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LIBRARY
Michigan State
University

 

 

 

This is to certify that the

thesis entitled

A Predictive Model for Pressure Dr0p
in Food Extruder Dies

presented by

Murray Donald Howkins

has been accepted towards fulfillment
of the requirements for

M. S . degree in Agricultural
Engineering

   

Major professor

0-7639 MS U i: an Affirmative Action/Equal Opportunity Institution

 

 

 

lV1ESI_l RETURNING MATERIALS:
Place in book drop to

usiumes remove this checkout from

All-ICIIIIL. your record. FINES will

 

 

be charged if book is
returned after the date
stamped below.

 

 

 

 

 

A PREDICTIVE MODEL FOR PRESSURE DROP IN FOOD EXTRUDER DIES

By

Murray Donald Howkins

A THESIS

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

Master of Science

Department of Agricultural Engineering

1987

ABSTRACT

A PREDICTIVE MODEL FOR PRESSURE DROP IN FOOD EXTRUDER DIES

By

Murray Donald Howkins

A model based on a generalized Reynold’s number and material
viscoelastic properties has been developed for predicting entrance
pressure drop through mulitiple hole food extruder dies. The model was
applied to data collected during twin-screw extrusion of potato dough,
defatted soy dough, and an inert food dough, and gave accurate
prediction of entrance pressure drop. This model, combined with
previous models for predicting die hole pressure drop, provides a method
for assessing total die pressure drop in an extruder for use in scale-up

and die modification applications.

ACKNOWLEDGEMENTS

The author expresses sincere gratitude to the following people for

their input on this thesis:

Dr. Ronnie G. Morgan for his invaluable professional and personal
guidance during this graduate program. His continued encouragement and
optimism were very much appreciated.

Dr. Fred W. Bakker-Arkema, Dr. Robert Y. Ofoli and Dr. Mark A.
Uebersax for their added expertise to this project as well as
encouragement and excellent advice for career plans including plans for
future overseas work.

The Food Engineering extrusion team for their assistance in data
collection and analysis. Special thanks goes to Barb Christensen, Kevin
Evans, Gary Garfield, John Keenan, D'Anne Larsen, and John Leen.

The entire Food Engineering/Agricultural Engineering Dept. at
Michigan State University for their personal friendship and advice.

Rudy Leschke of Nabisco Brands Inc. for his valuable input on the
methodology of this study.

Kevin Rose and Kirk Dolan, fellow Agricultural Engineering graduate
students, who helped, encouraged, and befriended the author throughout
his graduate program.

The Author's parents, John and Beryl Howkins, for their continued
support, prayers, patience, and encouragement throughout the author's

academic career.

iii

TABLE OF CONTENTS

CHAPTER

LIST OF TABLES .

LIST OF FIGURES
NOMENCLATURE .

I. INTRODUCTION

II. REVIEW OF LITERATURE

Discussion of need
Pressure drop modeling

III. THEORETICAL DEVELOPMENT .

Pressure drop equations .
Elasticity equations
Dimensional analysis

IV. EXPERIMENTAL PROCEDURES .

Experimental design . . .
Capillary rheometer procedures
Twin- screw extrusion procedures .
TSE sample preparation .
TSE extrusion techniques .
Moisture content analysis .
Data analysis .
Slip .
Generalized viscosity models .
Data analysis techniques .

V. RESULTS AND DISCUSSION

Experimental data .
Rheological parameters of
capillary rheometer data .
Twin screw extruder operation
Rheological parameters of TSE data .
Elasticity . . .
Entrance pressure drop modeling .
Pi (H) term coefficients .
Validity of n term coefficients
Entrance pressure prediction accuracy

VI. CONCLUSIONS .

iv

Page

0‘00

10

10
18
22

25
25

32
32
32
35
36
39

41
42
42

42
48
50
57
59
59
62

78

TABLE OF CONTENTS (Cont'd)

CHAPTER

RECOMMENDATIONS

APPENDICES

A.

CHECK OF INDEPENDENCE OF n TERMS .

. DIE DIMENSIONS .

CAPILLARY RHEOMETER CALCULATIONS .
FLOUR CALIBRATION PROGRAM
DIE SLIP ANALYSIS

SAS PROGRAM TO COMPUTE CR RHEOLOGICAL PROPERTIES

. GENERAL SAS PROGRAM TO COMPUTE TSE

RHEOLOGICAL PROPERTIES .

. SPS DATA TESTED ON CAPILLARY RHEOMETER .

. SPS SHEAR STRESS VS. SHEAR RATE DATA FROM

CAPILLARY RHEOMETER

. SPS DATA COLLECTED ON TWIN SCREW EXTRUDER

. POTATO DOUGH DATA COLLECTED ON TWIN SCREW

EXTRUDER

. DEFATTED SOY DOUGH DATA COLLECTED ON TWIN

SCREW EXTRUDER .

. SHEAR RATE AND SHEAR STRESS VALUES FOR

EXTRUDED SPS .

. SHEAR RATE AND SHEAR STRESS VALUES FOR

EXTRUDED POTATO DOUGH.

. SHEAR RATE AND SHEAR STRESS VALUES FOR

EXTRUDED DEFATTED SOY DOUGH

Q. ENTRANCE PRESSURE DROP DATA FROM LITERATURE

. EXPERIMENTAL DATA USED IN COMPUTING ENTRANCE

PRESSURE DROP

. SAS PROGRAM FOR COMPUTING ENTRANCE PRESSURE

. ANOVA TABLES FOR STEPWISE FORWARD REGRESSION

OF EQN. 27 .

Page

79

81
82
86
90
93

94

95

97

101

102

105

107

108

108

109
110

113

115

117

TABLE OF CONTENTS (Cont'd)

CHAPTER Page
U. ANOVA TABLES FOR LINEAR REGRESSION . . . . . . . 124

V. INDUSTRIAL APPLICATIONS OF THE DIE PRESSURE
DROP MODEL . . . . . . . . . . . . . . . . . . . 130
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . 135
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . 138

vi

LIST OF TABLES

TABLE

10

Coefficients for Boger (1982) entrance pressure
drop model (Eqn. 1)

Variables affecting entrance pressure drop in
food extruder dies .

List of H Terms

Data from published literature sources
(raw data given in appendix Q)

Experimental design for capillary rheometer
Experimental design for twin-screw extruder
Twin-screw extruder die dimensions .

Screw configurations of twin-screw extruder

Power law parameters for SP8 determined using
a capillary rheometer

Rheological properties of extruded materials

determined using a capillary rheometer .

ll

12
13

14

15

Moisture content and product rate calibration
values for SP8 and defatted soy dough

Rheological properties of twin-screw extruder data

Coefficients for Eqn. (21) and their corresponding
model r (determined by stepwise forward regression)

Contribution of H terms 50 model accuracy
(determined by partial r given by each term)

Coefficients fog Eqn. (28) and the correlation
coefficients (r ) for APent predicted by

Eqn. (28) vs observed APent

vii

Page

17

24

26
28
29
33

34

45

45

49

50

61

61

68

Figure

1 Effects of changes in die AP vs. Q
relationships on extruder operating performance.

2 Schematic of effects of die change on extrusion
parameters and extrudate quality .

3 Flow coefficient, fc, (from Michaeli, 1984) vs.
shape factor, F, for non-Newtonian flow through
irregular cross-sectioned die holes

4 Definition of die hole shape factor, F .

5 Definition of die hole spacing, s

6 Definition of die entrance angle, a, and conduit
entrance diameter, Dc

7 Primary normal stress difference (N ) vs. shear
rate data for various polymers studied by Crater
and Cuculo (1984) and White and Roman (1976)

8 Schematic of proposed method (Williams, 1977)
for determining A (at constant shear rate
and hole diameter

9 Illustration of capillary extrusion process.

10 Schematic of end effects for AP vs P through
dies of same diameter, differenf lengths

11 Relationship of entry length and Power law index.
(Analysis by Collins and Schowalter (1963))

12 Shear stress vs shear rate for SP8 extruded with
a capillary rheometer (data points are means of
four observations)

13 Shear stress vs shear rate for SP8 extruded with
a capillary rheometer (Data points are means of
four observations)

14 Power law consistency coefficient, m, vs l/T for
SP8 (50% MC) extruded with a capillary rheometer
(data points are means of four observations)

15 0 vs 1/T for potato dough (33.7% MC)

LIST OF FIGURES

(Apparent viscosity adjusted to 7 - 100 sec-l)
(Mackey et a1. 1986) , . . . _ 0 .

viii

Page

14
15

16

16

19

21

31

37

38

43

44

46

47

LIST OF FIGURES (Cont'd)

Figure

16

17

18

19

20

21

22

23

24

25

26

27

28

Shear stress vs. shear rate for SP3 (58% MC, 66.60C)
(data points are means of four observations)

Shear stress vs shear rate for SP8 (64.3% MC, 59.30C)
Twin screw extruder data (data points are means of
four observations)

Shear stress vsoshear rate for potato dough
(MC-50%, T-54.4 C) (data points are means of
two to four observations) . . . . . .

Shear stress vs shear rate for defatted soy dough
(MC-40.0, T-46.8 C) (data points are means of
four observations) . . . . . . . . . .

Analysis of slip for SP8 TSE data (58% MC)
(data points are means of four observations)

Material time constant determined for extruded
potato flour at 50% M.C. (data points are means
of two observations) . . .

Predicted vs. observed «1 for all published and
experimental data . . . . . . . . . .

Predicted vs. observed APent for all published and
experimental data (solid points are plastic polymers
and open points are food doughs) . . . . . . . .

Predicted vs. observed AP for published
ent
polymer data . . . . . . . . . . .

Predicted vs. observed APent for published
defatted soy data . . . . . . . . . .

Predicted vs. observed APen for twin screw
extruder data (data points are means of
four observations)

Predicted vs observed APen for extruded potato
dough data (data points are means of two to four
observations)

Predicted vs observed AP for extruded

defatted soy dough data Iagta points are means
of four observations)

ix

Page

51

52

53

54

56

58

66

67

71

72

73

74

75

LIST OF FIGURES (Cont'd)

Figure
29 Predicted vs
(data points
30 Boger (1982)
for all data .
A. Schematic of
B. Schematic of

observed AP n for extruded SPS data
are means of four observations)

model predicted vs observed APent

capillary rheometer extensions

chart plots

Page

76

77
87

88

r* F: 5*

r‘

ent

a.

MC

AP adj

APdhole
AP

e
APent

AP
ex

APobs

Empirical constant

Moisture content adjustment for genralized viscosity
term

1

Diameter of barrel conduit (m)

Empirical exponent for 1

Die Diameter (m)

Activation energy (cal/g mol)

Shape Factor

Coefficient in eqn 24

Constant used in equating N1 (eqn 18) (Pa)

Die length (m)

Die end length (equivalent length added to die hole
length accounting for end pressure drop (m)

Entry length region before fully developed flow (m)

Power law consistency coefficient (Pa-sec“)

Mass rate (kg/hr)

Moisture content (percent wet basis)

Reference moisture content (percent wet basis)

Power law flow behavior index

Number of die holes

Primary normal stress differecne (Pa)

Exponent used in equating N1 (Eqn. 17)

Total pressure adjusted for temperature (Pa)

Die hole pressure drop (Pa)

End pressure drop (Pa)

Entrance pressure drop (Pa)

Exit pressure drop (Pa)

Total die pressure drop at observed temperature (Pa)

xi

gen

Total predicted pressure drop (Pa)
Volumetric flow rate (m3/s)

Hydraulic radius of die hole (m)

Die radius (m)

Generalized reynold's number

Universal gas constant (1.987 cal/gmol-OK)
Die hole center spacing (m)

Temperature (OK)

Reference temperature (OK)

Average velocity in die (m/s)

coefficient in eqn 24.

Die entrance angle (deg)

Jet swell ratio (extrudate dia./die dia.)
coefficient used in eqn 24.

slip coefficient

True shear rate (5.1)

Apparent shear rate (3.1)
Time constant (3)
Proposed alternative time constant (3)
Viscosity (Pa 3)

Independent dimensionless term (Table 2)
Density of material at the die (kg/m3)
Shear stress at the wall (Pa)
Temperature-time history (OC-s)

Shear history

xii

CHAPTER I.

INTRODUCTION

The uniqueness and efficiency of extrusion has led to its wide
acceptance for manufacturing several different types of food products.
Single screw extrusion originated in the mid 1930's with development of
the Collet extruder for producing puffed corn curls (Harper, 1981).
Then, in the mid 1950's, single screw cooking extrusion grew rapidly as
an efficient means of producing expanded pet foods. In the late 1970's
twin-screw extrusion began to receive moderate attention in the food
industry as an improved extrusion technology for specific applications.
Today, twin-screw extrusion technologies are growing at significant
rates and are used to manufacture a host of various food products.
Among these products are breakfast cereals, snack foods, pet food,
beverage powders and bread dough.

Use of extruders in the food industry is constrained due to lack of
adequate knowledge about how process conditions affect machine
performance and product quality. This lack of knowledge restricts
engineering scale-up of the processes. Typical scale-up is still an
art, relying on personal expertise and experience. This is largely due
to geometric complexity, irreversible physicochemical reactions and non-
Newtonian behavior of foods.

One critical phenomenon in extrusion scale-up involves the pressure
drop versus flow rate (AP vs. Q) relationship through the die assembly.
Changes in this relationship directly affect extruder performance by
changing residence time, percent screw fill, and power requirements.
These in turn alter shear history, thermal history, and thus viscosity.

These parameters directly affect extrudate quality, especially in starch

l

or protein products where starch gelatinization and/or protein
denaturation significantly alter the product properties.

A common need is to alter extrudate size and/or shape without
affecting process history within the extruder. Therefore, one needs to
change die assemblies without altering its overall AP vs Q relationship.
A major problem in achieving this goal is the lack of reliable methods
for predicting die entrance pressure drop for non-Newtonian food
materials flowing through multiple non-circular holes. Hence the
objectives for this investigation are:

1. To develop an engineering analysis technique for predicting entrance
pressure loss in food extruder dies as a function of die geometry,
material rheology, and process conditions.

2. To use experimental data for plastic polymers and biological
materials to verify the proposed technique.

Although total AP vs. Q is the primary die design factor affecting
extruder performance, practitioners should note that parameters such as
maximum shear rate and die roughness may also impact product quality
(Harper,l986). The present study only emphasizes the assessment of

pressure drop phenomenon of extruder dies, not product quality.

CHAPTER II.

REVIEW OF LITERATURE

DISCUSSION OF NEED

An extruder's total output is directly affected by the pressure
drop-flow rate relationship of the screw and die. In a screw extruder,
net flow is equal to the drag flow caused by the forward thrust of the
screws, minus the back flow caused by the die pressure (Harper, 1981).
The point at which net flow is equal to the die flow for a given product
rate is known as the extruder operating point. Figure 1 depicts how a
change in die AP vs. Q changes the extruder's operating point. Changing
from die #1 to die #2 (Figure 1) causes a change in the die AP vs. Q,
thus shifting the operating point.

Shifting the extruder operating point changes process parameters
such as residence time, power input and percent screw fill. These
parameters in turn affect process kinetics. Figure 2 schematically
illustrates how die AP vs. Q characteristics can affect extruder
performance and extrudate quality. Note that quality is application
specific and denotes the desired physical and physicochemical properties
such as texture, puffing, percent gelatinization or denaturation.

Change in die geometry affects the extruder power requirement.

While extruding a nonreactive non-Newtonian dough, the author observed a
40 to 50 percent increase in power input when changing die L/D from one
to eight on a twin-screw extruder. Harper (1981) shows that total power

of a single-screw extruder is a function of extruder die pressure.

Die #1

Die #2

 

 

“~\‘\“‘~‘~‘—_—_-

EXTRUDER OPERATING
CURVE

 

 

 

 

Q1 Q2
0

Figure 1. Effects of changes in die AP vs.Q relationships
on extruder operating performance.

 

 

 

CHANGE IN DIE HOLE, ‘ CONSTANT

SIZE, SHAPE, QUANTITY,

 

 

 

EXTRUDER CONDITIONS
(RPM, MASS RATE, ETC.)

 

 

p“% FILL,

 

 

 

 

L

 

 

 

 

 

 

 

 

L___.

 

 

 

 

 

 

 

 

DIE AP vs Q ALTER
RESIDENCE SHEAR
TIME & WORK
INPUT
ALTER OPERATING _‘
POINT OF EXTRUDER
‘7

 

 

 

 

 

TEMPERATURE-TIME
HISTORY

 

 

 

it

 

 

 

L

EXTRUDATE

 

STRAIN
HISTORY

 

 

QUALITY
ALTERATION IN PUFFING;
TEXTURE, VISCOSITY,
NUTRIENTS, FLAVOR, ETc.

 

 

 

Figure 2. Schematic of
extrusion parameters and

effects of die change on

extrudate quality.

