.37E+04
1.64E+04
5.008+04
1.998+04
4.4lE+04
2.998+04
2.078+04
4.413+04
2.992+04
2.07E+04
25.81
94.06
37.13
19.15
130.85
49.27
18.66
144.68
14.27
150.37
53.52
22.99
163.09
52.78
19.32
218.7
314.4
236.6
229.4
382.0
683.4
878.9
345.4
1395.6
293.4
558.1
900.0
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105.25
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6.128+04
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109.43
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