 

 

Change in residence time directly affects process kinetics. Bigg
and Middleman (1974) and Bruin et al. (1978) showed significant effects
of die pressure drop on residence time for a single-screw extruder.
Changes in residence time and power input change the temperature-time
history, W, and strain history, Q. Changes in W and O alter process

kinetics, which change extrudate quality (Morgan, 1979; Dolan, 1986).
PRESSURE DROP MODELING

Pressure loss across extruder die assemblies can be separated into
three components: entrance pressure drop, capillary (die hole) pressure
drop, and exit pressure drop. Entrance pressure drop (APent) consists
of momentum losses due to changes in fluid velocity and flow direction,
and energy required to overcome elastic forces. Exit pressure losses
are due to the relaxation of elastic forces created during material
contractions at the die entrance. Crater and Cuculo (1984) showed that
APex is less than 20% of APent for high molecular weight polymers at
shear rates of 100-2000 5-1. Han and Kim (1971) showed APex to be one
to six percent of APent for polyethylene in a shear rate range of 100-

l

6003- with varying cone entry to capillary diameter contraction ratios.

APex's of 10-30 percent of APen were reported for high and low

t
molecular weight polymers in a shear rate range of 100-1000 5-1 over
various ranges of die entrance angles (Han, 1973). Assuming that elastic
effects of food materials are orders of magnitude less than those for

polymers, the author assumed APex << APent for food extrusion dies and

therefore can be neglected.

Entrance pressure drop cannot be neglected when assessing total
pressure drop across most food extruder dies. Morgan (1979)
demonstrated that APent for soy dough represented 50 to 70 percent of
total AP for capillary extrusion with the die L/D ranging from two to
eight. APent for soy dough ranged from 20 to 50 percent of total AP in
a capillary extruder having L/D ratios of 20 to 80 (Remsen and Clark,
1978). Pena et al. (1981) showed APent to be 83 percent of total AP for
several polymers. From the above data it is concluded that entrance
pressure drop is often the largest single component of total pressure
drop. Die hole pressure drop was and assumed to account for the
remainder of the total pressure drop.

Research has been conducted using finite element analysis to study
capillary entrance pressure loss of polymers through single circular
holes (Kim-E, 1983; Keunings and Crochet, 1984; Boger, 1982; Tanner et
al., 1975; Mitsoulos et al., 1985). These models are limited to fixed
contraction ratios and do not apply to multiple die holes. Other
research has involved experimental data analysis of die entrance
pressure loss through singular die holes (Crater and Cuculo, 1984;
Jasberg et al., 1981; Ballenger et al., 1971; Jao and Chen, 1978;
Morgan, 1979; Han et al., 1969; Han et al., 1970; Han and Kim, 1971;
Han, 1973). These researchers did not develop a generalized model to
relate entrance pressure to flow rate, material rheology and die
geometry.

Boger (1982) developed the following model for predicting entrance
loss through circular die geometries using non-elastic, non-Newtonian

power law polymers:

E. .
APent - 21w [ 32 (C + 1) + nc ] (1)

where Re' is the generalized Reynold's number given as

 

Re' - p DnVZ-n (2)
8n-1m 39+; n
4n

and C' and n'c are coefficients based on the flow behavior index and are
given in Table 1.

This model does not account for elasticity and has not been tested
for food materials. However, it is the only model that the author found
that could possibly be adapted to predict entrance pressure drop of food
materials flowing through multiple die holes with irregular shapes.
Hence, Boger's model is tested in this study for its applicability to
foods, and it is compared to the model developed in this study.

Die hole pressure drop can be developed from simple momentum
balances within a capillary. For Newtonian flow the Hagen-Poiseuille
equation relates capillary pressure drop to flow rate, die length and
radius (Bird et al., 1960). A similar development for non-Newtonian
cases have been used by Shanoy and Saini (1985) and Michaeli (1984) for
irregularly shaped die cross sections. Michaeli (1984) and Shanoy and
Saini (1985) introduced factors to account for irregular cross sections.
Shanoy and Saini (1985) also substituted the apparent viscosity of a
Power law fluid in place of the Newtonian viscosity used in the

Hagen-Pouiseuille equation.

Table 1. Coefficients for Boger (1982) entrance pressure drop model
(Eqn- 1)

 

Flow Behavior Index Loss Coefficient Couette Correction
n C' n’
c

1.0 1.33 0.59
0.9 1.25 0.70
0.8 1.17 0.85
0.7 1.08 1.01
0.6 0.97 1.15
0.5 0.85 1.34
0.4 0.7 1.53
0.3 0.53 1.76

 

CHAPTER III.

THEORETICAL DEVELOPMENT
PRESSURE DROP EQUATIONS
Total pressure loss across an extruder die hole can be expressed as

AP (3)

AP - AP t + APdhole + ex

T en

As discussed previously, exit pressure drop is assumed negligible for
this study. The die hole pressure drop term of Eqn. (3) can be
determined from transport phenomena equations of viscometric tube flow.
For non-Newtonian non-elastic viscometric flow in the absence of slip, a

force balance on a cylindrical element results in

_ ZL
APdhole R rw (4)

For Newtonian tube flow, derivation of shear rate at the tube wall

results in
_ 59
F «R3 (5)

For a non-Newtonian fluid, true shear rate, 7, is given as a function of

F as (Darby, 1976):

where n' is the Rabinowitsch correction factor (Whorlow, 1980) given as

10

11

d 1n 1
' ______E
d 1n F

n!

(7)

There are several models developed for describing rheological properties
of non-Newtonian fluids. The most popular and simplest of these models

for a shear thinning material is the Power-law model:
1 - m 1 (8)

Hermann and Harper (1973) concluded that the Power-law model adequately
describes the relationship, for a limited range of 7, for extruded
cereal doughs. For a Power-law fluid, the Rabinowitsch correction
factor n' - n. Hence, for circular die flow of a Power-law fluid, shear

rate at the wall is described by

_}_aflAQ

7 4n nR3 (9)
substituting equations (5) and (6) into (4) and (8) yields an expression
for die hole pressure loss as a function of rheological properties, size

and flow rate for circular holes:

2_L_m 3n+l n n
dhole - «nR3n+1 [ n ] (Q) (10)

AP
There is a need to reformulate Eqn. (10) for irregularly shaped
conduits. However, solution of the equations of motion for irregularly

shaped cross sections is complex and usually requires a numerical
methods solution. Some authors have developed flow coefficients for
specific geometries which are used to adjust the Hagen-Poiseuille

equation for flow through irregular cross sections. Michaeli (1984)

12

lists flow coefficients, fp, for some cross sections of known aspect

ratios, (height/width), and gives APdhole as

APdhole ' lZ—IL-Q—L— l (11)

EH3 f

P
Irregular cross-sections without actual height and width dimensions
such as hearts, moons, stars etc. are commonly used in food extrusion of
snack foods and breakfast cereals. For this reason, it is essential
that the die pressure drop model is not limited to dies of a given cross
section or measurement of an aspect ratio.

Classical fluid dynamics makes use of the hydraulic radius,

defined as:
r _ Cross-Section of Flow Area (12)
h Wetted Perimeter of Cross-section

for evaluating pressure loss of turbulent Newtonian flow in irregularly
shaped conduits (McCabe and Smith, 1976). Note that for a circular
cross section, rh - R/2. For laminar flow, use of the hydraulic radius
without a flow coefficient is only an approximation (Michaeli, 1983;
McCabe and Smith, 1976). However, combining the concept of the hydraulic
radius with a flow coefficient might result in an effective solution of
APdhole without requiring use of an aspect ratio. For non-Newtonian flow

through irregular conduits, the following combination of equations

(10),(1l) and (12) is proposed:

Lg sad)“Qn

1
APdhole - (8“)nrh(3n+l) [ n f

c (13)

13

where 2rh has been substituted for R and the flow coefficient, fc’ has
been adapted from fp values of Michaeli (1984) and are listed in
Figure 3 as a function of a shape factor, F. 'The shape factor is
defined as the ratio of the diameter of the smallest circle (circle A,
Figure 4) which totally encloses the die hole cross section to the
diameter of the largest circle (circle B, Figure 4) which will fit
completely inside the die hole cross section. Flow coefficients for
other irregular shapes need to be developed but is beyond the scope of
this study.

The entrance pressure drop term of Eqn. (3) is also a function of
rheological properties as well as several die geometric variables.
Table 2 lists variables which should be considered in determining die
entrance losses for food materials. The die hole center spacing (s) is
the distance between each hole on a concentric circle configuration as
shown in Figure 5. The die inset angle (a) and the conduit entrance
diameter, Dc’ are defined in Figure 6.

No published literature was found for assessment of APent for
non-circular holes. For initial development, the author proposes that,
the shape factor, F, along with the hydraulic radius would be sufficient 0
to describe the effect of noncircular cross-sections on entrance

pressure.

l4

 

 

 

1-5 ' I . . I . I ' I I I
A EXTENDED SEMI CIRCLE
. e EXTENDED CIRCLE
CI RECTANGLE
1.0— mf‘°\‘9
e
Ara—A
- ////////;’,B—'E;_—-4J [3
a—"'— -—~
2%.:
0.5-4 /0
CI
0.0 I I l l I I I I I I
0.0 O 2 O 4 0.6 O 8 l 0

Figure 3.

vs.shape factor, F, for non-Newtonian flow through irregular

Flow coefficient, f , (from Michaeli, 1984)

cross-sectioned die holes.

 

15

 

\

 

 

Die \ /
cross section \-"
I‘F--‘l)c, --4F'
I 01
Shape Factor F =
00

Figure 4. Definition of die hole shape factor, F.

l6.

 

(Assume mult ple rows are spaced 5 distance)

Figure 5. Definition of die hole spacing, s.

 

 

r—ifi

—

 

Barrel as I fifi_ Die

‘

Figure 6. Definition of die entrance angle, a, and conduit entrance
diameter, DC.

17

Table 2. variables affecting entrance pressure drop in food extruder

dies

e Veri e
Entrance pressure loss of die assembly

Total volumetric flow rate

Die_£egnes:y
# of die holes

Hydraulic radius of die holes

Shape factor of die holes

Diameter of upstream conduit at die entrance
Die hole center spacing

Die entrance angle

e i 'e
Shear thinning flow behavior index
Power law consistency coefficent
Characteristic time constant

Density of fluid at die entrance

 

 

Notation Dimensions

AP ML’lt'2
ent

Q L3t-1

nd ---

rh L

F ---

D L
c

s L

a deg

n ---

m ML'lcz'n

A t

p ML-3

18

ELASTICITY EQUATIONS

Little is understood about the influence of elastic properties of
viscoelastic fluids on entry pressure drop (Boger, 1982). Some authors
report that entrance losses for viscoelastic fluids may in fact be less
than Newtonian cases (Black et al., 1975; Tanner, 1976; Yiriyayuthakorn
and Caswell, 1980 (from Boger, 1982)).

Elastic fluids are generally characterized by the Weissenberg or

Deborah numbers

>-
d

We - —— (14)

De - -—" (15)

The author elected to use the Weissenberg number as it is more commonly
seen in published literature. The characteristic diameter, D, is
assumed to be the die diameter.

Boger (1982) defines a characteristic time constant, A by

A - —-l—— (16)

Huang and White (1980) used this equation in their investigation of
the relationship between jet swell and the Weissenberg number. Eqn (16)
is further reduced by relating N1 to F. Analysis of plastic polymer
data from Crater and Cuculo (1984) and White and Roman (1976) (Figure 7)
shows that the primary normal stress difference (N1) of some polymers
can also be approximated by a power law function of the Newtonian shear

rate as

N1 (PA)

6

 

U III I '7"! U U U" I I ‘j' f Ur‘l U

19

X?”

.96 PET 285 C
.96 PET 265 C
PS 180 C
PP 180 C
S-HDPE 180 C
.lr-HDPE 180 C

10‘1 100 101 102 103, ' 104
APPARENT SHEAR RATE, I‘,(SEc-1)

OD>°¢9

Figure 7. Primary normal stress difference (N1) vs. shear

rate data for various polymers studied by Crater
and Cuculo (1984) and White and Roman (1976).

 

20

N1 - K mp (17)
where p was found to range from 0.9 to 1.1. Values of K from data of
White and Roman (1976) ranged from 10,000-30,000 Pa-secp for various
polymers at 180 oC. Data from Crater and Cuculo (1984) yielded K values
of 2000 and 5000 Pa-secp for polyethylene at temperatures of 285 oC and
265 °C, respectively, for shear rates of 200-2000 sec'l. Substituting

equations (6),(8),(9) and (17) into (16) gives

- -.-_ ‘Tm—T

Q ]p-n-1

K 3
A - 2“‘u (18)

2 {311+} ] n+1
m
4n

 

Accurate measurement of N1 vs. F data for extruded doughs is very
difficult due to the presence of a yield stress and the need to simulate
extrusion process conditions, e.g. temperature, shear rate and pressure,
during measurement. For this reason a different method for estimating
the time constant is suggested.

An alternative pseudo material time constant, Aa, based on a
treatise by Williams (1977), is defined as the first order time decay
constant for jet swell (Figure 8). The Aa is related to the jet swell

ratio (fl) and die residence time (t) by the following,

fl - 3m + (fio- 3,) exp <-t/Aa> (19)

where 5 is the ratio of the instantaneous swell to the die diameter and
flo and ,6co are the swell ratio at zero and infinite die lengths,
respectively. B vs. residence time data are obtained by varying die L/D

and measuring swell while holding Q and D constant.

21

Swell
Ratio

 

 

 

Die residence time

Figure 8. Schematic of proposed method (Williams, 1977)
for determining A8 (at constant shear rate and hole diameter).

22

DIMENSIONAL ANALYSIS

Dimensional analysis was chosen for quantifying APent because it
most efficiently incorporates numerous parameters such as those listed
in Table 2, and does not require solution of complex velocity profiles
as would be necessary if the equations of motion were used. Astarita
(1974) addresses theoretical limitations of using dimensional analysis
to characterize flow of viscoelastic fluids when the same fluid is used
for model and prototype scales. He implied that the only means by which i
all dimensional analysis criteria can be met is to use homologous non-

Newtonian fluids, that is, two materials characterized by the same
dimensionless operator of deformation histories but of unequal viscosity
parameters.

The author elected to pursue a dimensional analysis approach despite

the position presented by Astarita (1974) because this approach appears
to be the only practical method for modeling die flow phenomena for food
materials. Also, the relative elasticity of food materials is unknown.
As previously mentioned, the elasticity of food materials is assumed to
be much less than the elasticity of polymers and hence may not cause the
significant error that Astarita (1974) found for highly elastic
materials.

The desired relationship resulting from dimensional analysis of the

parameters in Table 2 is

APent - f(Q. nd. rh. F. Dc. 5. a. m. n. A. p) (20)
Eqn. (20) is reduced by the Buckingham Pi Theorem which states that the
number of dimensionless and independent quantities required to express a

relationship among the variables in any phenomena is equal to the number

23

of quantities involved, minus the number of dimensions in which these
quantities may be measured (Murphy, 1950). In this study there are
three dimensions: length, mass and time. The resulting number of Pi
terms developed from the variables of Table 2 is 9 (12-3).

Nine H terms (Table 3) were derived to yield relationships
considered meaningful in fluid mechanics. The «1 term is based on the
Euler number, the ratio of pressure forces to inertial forces. In this
case, the pressure forces are entrance pressure forces.

The «2 term is a simplified Reynold's number, the ratio of inertial
forces to viscous forces. The Newtonian viscosity in the standard
Reynold's number is replaced with the apparent viscosity of a Power law
fluid evaluated at the wall. In place of the Power law model,
another fluid model may be used to find an expression for the apparent
viscosity in £2.

The «5 term is the Rabinowitsch correction factor and the «6 term is
the die contraction ratio. The "8 term was based on the Weissenberg
number and was defined to ensure a non-zero number (1.0) for inelastic
fluids having a Weissenberg number at or near zero. Likewise «9 was
defined to be non-zero for single hole dies. n3,n4,n7, and «9 describe
die geometry.

Assuming the H terms are differentiable over the range of the
variables considered, then the product solution method (Murphy, 1950)

can be used to express n as

1

b b b b b b b b
2 3 4 5 6 7 8 9
«1 - a (”2) (”3) ("4) ("5) ("6) (W7) ("8) («9) (21)
This form of the equation significantly reduces the number of

experimental runs necessary to determine empirical constants.

Independence of the H terms is verified in Appendix A.

24

Table 3. List of n terms

 

 

H Term Description
2 4 Entrance Euler number - ratio of
_ 16 nd rh APe t entrance pressure forces to iner-
1r1 2 ”‘3' tial forces (based on entrance
p Q pressure loss)
«2 - p 0 Simplified Reynold's number
undrh; analogous to Generalized Re
where

n _ m 0 n-l [3n+1]n-1
(7 ' lwaII) 21mdrh3 4“

for a Power law fluid.

«3 - nd # holes in die head
«4 - F Shape Factor

«5 - (3n+l)/(4n) Rabinowitsch Correction Factor

16nr2
n6 - g h Ratio of the total die hole area
D 2 to the entry conduit area
c

«7 - a Die entrance angle

"8 - 1 + -—-A—Q-—§ 1 + Weissenberg number

16w ndrh
n - s + 1 Die hole center spacing

‘

CHAPTER IV.

EXPERIMENTAL PROCEDURES

In order to verify the model, data from published literature were
chosen to develop initial empirical constants, then experimental data
were collected for various food materials and checked against the model.
Data from six published sources (Table 4) were chosen for initial

development. Published data for APen vs. Q were mainly from the

t
plastics industry and did not incorporate effects for irregular shapes
nor multiple die holes. Therefore, experimental data were also

collected to develop empirical constants for food materials flowing

through irregularly shaped and multiple die holes.

EXPERIMENTAL DESIGN

A Baker Perkins 50mm twin-screw extruder (TSE) and an Instron (model
#4202) capillary rheometer (CR) were used to conduct extrusion die
experiments. The TSE was chosen because of its increasing popularity in
the food industry. In addition, due to the fact that the TSE is pilot
plant size, data collected on this machine should give model parameters
which can be realistically used in the food industry. Also, as the
extruder is a twin-screw, its operating point is less altered by die
changes than for a single-screw extruder. It is important that the same
food product be delivered to all dies in order to measure effects of the
various die changes without the compounding effects of varying

rheological properties.

25

I. .u...
II
A

26

TABLE 4. Data frml Literature Sources (Raw Data given in.Appendix Q)

.72 PE Terephthalate at 285°C

.72 PE Terephthalate at 265°C

.96 PE Terephthalate at 285°C

.96 PE Terephthalate at 265°C

Polyethylene (PE)

HDPE(1)

LDPE(2)

Soy Dough 32% MC.
Soy Dough 30% MC.
Soy Dough 34% MC.

Soy Dough 35% MC.

so °C
120 °C
24 °C

160 °C

(1) High density polyethylene

(2) Low density polyethylene

Crater and Cuculo (1984)
Crater and Cuculo (1984)
Crater and Cuculo (1984)
Crater and Cuculo (1984)
Jasberg et al. (1981)
Han (1973)

Han (1973)

Remsen and Clark (1978)
Jasberg et a1. (1981)
Morgan (1979)

Morgan (1979)

150-1250
150-1250
300-1600
100-1000
200-5000
100-600
100-800
3-150
100-3000
1-19

47-950

_._4

27

The CR was selected because of its ability to maintain constant
temperature. Data collected with the CR can be used to model effects of
moisture content,temperature, shear rate and thermal kinetics as shown
by Morgan (1979) and Mackey et a1. (1987). However, the CR is limited
to the case of single hole dies and zero shear history. Hence, data
from the TSE and CR compliment each other well. Rheological properties
were changed by varying shear rate, moisture content, extrusion

p4

temperature and thermal history.

“he. .1

Three materials (soy polysaccharide (SPS), potato dough and
defatted soy dough.) were selected for experimental tests to verify the
model for a wide range of food materials. Criteria of the test
materials were that one be a starch based dough, one a protein based
dough, and another a food type dough which does not undergo significant
physicochemical changes during extrusion. Potato flour, defatted soy
flour and soy polysaccharide (SPS) were chosen to meet these criteria,
respectively. Potato flour (Lamb-Weston Company Portland, OR) was
chosen as the starch based material because it was pregelatinized and
hence would not significantly undergo further gelatinization during
experimentation (Mackey et al., 1987). Pregelatinization of the starch
dough was desired in order that the rheological properties of the dough
would not have to be adjusted for gelatinization effects. Defatted soy
flour was selected because denaturation effects of this dough occurred
only above 70°C and could be adjusted for by a model developed by Morgan
(1979). Soyafluff 200w soy flour from Central Soya (Ft. Wayne, IN), was
used for preparing soy doughs. Soy polysaccharide (SPS) was chosen as
an inert type food substance as it shows no significant kinetic effects
due to gelatinization or denaturation under normal extrusion conditions.
SPS was donated by the Protein Technology Division of the Ralston Purina

Company (St. Louis, MO).

28

Tables 5 and 6 outline the experimental design used in this study.

Two duplications of tests on SPS were conducted on the capillary

rheometer and TSE. Spot check replications were made for potato flour

on the TSE at the same RPM and most tests were duplicated at two

different RPMs. Defatted soy flour was held at a constant pressure for

a minimum of three to four minutes before measurements were recorded.

TABLE 5. Experimental design for capillary rheometer

52312211sasshari§e

7‘. 1?:
L51

1. _!‘I
1‘ .

 

 

 

 

 

Temperature Crossheid Die (2) Die Moisture
of capilla Speed Diameter Length Content
Rheomeger ( C) (mmfimin) (cm), (cm) (%)
25 100,300,500 0.15875 O.8,5.0 60
0.3175 5.2
25,50,70 100,300,500 0.15875 0.8,5.0 50,70
0.3175 5.2
(l) 2 < r < 1500 s'1
(2) 2 < L/D < 35

29

TABLE 6. Experimental design for twin screw-extruder

DIE(1)

 

 

 

 

 

INGREDIENT BARREL SCREW FLOW MOI STURE REPS
TEMP SPEED RATE CONTENT
(°C) (rpm) (kg/hr) (% wet basis
DEFATTED Q:L,S 155 150 31.8,49.9, 56
SOY 8TH:L,S 280,350 68.1
DOUGH
Q:L,S 55,200 280 31.8,49.9 56
8TH:L,S 68.1
QzM 155 280 31.8,49.9 56
8TH:M 68.1
POTATO RECT. 12.8 100,300 31.8,49.9 50
DOUGH Q:L,S 68.1
8TH: ,
3H:L,S
FF:L,S
SPS Q:M,S 12.8 350 31.8,49.9 64.8
DOUGH 8TH:L,S 68.1
3H:L,S
FF.L,S
RECT:L,S
21H:S
3 SLIT: S
Q:M,S 12.8 240 31.8,49.9 58.6
8TH:L,S 68.1
3H:L,S
FF:L,S
RECT:L,S
21H:S
3 SLIT: S

 

 

(1) Die notation and dimensions given in Table 7.

30

CAPILLARY RHEOMETER PROCEDURES

The capillary rheometer was used to collect data for determining
viscosity as a function of temperature. The viscosity-temperature
relationship is needed to adjust twin-screw extruder data to an average
die temperature for each material. Capillary rheometry was performed on
SPS; previous data for defatted soy dough and potato dough had been
collected and analyzed by Morgan (1978) and Mackey et a1. (1986) [1
respectively. f

The CR was preheated to a constant barrel temperature for
approximately 30 to 60 minutes before testing. Tests were conducted by
rapidly loading the CR by dropping twin-screw extruded SPS strips into
the CR barrel and tamping with a ramrod until the barrel was full. The
sample was then compressed at 500 mm/min with the plunger until
extrudate appeared at the die (Figure 9). As soon as product began to
exit the die, the plunger was immediately stopped, and the heating time
began. Time required for sample loading and precompression was typically
30—60 seconds. Morgan (1979) estimated that a two minute heating time
after the material was precompressed was required to bring the material
center temperature to within one degree celcius of the wall temperature.
After the two minute heating time was reached, the sample was then
extruded at a constant plunger velocity. Three constant plunger
velocities were used per sample loading, (500, 300, and 100 mm/min) thus
giving a range of shear rates. A ten KN Instron cross-head load cell
measured the plunger force as a function of time, recorded by an XY
chart recorder. The resulting force-velocity (Fxh- Vxh) data could then
be converted to AP vs. Q and 7w vs. F data using the CR barrel and die

dimensions (Appendix C).

U
H

\\\\\\\<§

z”RRYRRRRV\K\\\\\\\\\\§

//////1
\/\/\M\
s\”“\\1

 

PLUNGER ROD

EXTRUDER
BARREL———

 

 

 

CONED TEFLON
PLUG

 

FLOUR
MELT

 

\\\\\\\\\\\I\\\\\\\s

0 o 5 o. //
.05 :‘ra°°° 'ggo /
no. In ‘6‘ e

on

 

 

go
Q
0

ME CAP

 

°° '000
o °e
OOOOOCQQ.G ‘0

DIE v/z/

 

 

 

 

 

/
L3.

 

rs

Swmhl

 

EXTRUDATE

Figure 9. Illustration of capillary extrusion process.

32

TWIN SCREW EXTRUSION PROCEDURES
TSE SAMPLE PREPARATION

As the TSE is an excellent mixer of solids and liquids, there was no
need to pre-mix the test doughs. Flour was metered directly into the
extruder by means of a K-Tron feeder and water was injected at a
downstream distance of one L/D from the dry feed port. The water EA
injection pump and K-Tron feeder were calibrated to determine water (
injection rate and flour feed rate at given set points of the pump and
feeder respectively, and the resulting calibrations were used to
preselect moisture content for a given product rate. A calibration
program for determining moisture content and product rate given feeder

and injection pump set points is given in Appendix D.

TSE EXTRUSION TECHNIQUES

Brass extruder dies (Table 7) were mounted in pairs in a Baker
Perkins twin hole die head. Die temperature was recorded with an Omega
digital thermometer (model HH-70TF) with a veterinarian hypodermic
needle used as a thermocouple probe The probe was inserted through a
die hole to a specified distance. Preliminary extrusion runs were made
to determine screw configurations, barrel temperatures and product
moisture contents which gave a motor load of less than 70% and a non-
puffed extrudate. The non-puffing criterion was specified to ensure
that there was no flashing inside the extruder die, because the flashing
may cause significant end effect errors. Screw configurations for each

test material are listed in Table 8.

33

TABLE 7. Thin-screw extruder die dimensions(1)

 

 

DIE ENTRANCE LENGTH DIAMETER NUMBER
NOTATION ANGLE (cm) (cm) OF HOLES
(degrees)
Q:L(Z) 90 5.16 0.635 1
Q:M 90 2.625 0.635 1
0:8 90 .642 0.635 1
8TH:L 90 2.6 0.3175 1
8TH:M 90 1.245 0.3175 1
8TH'S 90 0.4 0.3175 1
FF:L 90 2.67 0.3175 1
FF:S 90 .405 0.3175 1
3H:L 90 2.58 0.3175 3
3H:S 90 0.37 0.3175 3
RECT:L 180 3.18 .625x.318 1
RECT:S 180 0.2 .625x.318 l

(1) Dimensions per die. Dies were mounted in pairs.
(2) The shorthand die notation names signify the following:

Q: large circular diameter

8th: narrow circular diameter
FF: full flange entry die

3H: three hole die

RECT: rectangular cross section
L: Long die length

M: Medium die length

S: Short die lengths

Figures of cross sections for dies without 180 degree entrance angle are
given in appendix B.

34

Table 8. Screw configurations of MPF-SOD/ZS Baker-Perkins twin-screw
extruder.

MATERIAL: POTATO DEFATTED SOY SPS
EXTRUDER L/D: 15 15 15

SCREW CONFIGURATION

LENGTH SCREW LENGTH SCREW LENGTH SCREW
(cm) TYPE (cm) TYPE (cm) TYPE

17.78 FS 17.78 FS 20.32 FS
7.62 30F 7.62 30F 6.35 30F
7.62 FS 7.62 FS 5.08 FS
5.08 30F 5.08 30F 3.81 30F
2.54 45F 5.08 FS 7.62 FS
5.08 FS 3.81 30F 3.81 30F
6.35 30F 8.89 30F 5.08 FS
5.08 FS 27.94 FS 5.08 30F
5.08 30F 17.78 SL
12.7 SL

NOTATION

FS - Feed Screw

30F - 30 degrees Forwarding Paddles
45F - 45 degrees Forwarding Paddles
SL - Single Lead screws

 

Different extrusion techniques were used for each material. Potato
flour was extruded at various RPMs to determine effects of work input on
extrudate properties. Water was injected by means of a Bran & Lubbe
injection pump (type w-p33) and pressure was measured with a Gentran 0-
3000 PSI (0-20684 KPa) transducer (mode1# GT75K-3M) and recorded with a
Gentran digital readout. Temperature was measured by holding the
thermocouple probe through the die holes at a distance of 2.54 cm from
the extruder screw tips. Product rates were altered for each die while
the die was in place. The extruder was shut down while dies were
changed.

SPS was extruded at a low RPM to decrease work input and
temperature of the material. Water was injected with a Cole Parmer
parastolic pump (model# 7015) attached to a variable speed motor.

Pressure was recorded with the Gentran transducer and digital readout.

IA 523‘ ,.
rd!

35

Temperature was recorded in the same manner as during potato dough
extrusion. Product rates for a given calibrated moisture content were
altered for each die and only the flour feeder was shut off while the
dies were changed. Experiments for each die were repeated at each
calibrated moisture content.

Defatted soy flour was extruded at a low RPM to decrease work input
and temperature, yet at a high enough RPM to ensure the flour would not
back up in the feed hopper. Water was injected with the Bran & Lubbe
Pump. Temperature was recorded by inserting the thermocouple probe to
the die entrance, and pressure was measured with a Dynisco 0-500 PSI
(0-3447 KPa) transducer (model# PT415-SC-6) and recorded with an Omega
strip chart recorder (model# RD2020). The product rate was held
constant and pressure measurements were made on all dies before the
product rate was changed. During die changes the feeder was shut off
long enough to remove the die head bolts, then immediately turned back
on. The die head was remounted with the extruder operating at

calibrated production rate.

MOISTURE CONTENT ANALYSIS

A11 moisture contents were determined by oven drying the material
at 100°C for 24 hours (ASAE std. 8358). Samples of material were placed
in small aluminum weighing dishes and dried in a Central Scientific Co.
oven (Cat. # 95100 A). Three moisture checks were taken on the CR
samples and one on the TSE samples. However, as the extruder was
operated at the same calibrated moisture content for several dies,
several TSE samples of the same calibrated moisture content were

actually taken.

‘. .‘bu-“.!:I

36

DATA ANALYSIS

Flow through the extruder die was assumed to be viscometric
capillary flow (steady axial laminar flow of an incompressible fluid)
and AP vs. Q data were analyzed by the procedures outlined by Darby

(1976) to obtain APent and rw vs. 1 data. Eqn. 4 can be rearranged as

r - APdholeR (22)

w 2L

I II. ”‘A‘Ol'

Where AP is expressed as AP minus AP . For noncircular
dhole e

T nt

holes, shear stress was assumed to be the same as rw for circular holes
for the same extrusion conditions. fw was not calculated for
noncircular holes as it is a function of radius, and the relationship
between 7w and hydraulic radius requires further study before accurate
computation for noncircular holes can be made.

APT was measured for all experimental data. APent was determined
by Bagley's technique (Bagley, 1957), by conducting extrusion tests with
dies of the same diameter but different lengths and plotting the values
of AP vs. L/D of the die for constant F. For fully developed non-slip

T

flow, AP is linearly related to die L/D with end effects pressure drop,

T
APe, being the intercept at L/D - 0 (Figure 10). End effects pressure
drop is a combination of entrance and exit pressure drop but, as
previously discussed, exit pressure drop is assumed to be negligible
compared to entrance pressure drop. To ensure accurate measurement of
APent’ dies were chosen to be as short as possible to decrease the
extrapolation distance, yet long enough such that flow was fully
developed within the die. Collins and Schowalter (1963) give a

prediction for entrance length vs. flow behavior index, n, for circular

contractions (Figure 11). For low Reynold's numbers (less than one)

37

A /‘

 

l
/’// :3
////
Akfar //// ‘/’/’/’ I}!
// // /r
// z’
/ / //
// / /
APe / / /
\/ ,&
//’:/:>%§:Jz’/'
/ / //
z’ z/ z’
z’ /’ ./’ _J,
Lem—v L/R

 

Figure 10. Schematic of end effects for AP vs.r through
dies of same diameter, different lengths. A and L /R
correspond to the y-intercept and x-intercepf of eacheshear
rate line respectively (F3 > F2 > F1).

38

 

 

0.0

 

 

0.2 0.4 0.6 0.8 1-0

Figure 11. Relationship of entry length and Power law index
(Analysis by Collins and Schowalter (1963)).

39

as occur in food extruder dies, L/D of one is well within the fully
developed region. Measurement of the jet swell ratio, 6', for assessing
the elastic time constant (Eqn. 19) was conducted by use of close-up

photography using three dies of constant diameter but different lengths.

SLIP

An error which may occur during the measurement of rheological
properties in an extruder die is slip, which is a non-zero velocity of
material at the die wall. This is a sliding surface phenomenon. All
previous development assumes a zero velocity at the capillary wall. The
presence of slip causes an error in measuring F. As die AP vs. F data
are directly related to 1w vs. 1, the error in F induced by slip would
translate into erroneous rheological data. Other authors have found the
occurance of slip prevalent in their research on single screw extrusion
of polymer melts (Worth and Parnaby, 1977; Mennig, 1976). Methods for

analyzing for slip are given in Appendix E.

GENERALIZED VISCOSITY MODELS

During TSE extrusion, changes in die geometry induces changes in
thermal and shear history and hence protein denaturation and/or starch
gelatinization. This in turn directly affects material viscosity at the
die. All data analysis methods presented in this study assume constant
viscosity from die to die. Hence, a technique is needed to account for
changes in die viscosity due to variation in die temperature and TSE
process histories. This was accomplished by the use of a generalized
viscosity model similar to that presented by Morgan et a1. (1987) for

defatted soy flour. The model by Morgan et a1. (1987) predicts apparent

40

viscosity as a function of moisture content, shear rate, temperature and

an integral temperature-time history defined as

t
W(T,t) - IT(t) eAE/RT“) dt; T: (T(t) < Tt

O

h) - O (23)
where the threshhold temperature is 70°C (denaturation temperature for
protein). Morgan et a1. (1987) developed a generalized viscosity model

based the Heinz Casson flow model. Adapting the flow model to a Power

law fluid model yields:

1_A4

"(V’TPMC9W) -

-1 -1
AEx[T i-TR ]+b[MC-MCR]

R n-l

¢e m1 [1 + 52(1-MC)°‘(1-e'k w(T't)

)“I (24)

Bagley's technique of determining entrance pressure assumes
constant viscosity of material for all die lengths. The generalized
viscosity model used to adjust die pressure for changes in viscosity due

to temperature and moisture effects is:

AE2[T'1+TR'1]+b[MC-MCR]
AP - AP R

adj obse (25)
Eqn. (25) assumes extrusion temperatures below the denaturation
threshhold temperature for protein doughs and neglects any viscosity
Changes due to gelatinization of starch doughs.

Because of lack of available information on shear history effects

on viscosity of extruded protein or starch doughs, no attempt was made

41

to adjust AP data for variations in shear history within the TSE.

However, work input to the material was calculated for each test as:

W.I. - 0.00336 x % quRPM (kw-hr/kg) (26)
M

for a Baker Perkins 50mm twin screw extruder where % Tq is the percent

of maximum full load torque.

DATA ANALYSIS TECHNIQUES

Because of the difficulties maintaining a constant extrudate
viscosity from the TSE extruder, a large amount of error in its
measurement is expected. Much error is due to the difficulty of
measuring die temperature accurately, and inaccurate pressure recordings
due to slip in the die. In order to reduce effects of error, a standard
was determined for objectively screening data for analysis. The
coefficient of variance was chosen for this standard even though only
two or three replications of each point were taken. Since there are no
statistical guidelines for this method, the coefficient of variance was
used strictly as an arbitrary standard with no statistical significance.
All pressure data replications with a coefficient of variance greater
than 20 percent after adjusting for temperature were excluded from
analysis. Also, all data with a coefficient of variance of greater than
20 percent for fw calculated from long and short dies were excluded from
the analysis. Data with Tw at highest F lower than the 7w at the lowest
F were excluded from the analysis.

Rheological properties of all data were determined by SAS analysis
(SAS, version 5). SAS programs for analyzing data for the CR and the

TSE are listed in appendices F and C respectively.

CHAPTER V.

RESULTS AND DISCUSSION

EXPERIMENTAL DATA

RHEOLOGICAL PARAMETERS OF CAPILLARY RHEOMETER DATA

Rheological properties including a temperature correction factor
were determined by using the capillary rheometer. Plunger force at the
die, Fxh’ vs cross-head velocity, Vxh data for SP8 are given in Appendix
H. Calculated 'w vs. F values for SP8 at given moisture contents and
temperatures are given in Appendix I. For a constant moisture content
and temperature, data from the 0.15875 cm and 0.3175 cm diameter dies
were combined to give a wide range of shear rates. Plots of 7w vs. F
for 50% and 60% MC are given in Figures 12 and 13 respectively. As the
shear stress data for both die diameters overlayed each other well, it
was assumed that slip was insignificant.

The Power-law consistency coefficient, m, and the flow behavior
index, n, were computed from Appendix I data assuming that over a small
range of moisture content and temperature, n is not a function of
moisture content or temperature (Harper, 1981). Values for computed m
and n from the 50% and 60% MC SPS data are given in Table 9. Variation
in n was insignificant and hence an average n value was used. CR data
for the 70% MC SPS had significant scatter and hence, calculation of m

and n values from the data were not made.

42

7w (kPo)

43

 

1000 . I . 1 i

 

 

 

 

4: €
‘3 '1
.
i 0 SP8 50% MC, 25%, r2=.95 _
A SPS 50% MC, 50°C, r2=.9o
10 a SIDS 50% MC, 700C, r2=.93
I l I I l
10 100 1000 1E+04

7 (8")

Figure 12. Shear stress vs.shear rate for SP8 extruded with
a capillary rheometer (data points are means of four
observations).

Tw (kPo)

44

1000 I I T T I

 

LILII
.1111

l
I
i

l
l

l
l

. [1].!

l

1
I

0 SP3 60% MC,'250C, r2=.96
I I I

10 , ,
10 I 00 1000 1E-+04

 

 

 

7 (5")

Figure 13. Shear stress vs shear rate for SP5 extruded with
a capillary rheometer (Data points are means of four
observations).

45

Table 9. Power law parameters for SP5 determined by using a capillary

 

rheometer
MC TEMP m n r2
(%) (,C) (KPa)
50 25 86 .22 0.95
50 50 64.4 .19 0.90
50 70 30.4 .28 0.93
60 25 32.2 .25 0.96

 

The activation energy, Ev’ was computed to be 4520 cal/gmol which
compares to Ev values of 4500-8500 cal/gmol for food materials (Harper,
1981). A plot of log m vs l/T is given in Figure 14. No moisture
correction term was calculated as not enough data were available, and
this term was not needed for correcting extrusion data. Resulting
general viscosity parameters (Eqn. 24) are given in Table 10 along with
those given by Mackey et a1. (1987) for potato flour, and Morgan et a1.
(1987) for defatted soy flour. A plot of log n vs. l/T for shear rate
of 100 sec.1 for potato flour is given in Figure 15. The observed data
points for n vs. 1/T (Figure 15) were used for adjusting the TSE potato

data for temperature using Eqn. 25.

Table 10. Rheological properties of extruded.materials determined.by
using a capillary rheometer

 

Matl MC T m n r2 E b
ref ref v
(%) (0C) (KPa) (cal/gmol)
sps 50.0 50 64.4 .23 .9 4520 --
PF(1) 35.0 60 34.9 .25 -- 8729 -8.63
DSF(2) 34.0 68 8.58 .5 -- 6800 -21

(1) Potato Dough (Mackey et al., 1987)
(2) Defatted soy dough (Morgan et al., 1987), Power law approximation

 

m (kPo)

46-

 

 

 

". .1
e O

1

. m _ f, e<2275/T)}
a r2 - 0.88 ..
AEv - 4520 cal/gmol
10 . , I I .
2.70 2.90 3.10 3.30

l/T x10 3 (OK-1)
Figure 14. Power law consistency coefficient, m, vs.l/T for SPS (50% MC)

 

3.50

extruded with a capillary rheometer (data points are means of four

observations).

APPARENT VISCOSITY

AT 100 SEC"1

7) l(l()

'47

 

IE+O4 I I

1000:
7 ’ 4393/T)
,9 "100 ' f‘ e I -
r2 - 0.945
‘ AEv - 8729 cal/gmol I
ICDC)

1111

 

 

 

I I I I
2.7 2.8 2.9 3.0 3.1

I I
3.2 3.3

INVERSE ABSOLUTE TEMPERATURE
1/Tx103 0<“)

Figure 15. n vs.l/T for potato dough (33.7% MC)

(Apparent viscosity adjusted to 7 - 100 sec- )

(Mackey et a1.

1986).

 

48

TWIN-SCREW EXTRUDER OPERATION

Moisture content/product rate calibration values for SPS and
defatted soy flour (Table 11) indicate that the calibrated moisture
contents for each product rate were the same, although they were below
the predicted moisture content. Moisture contents of extruded potato
flour were not obtained as the moisture samples case hardened upon oven
drying, causing the release of moisture from the samples to be
impossible. From the moisture content prediction results of the
defatted soy and SPS calibrations (Table 11), it was assumed that
correction of pressure for moisture content of all three materials was
unnecessary. The moisture content of potato extrudate was assumed to be
50 percent as Table 11 indicates that the moisture content calibrations
of both SPS and defatted soy dough predicted within four percent of
their measured moisture contents. The measured product rates did not
fluctuate significantly during the extrusion runs and hence, measured
product rates were used in the calculation of shear rate. By comparing
the moisture content fluctuation of SP3 and soy dough (Table 11) it is
concluded that use of the parastolic pumps gave a much more stable water
injection rate.

Use of a strip chart recorder as opposed to a digital pressure
readout for recording pressure is highly recommended for pressure
measurement as the extruder operator can easily see when the die
pressure is stable. Also, use of a pressure transducer with a maximum
range just above the maximum pressures measured would increase the

accuracy of the pressure readings.

49

Table 11. Moisture content and product rate calibration.values for SPS
and defatted soy flour.

SPS CALIBRATION

 

 

 

MC M_C(1) C.V. (1) Sic-2(2) C.V. 91(3) M (3) c.v.'
pred MC pred meas

(’3) (is) (is) (is) (is) (kg/S) (kg/S) (is)
58.6 57.3 1.1 58.0 1.7 0.0088 0.009 2.9
58.6 57.9 1.4 58.0 1.7 0.0138 0.0142 1.9
58.6 58.9 1.5 58.0 1.7 0.0189 0.0195 2.9
64.8 63.8 1.6 64.3 1.5 0.0088 0.0089 5.0
64.8 64.3 1.4 64.3 1.5 0.0138 0.014 1.7
64.8 64.8 1.4 64.3 1.5 0.0189 0.0195 1.2
DEFATTED SOY DOUGH CALIBRATION

—(1) (l) —(2) '(3) '(3) -
MCpred MC C.V.MC MC C.V. Mpred Mmeas C.V.
(’8) (is) (’8) (‘8) (’3) (KG/S) (KG/S) (’3)
44 41.6 2.3 40.0 4.8 0.0088 0.0103 7.1
44 38.9 2.4 40.0 4.8 0.0113 0.0124 4.2
44 40.2 4.6 40.0 4.8 0.0138 0.0152 2.7
44 38.3 2.5 40.0 4.8 0.0151 0.0171 1.7
44 41.0 4.6 40.0 4.8 0.0176 0.0191 2.5

 

(1) Average MC (wet basis) for each predicted MC and product rate, M.
(2) Average MC (wet basis) for each predicted MC (all product rates).

(3) Product rate measured as mass per 30 sec.

(C.V. is coefficient of variance based on 60 to 80 data points)

50

RHEOLOGICAL PROPERTIES OF TSE DATA

Appendices J to L give the raw data for extruded SPS, potato flour,
and defatted soy flour respectively. Barrel temperatures were below the
denaturation threshhold temperature (70°C) for defatted soy flour, hence
pressure need not be corrected for temperature-time history. In
order to reduce viscosity change due to shear history, all potato dough
data with work inputs above 0.0002 kw-hr/kg were assumed to be altered
by high viscous dissipation and shear effects and were thus excluded
from the analysis. This accounted for about five percent of the potato
data. Work input did not vary significantly during soy dough or SPS
extrusion.

Shear stress vs. shear rate values are given in Appendices M to P
and are plotted in Figures 16 to 19 with the corresponding rheological
model determined by use of the capillary rheometer. Each rw value is
the combination of four data points: two duplications of two die
lengths. Table 12 gives a summary of Power law coefficients for each
extruded material. Viscosity was adjusted to the midrange of the

measured extruder die temperatures.

TABLE 12. Rheological properties of twin-screw extruder data

 

2 1 1
MATL MCRef TRef m n r m(CR) m(CR)
(8) (°C) (KPa)
SPS 58.0 66.6 132.8 .27 0.80 32 .23
SPS 64.3 59.3 76.7 .28 0.93 -- .23
POTATO 50 54.4 0.501 .85 0.82 11 .25
DSF 40.0 46.8 40.8 .23 0.60 10.3 .5

 

l. Capillary rheometer values adjusted to twin-screw extruder moisture
content and temperature. (Missing m value for 64.3 % MC SPS due to lack
of moisture correction factor for SPS)

Tw (kPo)

51

 

IE+O42 x I I .
5000i L
‘ rw - 132.887'27 (KPa) r2- .80 ~
I()()C)‘: -:
2 o A 2
500~ ° 3
T _
100_ rw - 327'23 (KPa) _
507 ,,4~*' v FFDE 1
‘ A. §3ti ENE: ‘
‘ D 8th DIE ‘

IO 0 Q DIE

 

 

I
100 1000

7 (5")

 

I E+O4

Figure 16. Shear stress vs shear rate for SP8 (58% MC, 66.6OC)

(data points are means of four observations).
-- indicates twin screw extruder prediction
--- indicates capillary rheometer prediction

7w (kPo)

52

 

 

 

IOOO I I I I I I I I I
II //i:/' -
500- . ‘ —
j . 0 1w - 76.77;:8(KPa) q
. r "' .
v FF DIE
A 3H DIE
I 8th DIE
100 0 Q DIE
I I I I I l I I
100 1000
7 (sec"‘)

 

IE+O4

Figure 17. Shear stress vs.shear rate for SP8 (64.3% MC, 59.3OC)
Twin screw extruder data (data points are means of four

observations).

‘rw (kPo)

53

 

I 000 I I I I I I I“"""'T—I-'

500- /// _
1w - .5017'85(KPa) I

r2 - .82

l!!!

  

l
" ‘t.’ Ti'rrfli

I

‘ A 8th DIE ~
I. .3II [3H:
0 FF DIE

 

 

 

10 . .’,.,
100 1000

I

IE+O4

7 (seC"‘)

Figure 18. Sheag stress vs.shear rate for potato dough

(MC-50%, T-Sh.h C) (data points are means of two to four
observations).

-- indicates twin screw extruder prediction

--- indicates capillary rheometer prediction (Mackey et al., 1987)

7w (kPo)

'54

 

‘I j
500“ rw - 40.87'23 (KPa) —
q 2 "

r -.50 ‘

 

/ rw - 10.37'S (KPa)

C] Q DIE

_ 0 8th DIE 4
0 3H DIE
A

 

 

FF DIE
IO . . . ,

' I
100 1000

 

I

IE-I-O4

7 (sec-I)

Figure 19. Shearostress vs.shear rate for defatted soy dough
(MC-40.0, T-46.8 C) (data points are means of four observations).
- 'indicates twin screw extruder prediction

--- indicates capillary rheometer prediction (Morgan et al., 1987)

55

Note the differences between each of the extruded Power-law
parameters and its corresponding capillary rheometer parameters. There
are several reasons for these differences. Sample preparation of
material for the CR and the TSE were very different. Potato and
defatted soy dough tested on the CR was hydrated and allowed to
equilibrate whereas the material for the TSE was mixed together and
extruded through the dies within a one to two minute residence time.
Although the SPS was prepared differently, it was allowed to cool before
reheating in the CR and also was held for ten hours at room temperature
during the CR testing. Ten hours was the amount of time it took to run
the capillary rheometer tests.

Effects of shear and work input within the extruder are unknown and
hence were not accounted for. The potato and defatted soy dough has
relatively little shear or work input when hydrated for CR testing as
compared to the TSE.

Slip had a significant effect on the pressure recorded during the
extrusion tests. 'Sharkskinning' caused by material slipping and
catching on the die walls was quite visible during extrusion tests,
particularly for SPS. Attempts to adjust for slip using the method
summarized by Darby (1976) yielded inconclusive results, as shown in

Figure 20.

IL_.(KPa sec)-1

6

T

(16

56

 

.0
.p.

JILILJLILJillllllJLlllllllllllJllJlllllllLlllllllllllllLJ

w

.0
m)

I

I
o QIME
0 8th DIE o

O

lLJIllllLlLilllllllllljllllllllllllill‘lljllljllllllllljJi

 

 

(l0
500

fi

 

LN
CD
CD

I I
900 1100
'w (KPa)

I
700

Figure 20. Analysis of slip for SP8 TSE data (58% MC)
(data points are means of four observations).

S7

The Gentran pressure transducer used to record die pressure has an
error of one percent of full scale pressure, resulting in significant
error at low pressure readings. Fluctuations in die temperature and
moisture content were adjusted for by means of coefficients developed on
the capillary rheometer which may not be entirely accurate under
extrusion conditions.

Switching between long and short dies induced significant changes
in process history, thus the assumption of a constant viscosity material
for all die lengths is questionable. This is particularly true for
materials susceptable to irreversible physicochemical changes such as
defatted soy dough or potato dough. This may partially explain why the
fw vs. 1 data of defatted soy dough and potato dough were scattered much
more than the corresponding data of SPS. Furthermore, surging within
the extruder at low product rates caused fluctuations in moisture
content and product rate. This was very noticeable with use of the Bran
& Lubbe injection pump as is seen by comparing the coefficient of
variation of moisture content of defatted soy to that of SPS. For the

above reasons, it is understandable that the correlation coefficients

were lower for the extruder data.

ELASTICITY

No die swell was observed for SPS and the SPS extrudate appeared to
be non-elastic. Die swell (fl) values for defatted soy flour ranged from
1.1 to 1.3 but no correlation of the fl vs. residence time could be made.
The author noticed that the defatted soy dough extrudate exhibited
elastic properties. Small balls of the dough could be bounced, and when
these balls were stretched, they partially relapsed back to their

original shape. However, because die swell was minimal, the elastic

58

 

 

 

 

 

 

2.5 I I I I I
L
h
2.” “\Q
U '\P- f.
JET \ -—l ”.12 ..LC
suELL o
p ()
° <3
0
L)
'05 ‘
50\ MC 0
30 < r < 70 c -1
157 < P < 2900 acc
. O ---- lee
0 -“” 8th die
I." , . . . I
0.0 u.I 0.2 0.3 0.4 0.5 0.6
RESIDENCE TIME, At (sec)
Figure 21. Material time constant determined for extruded potato

flour at 50% M.C. (data points are means of two
observations).

59

time constant, A, was assumed negligible. Figure 21 shows die swell, D,
as a function of residence time for potato flour. There is an obvious
correlation between die swell and die residence time, however,
significant scatter of data at low die residence times made prediction
of the time constant difficult. The curve in Fig. 21 was analyzed to
obtain A of 0.12 seconds, measured as the first order time decay

cons tant .

ENTRANCE PRESSURE DROP MODELING

PI (H) TERM COEFFICIENTS

As the experimental twin-screw extruder results were collected
using a twin hole die head, the entrance to the dies was complex and
could yield different results than those collected on a single hole die
head. For this reason, the flow rate and number of die holes were both
divided by two, resulting in the same data that would be given if a
single hole die head.

Dies that did not have a full flange 90 degree entrance (Appendix
B) were assumed to have an entrance of 180 degrees in this analysis as
the angle from the die edqes to the entry cone vertex is approximately
180 degrees.

Observed APen data and their corresponding H term variables (Table

t

2) are given in Appendices Q and R for experimental and published data
respectively. Stepwise forward regression (SAS, version 5) was used to
obtain the best-fit coefficients of the model form presented in

Eqn. (21) by means of the following model transformation:

lmr1 - lna+b21n12+b31nw3+b lnx +b51nn

4 4 +b6lnw6+b7lnn +b Inn (27)

5 7 8 8

60

where a equals the exponential of the intercept value given by stepwise
regression.

Note that effects of die hole spacing on APent were not assessed in
either experimental or published data and therefore, «9 is set to one
for this study. «3 and «4 were not assessed in the published
literature, hence coefficients for «3 and ”A of the published literature
were not developed.

Data were grouped in several different ways to assess effects of
model coefficients. The SAS program for computing the H terms and
evaluating their coefficients by stepwise forward regression for each
grouping is given in Appendix S. The resulting model correlation
coefficient (r2) and a term coefficients are given in Table 13 for each
of the group tested. The complete ANOVA given by SAS for stepwise
forward regression is given in appendix T.

The stepwise regression ANOVAs indicate that «2 had the most
significant contribution to the model accuracy, while the rest of the «
terms together increased the model accuracy by 1 to 24 percent (Table
14). Because 13 and «a were equal to one for most of the data analyzed,
their real contribution to the model may be larger than the ANOVAs
indicate. «3 and ”4 values other than one amount to less than five

percent of the entire data set analyzed.

61

Table 13. Coefficients for Eqn. (21) and their corresponding model r2
(determined by stepwise forward regression).

 

(1) 2

GROUP r a b2 b3 b4 b5 b6 b7 b8
1. .90 0.324 -1.24 -0.915 1.05 2.60 -0.l76 -0.143 0.558
2. .93 0.073 -0.968 -- -- 7.74 -l.0 -0.20 -0.907
3. .82 5.10 -0.763 -- -- 4.30 -0.491 -O.322 -O.228
4. .99 19302 -l.01 -- -- -2.71 -0.235 -1.236 --

5. .95 89322 -1.18 -0.763 0.85 -5.18 -- -1.63 -0.449
6. .93 13630 -l.12 -0.244 3.024 0.461 -1.85 0.798
7. .88 77.8 -.69 -- 0.15 0.461 -- -- 0.429

(1) SAS groups

. All literature and experimental data (biological and polymer).
. All literature data (biological and polymer).

. Polymer data from the literature.

. Biological data from literature.

. Experimental data and biological data from literature.
Experimental data.

Twin screw extruder data.

\lO‘LflJ-‘UONH

-- indicates coefficients that did not reach the 50% confidence level
(most of the missing coefficients are due to lack of variation in the
data)

Table 14. Contribution,of n terms to model accuracy (determined.by
partial r given by each term) -

 

canvp‘l) 1. 2. 3. 4. 5. 6. 7.
partial partial partial partial partial partial partial
2 2 2 2 2 2
r r r r r r
lnx2 0.859 0.839 0.578 0.985 0.919 0.845 0.668
lnar3 0.003 -- -- -- 0.001 0.001 --
lnxh 0.002 -- -- -- 0.002 -- 0.002
lnx5 0.005 0.049 0.183 0.006 0.011 0.003 --
lmr6 0.001 0.024 0.023 0.001 -- -.008 0.02
lmr7 -- 0.002 -- 0.001 0.012 0.04 --
lnar8 0.014 0.013 0.002 -- 0.006 0.026 0.187

(1) SAS groups

. All literature and experimental data (biological and polymer).
. All literature data (biological and polymer).
Polymer data from the literature.
Biological data from literature.

Experimental data and biological data from literature.
. Experimental data.

\JO‘U'PUNH

. Twin screw extruder data.

-- indicates coefficients that did not reach the 50% confidence level
(most of the missing coefficients are due to lack of variation in the
data)

62

VALIDITY OF H TERM COEFFICIENTS

The «2 exponent for each group (Table 13) varied from -0.69 to
-1.24. The sign of the exponent is intuitively correct because if all

variables except Q remain constant, APent increases as flow rate

increases. Also, if the consistency coefficient, m, is increased while
all other variables are held constant, «2 decreases causing

APent to increase. Thus, APent increases as viscosity increases. This

is the same trend that the Boger (1982) model indicates for the

relationship between the Reynold's number and APent'

The exponent of the a term ranged from -0.24 to -O.915 and the

3
sign is intuitively correct. As nd increases, the fluid becomes less
restricted and hence, total pressure drop, including APent’ should

decrease. Intuitively a realistic value for this exponent is negative
one because pressure drop appears to be linearly related to the number
of holes.

It is difficult to intuitively relate effects of «4 (shape factor)
to entrance pressure drop. The coefficient can possibly be related to
the relationship between the shape factor and APdhole' As the shape
factor increases, the flow coefficient, fc’ (Figure 3) increases. As fC
increases, APdhole decreases (Eqn. 13). If the shape factor has the
same relationship on APen as it does for AP the « coefficient

t dhole’ 4

should be a negative value. The exponent for x in groups 1 and 5 of

4
Table 13 are likely to be a statistical anomaly because about 95 peribnt
of the shape factor values are F-l, hence causing uneven weighting of F.
The «4 exponent of group 7 (Table 13) makes more sense statistically as
shape factors other than F-l account for 30 percent of the data of this
group. Although the positive sign on this exponent does not intuitively

make sense, the small magnitude of this value may indicate that the

63

exponent should be approximately zero. Further analysis of the effect
of irregular shaped holes on APent needs to be made.

Values for the «5 exponent (Table 13) are erratic in both magnitude
and sign. Reduction of the Boger (1982) model by Reynold's analogy
indicates that for typical die diameters (0.1 to 0.6 cm) and flow rates
(1x10.5 to 1x10.8 m3/s) used in food extrusion, the Boger (1982) model
can be reduced to the following approximation:

n -0.89
APent - f(0.67 1 n I (28)

According to Eqn. (28), as n increases (for shear thinning fluids),
APent increases. Since n is inversely related to «5, APent decreases as
«5 increases, indicating that the «5 coefficient would be negative for
the Boger (1982) model. Group 4 data of Table 13 (biological data from
literature) resulted in an exponent with an intuitively correct
(negative) sign. From Appendix Q it is seen that n values, on which «5
is based, are evenly distributed between 0.22 and 0.63. Data of group 5
(Table 13) also resulted in a negative exponent but this is due to the
effect of group 4 data on group 5 as group 5 is made up of groups 4 and
6 and group 6 data resulted in a positive «5 exponent. Looking at the
distribution of n values (Appendices Q and R) of all data groups (Table
13) it is seen that group 4 data are the only ones in which n values are
evenly distributed over a wide range. For example, two thirds of the n
values in group 3 are 0.33 and the rest of the n values range from 0.6
to 0.8. Therefore, it is concluded that for statistical analysis of «5,
data group 4 of Table 13 is the only group which has normally

distributed n values and the sign of the «5 exponent from group 4 agrees

with intuition.

64

The «6 coefficients were consistently negative among the groups.
This coefficient should be negative because as the cone entrance
increases, less resistance to flow occurs. Results of Morgan et a1.
(1978) can be rearranged to give a "6 coefficient of -0.73 for
defatted soy dough extruded with a capillary rheometer. This compares

favorably with the exponent of -0.23 to -l.0 in Table 13. The one

"6
exception occurs in data group 6 (experimental data from this study)
with a positive exponent of 0.46. A possible explanation for this
exponent is an anomaly produced by the combining of data collected by
two very different techniques: capillary rheometry and twin-screw
extrusion.

All «7 coefficients are consistently negative, but there is
considerable variance in its order of magnitude with a range of -0.2 to
-l.85. The value of the «7 coefficient for the experimental data
appears to be too large as Han (1973) showed little change in APent for
entrance angles of 90 deg. to 180 deg. for polymers. This is
particularly true for highly viscous materials because they tend to
build up in the corner of the entrance region, creating their own
entrance angle approximately equal to 90 deg. At first glance, the
negative exponent for the entrance angle term appears to be contrary to
intuition. However, Han (1973) showed that for polymer melts, entrance
pressure was inversely correlated to entrance angle for greater than 60
deg. This is explained by the increase in entrance cone length for
small a.

The '8 coefficient also varied significantly among the groupings
(Table 13). The computed ”8 term for experimental data added much
variance to the “8 coefficient as the elastic time constant, A, was

calculated by a different technique and resulted in a much larger A than

was observed for polymer data. Although the large time constant may be

65

accurate it was only proposed as an alternative constant. Further
research must be conducted to determine how this alternative time

constant corresponds to time constants determined by other techniques.
ENTRANCE PRESSURE PREDICTION ACCURACY

Because the H term coefficients were developed by use of linear
regression of parameters transformed to the log space (Eqn. 27), any
error in the model is exponentially magnified when converting to the
form of Eqn. 21. For example, the model developed for all data shows
good correlation for the predicted vs. observed «1 term (Figure 22).
However, the resulting predicted vs. observed correlation for entrance
pressure drop is poor (Figure 23). Much of the problem encountered is
due to the fact that the model is applied to a vast range of entrance
pressure drop data (nine decades) and materials. Hence, further
regression analysis was performed to apply the model to individual
groups of data bases on material type and source. Linear regression was
used to predict the accuracy of Eqn. (29) for the individual groups
(Appendix U). As expected, coefficient values developed by linear
regression analysis were similar to those developed by stepwise forward
regression. Table 15 gives the model coefficients developed for each
data group, and its corresponding fit for predicted vs. observed APe

nt’

where predicted APent is calculated as follows:

b b b b b b b

2 2 3 4 5 6 7 8
APent- —£—92_—Z- [3(12) (W3) (“4) (K5) (#6) (W7) (W8) I (29)
16nd rh

can emsmssnsa Ham you H

mo+m_

EP _ ____

mo+mP

—~P—

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_=.ou>mmmmo

mo+m_

——-L

000_

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k po>uomno.m> nouowpoum .NN ousmwm

o—

 

 

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no.0 I u
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m
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00 0%
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o o o oo
o
o
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o \\\\
o
o
o o
o o
o
_____ — ~-~~ _ _h_E_L__b . __~L p __Fm _ ___b _ __bb -

  

 

or

ooor

mo+m—

In OBLOIOBHd

mo+me

mo+m_

67

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muoexaoa odummam one muaaomotwaomv sump Aquamawuonxo
tam noanHQSQ Ham now u ma nm>uomno m> pouowpoum .mm ouswwm

Ann: 55% 8558.0

 

 

 

whim: BOTH: 00+“: mo+m: ¢O+me

b — LP L I—EE r I—I —E — — — —b P — bl ¢O+MF

I mm.o I «u I

m
I vmo+m_
w . . . woo+m_
w wno+m_

h —P b L _ —~ — b r W

 

 

mo+ni

(0d) Maw 0310mm

68

Tagle 15. Coefficients for Eqn. (28) and.the correlation coefficients
(r ) for AP predicted by Eqn. (28) vs. observedAPe

 

ent nt‘

GROUP(1)r2 a b b b b b b b

2 3 4 5 6 7 8
1. .93 5.10 -O.763 -- -- 4.30 -0.491 -0.322 -o.228
2. .89 19312 -1.01 -- -- -2.71 -0 23 -1.23 --
3. .90 125.1 -0.667 -o.013 0.191 -0.676 0.488 0.032 0.310
4. .99 7.46 -1.20 0.010 0.408 -- -- -0.07 -0.05
5. .86 2.49 -1.01 0.187 0.011 -- -o.11 -0.02 --
6. .99 0.88 -1.15 -0.483 0.29 -1.18 -o.22 -0.06 --

(1) SAS groups

Polymer data from the literature.

Defatted soy dough data from literature.

Twin screw extruder experimental data.

Potato dough collected on twin screw extruder.

Defatted soy dough data collected on twin screw extruder.
SPS data collected on twin screw extruder.

O‘UIvPU-INH

As seen from the correlation coefficients in Table 15, the model
fits well for groups of data of the same material or data collected on
the twin screw extruder. Note that the model fits well for published
polymer data collected by several different techniques by different
researchers (group 1, Table 15). Likewise, the model fit well for
published defatted soy dough data collected by different researchers
(group 2, Table 15). Figures 24 to 29 show the predicted vs. observed
APent for the following data groups respectively: published polymer,
published defatted soy dough, twin screw extruder, extruded potato
dough, extruded defatted soy dough, and extruded SP8. The model given
by Boger (1982) had a much lower accuracy as shown in Figure 30.

Because some of the H terms coefficients had a wide variation, it
is recommended that the coefficients be redeveloped for specific
applications. Results from stepwise forward regression (Table 14)
indicate that several H terms did not contribute significantly to the

. 2
model accuracy. A five percent increase in the model r was chosen as

69

criterion for minimum contribution to the model r2. With this standard,

the final model form for predicting APent is as follows:

2 b2 b5 b8
L [a(«2) («5) («8) ] (30)
l6nd rh4

APent-

Research conducted in fluid mechanics (Kim-E et al.,l983) indicates
that entrance pressure is highly dependent upon the contraction ratio.
The author hypothesizes that the contraction ratio was not found to be
significant in this study because of the small Reynold's numbers found
in food extrusion (Re<<l). Because the Reynold's number is small,
inertial forces are small relative to viscous forces and hence, pressure
drop due to change in flow direction in the die entrance is
insignificant compared to pressure drop due to change in the material
viscous and elastic properties. If the model is to be applied in cases

with a high Reynold's number, the following model form is recommended:

b b b b

APent- _2_03__Z_ [a(«2) 2(“5) 5(«6) 6(«8) 8] <31)

l6nd rh
Because of the large change in die hole pressure drop correction
for shape factors less than 0.5 (Figure 3), it is probable that small

shape factors will also effect APen significantly. Further research

t
needs to be done on the effect of small shape factors (e.g. slits or
sharp edged cross sections) on the accuracy of the APent model. As «3,
the number of die holes, had negligible effect on the accuracy of the
model, it is assumed that the «9 term also would not contribute to the

model accuracy. Note that for non-elastic fluids the «8 term can be

eliminated and for Newtonian fluids the «5 term can be eliminated. As

7O

Eqn. (30) requires no specific die geometry, the remaining n
coefficients and rheological properties can be gathered simultaneously
by use of a die with multiple pressure taps. Han (1973) shows the
application of a multiple pressure tap die for collecting APent’
APex, and rheological properties of plastic polymers and van Zuilichem
et al. (1983) gives the design of a slit die for measuring the
rheological properties of protein and starch doughs. The author
cautions against using a slit die with a small aspect ratio (H/W) until
further research is done on the effects of entrance to narrow slits and
die cross sections with sharp corners. Use of a slit die would
eliminate changing long and short dies but may still require temperature
correction due to cooling of the material along the die length.
Therefore, temperature should be measured at points along the die.

As the combined twin screw extruder data and each separate extruded
material data all resulted in a good model fit, it is concluded that the
model is effective for extrusion applications such as scale-up, die
modification, and change of material. For scale-up or die modification
where the material rheological properties remanin constant, «5 does not
change and hence can be excluded from the model as it becomes part of
the constant, a. A step by step procedure is outlined in Appendix V for
experimental testing and data analysis procedures for total pressure

drop modelling in food extrusion applications.

71

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76

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(Dd) W"‘dv 0310I038d

CHAPTER VI.

CONCLUSION

An effective model was successfully developed by means of
dimensional analysis and fluid mechanics to predict entrance pressure
drop in noncircular multiple hole food extruder dies. The dimensionless
parameters significantly effecting the dimensionless entrance pressure
drop term (Euler number) are the Reynold's number, Weissenberg number
and Rabinowitsch correction factor.

The model form effectively fit published polymer and biological
data as well as food dough data collected in this study using a Baker
Perkins twin-screw extruder. Food doughs used in this study are potato,
defatted soy, and soy polysaccharide.

Future research in extruder die pressure drop modeling should focus
on data collection techniques, viscosity prediction models for doughs
effected by process history, elasticity measurement, and effects of

irregularly shaped die cross-sections on pressure drop.

78

79

RECOMMENDATIONS

More data need to be collected on different materials to verify
that «3, “4’ “6 and «7 do not contribute to the model. Materials should
be non reactive and independent of temperature-time and shear histories
so that the ensuing data need not be corrected for these factors. Use
of a die with multiple pressure taps may simplify the data collection
and increase the accuracy of the measurement of rheological properties.
Reasearch needs to be conducted on the feasibility of the use of a
multiple pressure tap die for low moisture, high temperature doughs
where 'vapor flashing' is likely to occur.

Research needs to be conducted on the effects of work input and
shear on the viscosity of extruded materials. A model predicting shear
effects can be combined with the generalized model of Morgan et a1.
(1987) to predict viscosity of screw extruded materials. Further
research needs to be conducted for modeling the viscosity of
ungelatinized starch doughs.

More research needs to be conducted on eliminating slip, or
effectively correcting for error induced by slip. Ramamurthy (1986)
concludes that for capillary rheometers, slip can be eliminated by use
of a different material other than brass.

Further research needs to be done on the measurement techniques of
elasticity of extrudate. The assumption that the elasticity of food
materials is much less than that of polymers needs to be verified to
ensure that APex can be neglected for food materials. For further study
of APex for elastic materials, the author recommends review of research
done by Han (1976), Pena et al. (1981), and Carreau and Choplin (1985).

Further research needs to be conducted for determining correction

factors for calculating die hole pressure drop across irregularly shaped

I'CJ‘ID-i-f

80

dies. The author recommends review of research done by Lahti (1963),
Knudsen and Katz (1958) and Lenk and Fenkel (1981).

After the above proposed research on entrance pressure drop
and die hole pressure drop modeling and elasticity measurement, an
analysis of the total die pressure predicted vs. observed would be
useful to find how accurate the total pressure drop model is. This

analysis should demonstrate the ability of the total die pressure drop

. D
A

model to predict pressure drop in scale-up and die modification

applications.

fin «. a;
II.

81

APPENDIX A. CHECK OF INDEPENDENCE OF I TERMS

x terms are independent if the number of « terms is equal to the rank
(Murphy, 1950) of the following matrix.

APent Q

"1 G) / 12’
«2 x 7!
G)

D
'1

h F Dc a m n A p s

/
71/

d

 

”8 3’ X ”’3’ ®

CHECK: #« TERMS - RANK - 9 - 9 - 0. OK

82

APPENDIX B DIE DIMENSIONS (1:1 RATIO)

 

*-—3.175—4

 

 

 

9O

 

 

 

 

 

FF DIE

(Dimensions in cm)

90

”(,7

83

APPENDIX B (Cont'd)

LPN
1.27

‘--3.175-—"‘

 

 

 

‘O--------—---------

 

 

 

 

 

13 3.175
’,--_.-------.--—----- 2.54
’ I
L ‘
0.476
QDIE

(Dimensions in cm)

‘4: 3.5:?
.‘III

:5 "* To—aT
‘I‘.

84

APPENDIX B (Cont'd)

 

 

 

o \\_ --------- 2.54
90 ""'""""3-D' 3.175

’ I

—I—I

(Cross section per hole)

 

 

 

_J
L‘F—--L-———o

0.476

 

3H DIE
(Dimensions in cm)

0.1‘

85

APPENDIX B (Cont'd)

C9

D
H
1.59

 

 

“"——'3.l75‘--**

 

 

 

 

?\1 |_

90° "2.27.111: :1“, 93 2153.175

V _1_
LI

 

 

8TH DIE

(Dimensions in cm)

86

APPENDIX C CAPILLARY RHEOMETER CALCULATIONS

As the material in the CR is pushed out, drag of the material
against the CR barrel is decreased. The resulting force-time line
measured with the X-Y recorder must be extrapolated to toe force which
would be measured when the CR plunger was at the die. For three
different velocities per CR loading, extrapolation is accomplished as

follows.

e n n- ec der t me Relationshi

Figure A shows a schematic of how the CR plunger extension relates to
the corresponding time reading (X distance) on the XY recorder
(Figure B) for velocities v1<v2 <v3. Relating actual plunger extension

to the time (X distance) on the X-Y recorder gives:

yd xce yd
- ' - ° *
l or Xce 1 Xcti
Y Y
ai cti al

and die force is determined at the time distance of Xct + Xce .
i i
Note: the plotter pen moves at a specified rate, hence time is measured

in distance on the Plotter X direction.

Force

87

 

‘. mnfl:

 
    

o
m
<

 

 

 

‘T‘fi'T—Barrel Drag

 

 

 

---d---

I
I

 

 

 

 

I_-""I'_'
I

Time

Figure B. Schematic of chart plots where:

X (i-vl, v2, v3) - X dist. chart pen moved at i mm/min Vxh

ct,i
xce,i (i-vl, v2, v3) - X extrapolation dist. to point where chart

pen would record if plunger went to the die at i mm/min vxh'

88

Ext. - 0.

 

Ext. at precompression

 

 

 

 

 

 

I 1‘
ya v
’ 3
— + Ext. where v changed to v
ya,v2 3 2
ya,v1 g
ytotal =1
-._-.____.__ Ext. where v2 changed to V1
Y
yd
_._.._ _ __._____.. Maximum plunger ext.
I“ I
- , Ext. at die

 

 

 

 

Figure A. Schematic of capillary rheometer extensions where:

yT (yTotal) - (max. ext. - precompres'n ext.) + dist. to die
ya i (i-vl, v2, v3) - yactual at i mm/min crosshead velocity
yd,1 (i-vl, v2, v3) - distance from die to where Vxh was stopped

or changed.

89

APPENDIX C (Cont'd)

Capillary rheometer (CR) Crosshead force- Plotter Y relationship

The Crosshead force (Fxh) is related to the plotter y distance

measured at the extrapolated time distance minus the plunger drag as

follows:

Actual Force - (Plotter X - drag) * CR % scale * Load cell maximum
(Plotter max. Y)

Converting capillary rheometer FXh-Vxh to 1w-F.

l. Shear Rate

 

2
F - 4 Vxh .5h
3
Rd
2. Shear Stress
(F -F )1)
r - XhT Xhent d
w l
« Db2 L

where subscripts b and d refer to capillary rheometer barrel and die

diameter respectively.

90

APPENDIX D FLOUR CALIBRATION PROGRAM

C THIS PROGRAM WILL CALCULATE FEED AND H20 SET FOR SPECIFIED
C MOISTURE CONTENT AND FEED RATES.(EXTRUDER OPERATIONS!!!)
C

PROGRAM FLOUR

INTEGER J,K,M,N,I,W,Z,H,D

REAL A,B,A1,B1,MC,FLSET,FLRATE,HZOSET,H20RATE,P,MAX,X,Y,
+CAPXY,CAPX,CAPY,CAPX2,SUMXY,SUMX2,MEANX,MEANY,FX(10),
+R2,CAPY2,SUMY2,FY(10),R21,CAPXY1,CAPX1,CAPY1,CAPXZl,SUMXYl,
+SUMX21,MEANXl,MEANY1,AO,STX(10),STY(lO),STX1(10),STY1(10)
OPEN (4l,FILE-'a:OUTPUT.DTA')

C

9 CONTINUE
CAPXY-O I
CAPXFO ,
CAPY-O n
CAPX2-O a
MEANXFO
MEANY-O
CAPY2-0
I-O

C

C THE FOLLOWING CALCULATIONS ARE A LINEAR REGRESSION FOR THE FEED

CALIBRATION

C

10 CONTINUE
WRITE(*,*)'FROM FEED CALIBRATION VALUES, INPUT FLOUR RATE(lb/min)
+(return) INPUT FLOUR SET(return). WHEN ALL DATA ARE ENTERED,INPUT
+0.0(return), 0.0(return). INPUT FLOUR SET AS A REAL NUMBER.’
READ (*,15)X
READ(*,15)Y
15 FORMAT(F8.4)
IF (X.EQ.0.0.AND.Y.EQ.0.0)THEN
GOTO 20
ELSE
STX(I+1)-x
STY(I+l)-Y
16 FORMAT('Feed Points ',2F7.3)
I-I+1 .
FX(I)-LOC(X)
FY(I)-LOC(Y)
GOTO 10
END IF
20 DO 30 L-l,I
CAPXY-CAPXY+FX(L)*FY(L)
CAPX-CAPX+FX(L)
CAPY-CAPY+FY(L)
CAPXZ-CAPX2+FX(L)**2
CAPY2-CAPY2+FY(L)**2
30 CONTINUE
SUMXY-CAPXY-(CAPX*CAPY/I)
SUMX2-CAPX2-(CAPX**2/I)
SUMY2-CAPY2-(CAPY**2/I)
B-SUMXY/SUMXZ
MEANX-CAPX/I
MEANY-CAPY/I
A0-MEANY—B*MEANX
A-EXP(AO)

91

APPENDIX D (Cont'd)

34

C

R2-SUMXY**2/(SUMX2*SUMY2)

Write(*,*)'THE REGRESSION R VALUE FOR THE FEED CALIBRATION
+IS',R2,' IS THIS VALUE ACCEPTABLE? INPUT O-NO OR l-YES
READ(*.*)H

IF (H.EQ.O)THEN

GOTO 9

END IF

DO 3 LP1,I

WRITE(41,16)STX(L),STY(L)

CONTINUE

WRITE(41,44)

CONTINUE

CAPXYl-O

CAPXl-O

CAPYl-O

CAPXZl-O

MEANXl-O

MEANYl-O

CAPYZl-O

I-O

C THE FOLLOWING CALCULATIONS ARE LINEAR REGRESSION FOR THE H20
CALIBRATION

C
35

39

38

40

42

CONTINUE

WRITE(*,*)'FROM H20 CALIBRATION VALUES, INPUT H20 RATE(lb/min),
+(return), INPUT H20 SET(return). WHEN ALL DATA ARE ENTERED, INPUT
+0.0(return) ,0.0(return). INPUT H20 SET AS A REAL NUMBER.’

READ(*,39)X1

READ(*,39)Y1

FORMAT(F9.4)

IF (X1.EQ.0.0.AND.Y1.EQ.0.0) THEN

GOTO 40

ELSE

STX1(I+1)-X1

STY1(I+1)-Y1

FORMAT('Water Points ',2F7.3)

I-I+1

FX(I)-(X1)

FY(I)-(Y1)

GOTO 35

END IF

DO 42 L-1,I

CAPXYl-CAPXY1+FX(L)*FY(L)

CAPXl-CAPX1+FX(L)

CAPYl-CAPY1+FY(L)

CAPXZl-CAPX21+FX(L)**2

CAPY21-CAPY21+FY(L)**2

CONTINUE

SUMXYl-CAPXYl-(CAPX1*CAPY1)/I

SUMXZl-CAPXZI-(CAPX1**2/I)

SUMYZl-CAPYZI-(CAPY1**2/I)

Bl-SUMXYl/SUMXZI

MEANXl-CAPXI/I

MEANYl-CAPYl/I
A1-MEANY1-Bl*MEANX1
R21-SUMXY1**2/(SUMX21*SUMY21)

92

APPENDIX D (Cont'd)

WRITE(*,*)'THE REGRESSION R VALUE FOR H20 CALIBRATION IS'
+,R21, 'IS THIS VALUE ACCEPTABLE? INPUT O-NO OR l-YES.
+A VALUE ABOVE .99 (99%) IS GENERALLY ACCEPTABLE.’
READ(*.*)D
IF(D.EQ.0)THEN
GOTO 34
END IF
DO 4 L-1,I
WRITE(41,38)STX1(L),STY1(L)
4 CONTINUE
WRITE(41,44)
WRITE(41,43)A1,Bl,R21
43 FORMAT (5X,'Water regression model "A" is',F8.3,' and'
+' "B” is',F7.4,' and "R2" is',F6.4)
WRITE(41,44)
44 FORMAT (' ')
C
C THE FOLLOWING CALCULATES THE FEED AND H20 SET AT DESIRED MC AND FEED
RATE

.- . "‘1. T.—‘7{

1;-

C
WRITE (*,*)'Input minimum moisture desired (PERCENT)'
READ (*,70)J
WRITE(*,*)'Input maximum moisture desired (PERCENT)'
READ (*,70)K
WRITE(*,*)'Input moisture content increment(PERCENT)’
READ (*,70)Z
WRITE(*,*)’input minimum feed rate desired (1b/Hr)’
READ (*,70)M
WRITE(*,*)'Input maximum feed rate desired (1b/Hr)’
READ (*,70)N
WRITE(*,*)'Input feed rate increment(1b/hr)’
READ(*,70)W

70 FORMAT(IA)

C

WRITE(41,99)A,B,R2
99 FORMAT(SX,'Feed regression model "A" is',F8.3,' and’
+' ”B" is ',F7.4, ' and "R2" is ’,F6.5)
WRITE(41,101)
101 FORMAT(' ')
WRITE(41,102)
102 FORMAT(SX,'MC%',4X,'Feed Rate 1b/hr',Sx,'FEED SET',SX,'H20'
+' SET')
DO 140 I-J,K,Z
WRITE(41,150) I
150 FORMAT(AX,13)
DO 160 LPM,N,W
MC-I/100.0
P-L/60.0
FLRATE-(P-(P*MC))/O.92
H20RATE-MC*P-(.087*(P-MC*P))
FLSET-A*FLRATE**B
HZOSET-A1+(H20RATE*B1)
WRITE(41,175)L,FLSET,HZOSET
175 FORMAT(ISX,IA,12x,F7.2,7X,F6.2)
160 CONTINUE
140 CONTINUE
END

93

APPENDIX E DIE SLIP ANALYSIS

Darby (1976) summarizes a method for assessing effects of slip
through a coefficient, fi', which corrects P for a slip velocity. The

technique is as follows:

1. Using various tubes of the same length but different radii, Plot
(F/hrw) vs. fw for each tube. If fl'-O, these curves should coincide.

If not, the curves will be distinct, in which case proceed with step 2.

kg. ”.2

2. At constant fw’ plot (F/hfw vs. l/R) from the curves in step 1. This
plot should be linear with a slope - 5' for each rw.

3. Repeat 2 for various values of rw, and then plot 5' vs. Tw to obtain
a function fi'—f(rw). Then all 7w vs. P data should be adjusted by
correcting P as follows:

4fl'r
I‘no slip I‘slip measured - R w

 

where r is the measured value. Then 1 vs. P . data should be
w w no 811p

used to obtain rw vs. 1 data.

94

APPENDIX F SAS PROGRAM TO COMPUTE CR RHEOLOGICAL PROPERTIES

3%********************************************************************* ;

* PROGRAM TO EVALUATE SHEAR STRESS, SHEAR RATE, SLIP;
* FOR SPS RUN ON CAPILLARY RHEOMETER AT MSU;
**********************************************************************;
OPTIONS PS-SS LS-72;
TITLEI SPS DATA TESTED ON CAPILLARY RHEOMETER AT MSU;
DATA A;

INFILE ENTRY;

INPUT NUM MC TEMP L D VXH FXH;

LD- L/D;

RFD/2/2.54;

DINT-INT(D*IOOOO);

GAMMAF9.1782E'5*VXH/R**3;
*0

* CALCULATING ENTRANCE FORCE AND PRESSURE;
*.

PROC SORT; BY MC TEMP D VXH;

PROC NLIN; BY MC TEMP D VXH;

PARMS FENT— .05 Mp1;

MODEL FXH-FENT+LD*M;

OUTPUT OUT-NEW PREDICTED-PFXH FARMS-PENT M;
DATA B; SET NEW;
ERRORl-ABS(FXH-PFXH)*100/FXH;

PENT - 14109.1*FENT;

,, 2“?"
I - l'

*

* CALCULATING TAU;

*-

TAU - 3527.28*((FXH-FENT)/LD);
PTAU - 3527.28*((PFXH-FENT)/LD); ,
ERROR2-ABS(TAU-PTAU)*IOO/TAU;

*0

* AVERAGING TAU VALUES;

*o

PROC SORT; BY MC TEMP D VXH;

PROC MEANS MAXDEC-l; VAR TAU MC TEMP DINT VXH; BY MC TEMP D VXH;
OUTPUT OUT-AVE STD-SDEV MEAN-TAUAVE MCl TEMPI DINTl VXHI;
DATA AVE; SET AVE;

VXH-VXHI;

DINT-DINTl;

TEMP-TEMPI;

DATA C;

MERGE AVE B; BY MC TEMP DINT VXH;

CV- SDEV/TAUAVE*100;

SLIP- GAMMA/(4*PTAU);

*o
TAUAVE-INT(10*GAMMA)/10;
TAU-INT(lO*TAU)/10;
LD-INT(100*LD)/100;
CV-INT(10*CV)/10;
OUTPUT;

*;

PROC SORT; BY MC TEMP D VXH;
PROC PRINT; VAR MC TEMP D LD GAMMA PENT TAU TAUAVE CV;

95

APPENDIX C SAS PROGRAM TO COMPUTE TSE RHEOLOGICAL PROPERTIES

**************************************************************

* PROGRAM TO EVALUATE SHEAR STRESS, SHEAR RATE, PENT, SLIP;
* FOR MATERIALS RUN ON BAKER PERKINS TWIN SCREW EXTRUDER AT MSU;
* ONLY CIRCULAR DIES USED IN TAU - GAMMA ANALYSIS;
* UNITS: KPA, N, M, 8, DEC C;
***************************************************************;
OPTIONS LS-80;
TITLEl DATA TESTED ON BP AT MSU;
DATA A;
INFILE ENTRY;
INPUT DIE s MATL s LCM DCM ND MC TEMP MDOT PSI TQ RPM;
*0
* DATA CONVERSION FACTORS AND CONSTANTS;
*o
IF MATL

- 'SPS' THEN TADJ - 2275;
IF MATL - 'SPS' THEN RHO - 1200;
IF MATL - 'P' THEN TADJ - 4393;
IF MATL - 'P' THEN RHO - 1100;
*0
IF MATL - 'DSF' THEN TADJ-3422;
IF MATL - 'DSF' THEN RH0-1100;

PI - 3.141592654;

PRES - 6.89476*PSI;
T-5/9*(TEMP-32);

MASSR - 0.45359/3600*MD0T;
L - LCM/100;

D - DCM/100;

R - D/2;

*;

* CALCULATING GAMMA;

*0

Q - MASSR/RHO;

GAMMA - 4*Q/(PI*R**3*ND);
*.

* ADJUSTING PRESSURE FOR TEMPERATURE;
*0

PROC SORT; BY MC;
PROC MEANS MAXDEC-l; VAR T; BY MC;
OUTPUT OUT-C MEAN-TREF;
DATA D;
MERGE C A; BY MC;
IF DIE-'21H' THEN DELETE;
IF DIE-'BSLIT' THEN DELETE;
IF DIE-'SLIT' THEN DELETE;
TINV-(l/(T+273.15));
TINVR-(l/(TREF+273.15));
PADJ-PRES*EXP(TADJ*(TINVR-TINV));
*0
* CALCULATING PENT;
*.
LD-L/D;
PROC SORT; BY MC DIE GAMMA;
PROC NLIN; BY MC DIE GAMMA;
PARMS PENT- 0.05 2-1;
MODEL PADJ-PENT+LD*Z;
OUTPUT OUT-NEW PREDICTED-PPADJ FARMS-PENT Z;

96

APPENDIX C (Cont'd)

DATA E; SET NEW;
ERRORl-INT(ABS(PADJ-PPADJ)*100/PADJ);
*-
* CALCULATING TAU;
*0

IF DIE

- 'Q' THEN GROUP-l;
IF DIE - '8TH' THEN GROUP-2;
IF DIE - '3H' THEN GROUP-3;

- 'FF' THEN GROUP-4;

IF DIE
*o

'TAU - ((PADJ-PENT)/LD);
SLIP-INT<100*GAMMA/(4*TAU))/100;

*

PROC SORT; BY MC GROUP GAMMA;
PROC MEANS MAXDEC-l; VAR TAU; BY MC GROUP GAMMA;
OUTPUT OUT-G STD-SDEV MEAN-TAUAVE;
DATA H;
MERGE G E; BY MC GROUP GAMMA;
cv- SDEV/TAUAVE*100;
*.
* COMPUTING M, N;
*;
IF PENT < 0 THEN DELETE;
IF DIE-'Q' THEN VISC-l;
IF DIE-'8TH' THEN VISC-l;
IF DIE-'3H' THEN VISC-1;
IF DIE-'FF' THEN VISC-l;
LNGAM-LOG(GAMMA);
LNTAU—LOG(TAU);
PROC SORT; BY MC VISC;
PROC NLIN; BY MC VISC;
PARMS LNMPlOO N-.2;
MODEL LNTAU-LNM + N*LNGAM;
OUTPUT OUT-J PREDICTED - PLNTAU PARMS-LNM N STDP-FIT;
DATA K; SET J;
N—INT(100*N)/100;
M-INT (10*(EXP(LNM)/((3*N+1)/(4*N))**N))/IO;
PTAU-INT(LOG(PLNTAU));
T-INT(10*T)/10;
LCM-INT(10*LCM)/10;
TREF-INT(10*TREF)/10;
PADJ-INT(PADJ);
PRES-INT(PRES);
GAMMAFINT(GAMMA);
TAU-INT(TAU);
TAUAVE-INT(TAUAVE);
CV-INT(10*CV)/lO;
PENT-INT(PENT);
PROC PRINT NOOBS; VAR DIE MATL MC LCM PRES PADJ PENT GAMMA TAU
TAUAVE CV ERRORl M N TREF SLIP;

97

 

APPENDIX H SPS DATA TESTED ON CAPILLARY RHEOMETER
033 MC TEMP L D VXH FXH
(3) (°C) (m) (m) (mmzmig1__LRN1
1 50 25 0.0254 0 0015375 5 0.32
2 50 25 0.0254 0.0015375 5 0.94
3 50 25 0 0503 0 0015375 5 1.63
4 50 25 0.0503 0.0015375 5 1.63
5 50 25 0 0254 0.0015375 10 1.16
6 50 25 0.0254 0.0015375 10 1.10
7 50 25 0.0503 0.0015375 10 1.96
3 50 25 0.0503 0.0015375 10 2.00
9 50 25 0.0254 0 0015375 50 1.76
10 50 25 0 0254 0 0015375 50 1.43
11 50 25 0 0503 0 0015375 50 3.00
12 50 25 0.0503 0.0015375 50 2.96
13 50 25 0.0254 0 0015375 100 1.66
14 50 25 0 0254 0.0015375 100 2.16
15 50 25 0.0503 0.0015375 100 3.76
16 50 25 0.0503 0.0015375 100 4.60
17 50 25 0.0254 0.0015375 300 2.24
13 50 25 0.0254 0.0015375 300 2.33
19 50 25 0.0503 0.0015375 300 4.20
20 50 25 o 0503 0.0015375 300 4.64
21 50 25 0.0254 0 0015375 500 2.90
22 50 25 0.0254 0.0015375 500 3.23
23 50 25 0.0503 0.0015375 500 4.40
24 50 25 0.0503 0.0015375 500 3.96
25 50 25 0.0254 0.0031750 100 0.54
26 50 25 0.0254 0.0031750 100 0.70
27 50 25 0.0520 0.0031750 100 1.15
23 50 25 0 0520 0.0031750 100 1.17
29 50 25 0.0254 0.0031750 300 0.30
30 50 25 0.0254 0.0031750 300 0.91
31 50 25 0.0520 0.0031750 300 1.53
32 50 25 0.0520 0.0031750 300 1.56
33 50 25 0.0254 0.0031750 500 1.04
34 50 25 0.0254 0 0031750 500 1.14
35 50 25 0.0520 0.0031750 500 1.32
36 50 25 0.0520 0.0031750 500 1.37
37 50 50 0.0254 0.0015375 100 1.10
33 50 50 0.0254 0.0015375 100 1.16
39 50 50 0.0503 0.0015375 100 2.10
40 50 50 0.0503 0 0015375 100 2.02
41 50 50 0 0254 0 0015375 300 1.52
42 50 50 0.0254 0.0015375 300 1.64
43 50 50 0.0503 0.0015375 300 2.33
44 50 50 0.0503 0.0015375 300 2.36
45 50 50 o 0254 0.0015375 500 1.70
46 50 50 0.0254 0.0015375 500 1.96
47 50 50 0.0503 0 0015375 500 3.16
43 50 50 0.0503 0.0015375 500 3.16
49 50 50 0.0254 0.0031750 100 0.40
50 50 50 0 0254 0.0031750 100 0.44

APPENDIX H (Cont'd)

98

 

033 MC TEMP L D vxn FXH
(3) (°C) (m) (m) (mmzmigl__igfll
51 50 50 0 0520 0.0031750 100 0.74
52 50 50 0.0520 0.0031750 100 0.73
53 50 50 0.0254 0.0031750 300 0.53
54 50 50 0.0254 0.0031750 300 0.52
55 50 50 0 0520 0.0031750 300 0.96
56 50 50 0.0520 0.0031750 300 1.00
57 50 50 0.0254 0 0031750 500 0.53
53 50 50 0.0254 0 0031750 500 0.53
59 50 50 0.0520 0.0031750 500 1.14
60 50 50 0.0520 0.0031750 500 1.16
61 50 70 0.0254 0.0015375 100 0.94
62 50 70 0.0254 0.0015375 100 1.05
63 50 70 0.0503 0.0015375 100 1.64
64 50 70 0.0503 0.0015375 100 0.72
65 50 70 0.0254 0 0015375 300 1.20
66 50 70 0 0254 0.0015375 300 1.36
67 50 70 0.0503 0.0015375 300 2.16
68 50 70 0.0503 0.0015375 300 2.34
69 50 70 0.0254 0.0015375 500 1.43
70 50 70 0.0254 0.0015375 500 1.57
71 50 70 0 0503 0.0015375 500 2.40
72 50 70 0.0503 0 0015375 500 3.00
73 50 70 0.0254 0 0031750 100 0.41
74 50 70 0.0254 0.0031750 100 0.40
75 50 70 0.0520 0.0031750 100 0.63
76 50 70 0.0520 0.0031750 100 0.65
77 50 70 0.0254 0.0031750 300 0.47
73 50 70 0.0254 0.0031750 300 0.47
79 50 70 0.0520 0.0031750 300 0.73
30 50 70 0 0520 0.0031750 300 0.35
31 50 70 0.0254 0.0031750 500 0.53
32 50 70 0.0254 0.0031750 500 0.52
33 50 70 0.0520 0.0031750 500 0.77
34 50 70 0 0520 0.0031750 500 0.39
35 60 25 0.0254 0.0015375 100 0.32
36 60 25 0.0254 0.0015375 100 0.32
37 60 25 0.0503 0.0015375 100 1.40
33 60 25 0.0503 0.0015375 100 1.53
39 60 25 0.0254 0.0015375 300 1.03
90 60 25 0.0254 0.0015375 300 1.03
91 60 25 0 0503 0.0015375 300 1.30
92 60 25 0 0503 0.0015375 300 2.03
93 60 25 0 0254 0.0015375 500 1.13
94 60 25 0.0254 0.0015375 500 1.26
95 60 25 0.0503 0.0015375 500 2.32
96 60 25 0.0503 0.0015375 500 2.43
97 60 25 0.0254 0.0031750 100 0.26
93 60 25 0.0254 0.0031750 100 0.30
99 60 25 0.0520 0.0031750 100 0.43
100 60 25 0.0520 0.0031750 100 0.54

99

APPENDIX H (Cont'd)

 

OBS MC TEMP L D VXH FXH
(%) ( C) (m) (m) (mmlmigl__1£fll
101 60 25 0.0254 0.0031750 300 0.36
102 60 25 0.0254 0.0031750 300 0.38
103 60 25 0.0520 0.0031750 300 0.64
104 60 25 0.0520 0.0031750 300 0.68
105 60 25 0.0254 0.0031750 500 0.46
106 60 25 0.0254 0.0031750 500 0.44
107 60 25 0.0520 0.0031750 500 0.74
108 60 25 0.0520 0.0031750 500 0.80
109 70 25 0.0254 0.0015875 100 0.32
110 70 25 0.0254 0.0015875 100 0.24
111 70 25 0.0508 0.0015875 100 0.44
112 70 25 0.0508 0.0015875 100 0.48
113 70 25 0.0254 0.0015875 300 0.38
114 70 25 0.0254 0.0015875 300 0.32
115 70 25 0.0508 0.0015875 300 0.52
116 70 25 0.0508 0.0015875 300 0.56
117 70 25 0.0254 0.0015875 500 0.36
118 70 .25 0.0254 0.0015875 500 0.26
119 70 25 0.0508 0.0015875 500 0.58
120 70 25 0.0508 0.0015875 500 0.56
121 70 25 0.0254 0.0031750 100 0.12
122 70 25 0.0254 0.0031750 100 0.10
123 70 25 0.0520 0.0031750 100 0.18
124 70 25 0.0520 0.0031750 100 0.18
125 70 25 0.0254 0.0031750 300 0.16
126 70 25 0.0254 0.0031750 300 0.16
127 70 25 0.0520 0.0031750 300 0.22
128 70 25 0.0520 0.0031750 300 0.24
129 70 25 0.0254 0.0031750 500 0.22
130 70 25 0.0254 0.0031750 500 0.18
131 70 25 0.0520 0.0031750 500 0.26
132 70 25 0.0520 0.0031750 500 0.28
133 70 50 0.0254 0.0015875 100 0.20
134 70 50 0.0254 0.0015875 100 0.22
135 70 50 0.0508 0.0015875 100 0.42
136 70 50 0.0508 0.0015875 100 0.36
137 70 50 0.0254 0.0015875 300 0.30
138 70 50 0.0254 0.0015875 300 0.26
139 70 50 0.0508 0.0015875 300 0.52
140 70 50 0.0508 0.0015875 300 0.46
141 70 50 0.0254 0.0015875 500 0.30
142 70 50 0.0254 0.0015875 500 0.30
143 70 50 0.0508 0.0015875 500 0.62
144 70 50 0.0508 0.0015875 500 0.52
145 70 50 0.0254 0.0031750 100 0.12
146 70 50 0.0254 0.0031750 100 0.12
147 70 50 0.0520 0.0031750 100 \O.16
148 70 50 0.0520 0.0031750 100 0.14
149 70 50 0.0254 0.0031750 300 0.12
150 70 50 0.0254 0.0031750 300 0.14

100

APPENDIX H (Cont'd)

 

033 MC TEMP L D VXH FXH
(3) (°C) (@111 (m) (mmlmigl__£§fll
151 70 50 0 0520 0 0031750 300 0.20
152 70 50 0 0520 0.0031750 300 0.20
153 70 50 0.0254 0.0031750 500 0.12
154 70 50 0.0254 0.0031750 500 0.14
155 70 50 0.0520 0.0031750 500 0.13
156 70 50 0 0520 0 0031750 500 0.20
157 70 70 0.0254 0.0015375 100 0.20
153 70 70 0.0254 0 0015375 100 0.20
159 70 70 0.0503 0.0015375 100 0.31
160 70 70 0 0503 0.0015375 100 0.26
161 70 70 0.0254 0.0015375 300 0.22
162 70 70 0.0254 0 0015375 300 0.25
163 70 70 0 0503 0.0015375 300 0.35
164 70 70 o 0503 0 0015375 300 0.33
165 70 70 0 0254 0.0015375 500 0.27
166 70 70 0.0254 0.0015375 500 0.26
167 70 70 0 0503 0 0015375 500 0.36
168 70 70 0.0503 0.0015375 500 0.36
169 70 70 0.0254 0.0031750 100 0.11
170 70 70 0.0254 0.0031750 100 0.12
171 70 70 0.0520 0.0031750 100 0.13
172 70 70 0 0520 0.0031750 100 0.13
173 70 70 0.0254 0.0031750 300 0.09
174 70 70 0 0254 0.0031750 300 0.09
175 70 70 0.0520 0.0031750 300 0.16
176 70 70 0.0520 0.0031750 300 0.13
177 70 70 0 0254 0 0031750 500 0.10
173 70 70 0.0254 0.0031750 500 0.05
179 70 70 0 0520 0.0031750 500 0.14
130 70 70 0 0520 0.0031750 500 0.15

101

 

APPENDIX I SPS SHEAR STRESS VS. SHEAR RATE FROM CAPILLARY RHEOMETER
MC TEMP D I‘ _ r

(3) < 0) (cm) (sec > (KPa)
50 25 0.15875 30 187
50 25 0.15875 150 299.8
50 25 0.15875 902 410
50 25 0.3175 37.6 227
50 25 0.3175 113 290
50 25 0.3175 188 318
50 50 0.15875 301 205
50 50 0.15875 902 284
50 50 0.15875 1504 293
50 50 0.3175 37.6 227
50 50 0.3175 113 290
50 50 0.3175 188 318
50 70 0.15875 301 ---
50 70 0.15875 902 269
50 70 0.15875 1504 259
50 70 0.3175 37.6 98.9
50 70 0.3175 113 145
50 70 0.3175 188 128.4
60 25 0.15875 301 39.6
60 25 0.15875 902 41.9
60 25 0.15875 1504 57.3
60 25 0.3175 37.6 96.8
60 25 0.3175 113 122
60 25 0.3175 188 134.7

102

 

APPENDIX J SPS DATA COLLECTED ON TWIN SCREW EXTRUDER
DIE L D nd MASSR MC 3 PRES TQ RPM
(cm) (cm) (Kg/S) (8) ( C) (KPa) (%)

FF 2.670 0.3175 2 0.00892 57.0 92.7 6894.7 46 240
FF 2.670 0.3175 2 0.00892 57.2 96.6 6481.0 44 240
FF 0.405 0.3175 2 0.00892 57.8 63.8 3206.0 28 240
FF 0.405 0.3175 2 0.00892 57.6 65.5 3171.5 27 240
FF 2.670 0.3175 2 0.01406 57.3 91.6 7997.9 69 240
FF 2.670 0.3175 2 0.01436 57.6 94.4 7273.9 58 240
FF 0.405 0.3175 2 0.01406 57.8 61.6 3688.6 36 240
FF 0.405 0.3175 2 0.01375 57.2 62.7 3550.8 36 240
FF 2.670 0.3175 2 0.01874 57.9 90.0 7963.4 84 240
FF 2.670 0.3175 2 0.01874 58.6 86.1 7653.1 80 240
FF 0.405 0.3175 2 0.01980 58.9 60.5 3688.6 46 240
FF 0.405 0.3175 2 0.01950 59.0 61.1 3688.6 46 240
Q 0.642 0.6350 2 0.00907 57.9 57.7 1861.5 22 240

0.642 0.6350 2 0.00876 57.6 61.1 1930.5 23 240
Q 2.620 0.6350 2 0.00892 57.0 73.8 3447.3 29 240
Q 2.620 0.6350 2 0.00892 56.5 73.8 3378.4 29 240
Q 0.642 0.6350 2 0.01466 59.3 54.4 2068.4 27 240
Q 0.642 0.6350 2 0.01436 58.5 57.2 2102.9 29 240
Q 2.620 0.6350 2 0.01451 56.8 64.4 3792.1 38 240
Q 2.620 0.6350 2 0.01436 58.1 68.3 3619.7 37 240
Q 0.642 0.6350 2 0.01980 59.4 54.4 2171.8 36 240
Q 0.642 0.6350 2 0.01980 59.0 54.4 2206.3 37 240
Q 2.620 0.6350 2 0.01965 58.3 63.8 3723.1 47 240
Q 2.620 0.6350 2 0.01965 57.9 64.4 3723.1 47 240
RECT 3.180 0.4210 2 0.00892 57.5 85.0 4998.7 37 240
RECT 3.180 0.4210 2 0.00892 57.5 85.5 4929.7 36 240
RECT 0.200 0.4210 2 0.00922 58.3 57.7 1861.5 22 240
RECT 0.200 0.4210 2 0.00907 57.9 58.8 1861.5 24 240
RECT 3.180 0.4210 2 0.01421 58.3 80.5 5757.1 48 240
RECT 3.180 0.4210 2 0.01391 57.5 83.3 5550.2 48 240
RECT 0.200 0.4210 2 0.01421 58.6 55.5 2137.3 24 240
RECT 0.200 0.4210 2 0.01436 58.2 55.5 2068.4 28 240
RECT 3.180 0.4210 2 0.01950 58.9 81.6 5757.1 61 240
RECT 3.180 0.4210 2 0.01965 58.9 77.2 5757.1 61 240
RECT 0.200 0.4210 2 0.01965 59.4 54.4 2137.3 36 240
RECT 0.200 0.4210 2 0.01995 59.7 54.4 2137.3 36 240
3H 0.370 0.3175 6 0.00907 57.0 48.8 2378.6 25 240
3H 0.370 0.3175 6 0.00922 58.0 43.3 2275.2 25 240
3H 2.580 0.3175 6 0.00861 56.0 69.4 5515.8 40 240
3H 2.580 0.3175 6 0.00892 55.8 82.2 5240.0 38 240
3H 0.370 0.3175 6 0.01451 58.4 43.3 2654.4 30 240
3H 0.370 0.3175 6 0.01481 57.0 47.2 2654.4 34 240
3H 2.580 0.3175 6 0.01421 57.4 58.3 6308.7 52 240
3H 2.580 0.3175 6 0.01391 56.0 79.4 5998.4 50 240
3H 0.370 0.3175 6 0.01995 59.0 43.3 2620.0 39 240
3H 0.370 0.3175 6 0.01965 62.5 43.3 2620.0 39 240
3H 2.580 0.3175 6 0.01950 58.7 81.1 6205.2 65 240
3H 2.580 0.3175 6 0.01935 58.5 77.7 6032.9 63 240

APPENDIX J (Cont'd)

103

 

DIE L D n MASSR MC 3 PRES TQ RPM
(cg) ILcm) IKg/S) (%) ( C) (KPa) (%)
8TH 2.600 0.3175 2 0.00861 56.4 89.4 6412.1 42 240
8TH 2.600 0.3175 2 0.00892 57.3 96.1 6343.1 42 240
8TH 0.400 0.3175 2 0.00922 58.4 65.5 3033.6 27 240
8TH 0.400 0.3175 2 0.00907 57.7 68.3 3033.6 28 240
8TH 2.600 0.3175 2 0.01391 56.2 97.2 7101.6 58 240
8TH 2.600 0.3175 2 0.01406 58.0 94.4 7032.6 56 240
8TH 0.400 0.3175 2 0.01406 58.6 65.5 3481.8 35 240
8TH 0.400 0.3175 2 0.01406 58.2 66.6 3481.8 45 240
8TH 2.600 0.3175 2 0.01859 57.9 94.4 7446.3 91 240
8TH 2.600 0.3175 2 0.01769 57.9 86.1 7515.2 77 240
8TH 0.400 0.3175 2 0.01935 59.0 60.5 3550.8 44 240
8TH 0.400 0.3175 2 0.01920 59.2 63.8 3619.7 44 240
FF 0.405 0.3175 2 0.00907 63.0 64.4 1896.0 . 350
FF 0.405 0.3175 2 0.00876 63.0 62.7 1930.5 19 350
FF 2.670 0.3175 2 0.00861 63.3 86.1 4274.7 30 350
FF 2.670 0.3175 2 0.00831 63.2 86.1 4274.7 29 350
FF 0.405 0.3175 2 0.01391 66.2 55.5 2171.8 22 350
FF 0.405 0.3175 2 0.01406 61.7 60.0 2137.3 22 350
FF 2.670 0.3175 2 0.01391 63.3 80.0 4964.2 38 350
FF 2.670 0.3175 2 0.01360 63.1 80.0 4688.4 35 350
FF 0.405 0.3175 2 0.01965 64.1 52.7 2206.3 26 350
FF 0.405 0.3175 2 0.01950 64.7 56.1 2206.3 26 350
FF 2.670 0.3175 2 0.01920 64.8 65.5 4860.8 42 350
FF 2.670 0.3175 2 0.01905 64.0 65.5 4895.2 40 350
Q 0.642 0.6350 2 . 64.6 57.2 1034.2 16 350
Q 0.642 0.6350 2 0.00861 64.5 57.2 1068.6 16 350
Q 2.620 0.6350 2 0.00907 63.0 64.4 1896.0 18 350
Q 2.620 0.6350 2 0.00861 61.7 66.6 1930.5 20 350
Q 0.642 0.6350 2 0.01345 63.9 55.0 1172.1 18 350
Q 0.642 0.6350 2 0.01406 64.4 53.8 1172.1 18 350
Q 2.620 0.6350 2 0.01406 64.3 61.1 2240.7 22 350
Q 2.620 0.6350 2 0.01406 64.7 61.1 2137.3 22 350
Q 0.642 0.6350 2 0.01920 64.3 48.8 1172.1 20 350
Q 0.642 0.6350 2 0.01935 64.1 48.3 1206.5 21 350
Q 2.620 0.6350 2 0.01965 65.2 57.7 2275.2 26 350
Q 2.620 0.6350 2 0.01965 65.4 59.4 2275.2 26 350
RECT 0.200 0.4210 2 0.00892 64.2 43.3 1103.1 16 350
RECT 0.200 0.4210 2 0.00952 63.7 38.8 1103.1 16 350
RECT 3.180 0.4210 2 0.00892 63.9 76.6 3240.5 25 350
RECT 3.180 0.4210 2 0.00831 63.5 76.1 3240.5 26 350
RECT 0.200 0.4210 2 0.01391 64.4 46.1 1275.5 18 350
RECT 0.200 0.4210 2 0.01421 65.2 40.0 1172.1 18 350
RECT 3.180 0.4210 2 0.01421 66.2 51.6 3757.6 30 350
RECT 3.180 0.4210 2 0.01406 64.4 68.3 3654.2 29 350
RECT 0.200 0.4210 2 0.01980 65.4 41.6 1275.5 20 350
RECT 0.200 0.4210 2 0.01935 65.7 36.6 1206.5 20 350
RECT 3.18 0.4210 0.01950 64.8 58.8 3688.6 34 350
RECT 3.18 0.4210 0.01980 64.4 65.0 3688.6 34 350

APPENDIX J (Cont'd)

104

 

DIE L D d MASSR MC 3 PRES TQ RPM
(cm) (cm) (Kg/S) (%) ( C) (KPa) (%)
3H 0.37 0.3175 6 0.00892 65.7 52.2 1344.4 17 350
3H 0.37 v0.3175 6 0.00922 62.8 53.8 1344.4 17 350
3H 2.58 0.3175 6 0.00876 64.5 73.8 3447.3 26 350
3H 2.58 0.3175 6 0.01043 62.5 75.5 3309.4 26 350
3H 0.37 0.3175 6 0.01436 64.4 46.1 1516.8 . 350
3H 0.37 0.3175 6 0.01406 64.0 50.0 1482.3 20 350
3H 2.58 0.3175 6 0.01421 64.3 69.4 3895.5 31 350
3H 2.58 0.3175 6 0.01421 64.1 68.8 3861.0 30 350
3H 0.37 0.3175 6 0.01950 64.6 43.3 1516.8 22 350
3H 0.37 0.3175 6 0.01950 67.1 40.5 1516.8 22 350
3H 2.58 0.3175 6 0.01980 64.5 67.7 3998.9 45 350
3H 2.58 0.3175 6 0.01950 64.4 67.7 4033.4 46 350
8TH 0.40 0.3175 2 0.00876 64.7 60.5 1689.2 19 350
8TH 0.40 0.3175 2 0.00907 64.8 61.6 1654.7 19 350
8TH 2.60 0.3175 2 0.00876 64.0 83.3 4067.9 29 350
8TH 2.60 0.3175 2 0.00892 65.4 85.0 4136.8 29 350
8TH 0.40 0.3175 2 0.01375 65.2 58.3 2033.9 22 350
8TH 0.40 0.3175 2 0.01391 64.5 58.3 1965.0 22 350
8TH 2.60 0.3175 2 0.01391 63.7 77.2 4619.4 35 350
8TH 2.60 0.3175 2 0.01391 63.5 78.3 4585.0 35 350
8TH 0.40 0.3175 2 0.01905 64.7 56.1 2068.4 25 350
8TH 0.40 0.3175 2 0.01950 62.7 56.1 2033.9 26 350
8TH 2.60 0.3175 2 0.01935 64.6 71.6 4757.3 42 350
8TH 2.60 0.3175 2 0.01935 64.5 70.5 4722.9 41 350

APPENDIX K
DIE L
(M)

3TH 0.004
3TH 0.004
8TH 0.004
8TH 0.004
8TH 0.015
3TH 0.015
8TH 0 015
8TH 0 015
8TH 0 015
8TH 0.026
8TH 0.026
8TH 0.026
8TH 0 026
8TH 0.026
8TH 0.026

Q 0.00642
Q 0.00642
Q 0 00642
Q 0.00642
Q 0.02600
Q 0.02600
Q 0.02600
Q 0.02600
Q 0.02600
Q 0 02600
Q 0.05200
Q 0.05200
Q 0 05200
Q 0 05200
Q 0.05200
Q 0.05200
FF 0.00405
FF 0.00405
FF 0 00405
FF 0.00405
FF 0.00405
FF 0.00405
FF 0 00405
FF 0.02670
FF 0.02670
FF 0.02670
FF 0.02670
RECT 0.00200
RECT 0 00200
RECT 0.00200
RECT 0.00200
RECT 0.03130
RECT 0.03130
RECT 0.03130
RECT 0.03130

COCOCO000000000000OOOOOOOCOOOOOOOOOOOOOO0000000000

(M)

.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.006350
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.003175
.004210
.004210
.004210
.004210
.004210
.004210
.004210
.004210

D MC
(%)

POTATO DOUGH DATA

T
o

( C)

105

COLLECTED ON TWIN SCREW EXTRUDER

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

MASSR
(KG/S)

.01259
.01259
.02003
.02003
.00869
.00869
.01259
.01259
.02003
.00869
.00869
.01259
.01259
.02003
.02003
.01259
.01259
.02003
.02003
.00869
.00869
.01259
.01259
.02003
.02003
.00869
.00869
.01259
.01259
.02003
.02003
.00869
.00869
.00869
.01259
.01259
.02003
.02003
.00869
.01259
.01259
.02003
.00869
.01259
.01259
.02003
.00869
.01259
.01259
.02003

6205
2206
6687
3309
4171
4378
4757
4998
6481
6825
3309
8239
3930
8859
5619

792
2620
1137
3068
3171
3240
2551
3102
4067
4067
2792

999
3619
1413
4653
1930
5826
4136
3516
4343
4067
5377
5584
3619
5377
5102
7791
1310
2033
1827
2723
2757
3343
3550
5515

47
34
71

PRES TQ RPM n
(KPa) (%)

100
350
100
350
220
220
220
220
220
100
300
100
300
170
300
350
100
350
100
220
220
220
220
220
220
100
350
100
350
100
350
100
220
220
220
220
220
220
220
220
220
220
220
220
220
220
220
220
220
220

NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

NNNNHNNNNNNNNNNNN

NNNNNNNNNHHHHHHNHHNHN

NM

106

APPENDIX K (Cont'd)

DIE L D MC oT MASSR PRES TQ RPM
(M) (M) (95) ( C) (KG/S) (KPa) (‘3)
3H 0.00370 0.003175 50 53.3 0.00869 2033 28 220
3H 0.00370 0.003175 50 53.3 0.00869 1689 27 220
3H 0.00370 0.003175 50 50.0 0.01259 2516 29 220
3H 0.00370 0.003175 50 48.8 0.01259 2551 29 220
3H 0.00370 0.003175 50 46.6 0.02003 3792 36 220
3H 0.02580 0.003175 50 51.6 0.00869 2516 29 220
3H 0.02580 0.003175 50 53.3 0.01259 3688 30 220
3H 0.02580 0.003175 50 50.0 0.01259 3757 30 220
3H 0.02580 0.003175 50 49.4 0.02003 5481 39 220

O‘O‘O‘O‘QO‘O‘CfiO‘

‘t 5'75me

107

APPENDIX L DEFATTED SOY DOUGH DATA COLLECTED ON TWIN SCREW EXTRUDER

 

 

DIE L D nd MC 3 MASSR PRES TQ RPM
(cm) (cm) (%) ( C) (kg1§) (KPa), (%)
8TH 2.600 0.3175 2 43.5 50.0 0.0184 2275 55 110
8TH 0.400 0.3175 2 43.0 43.3 0.0182 1116 25 110
FF 2.670 0.3175 2 41.1 56.1 0.0196 2323 54 150
FF 0.405 0.3175 2 41.7 50.0 0.0193 1103 35 150
Q 2.620 0.6350 2 38.9 45.5 0.0193 1172 37 150
Q 0.642 0.6350 2 39.2 44.4 0.0188 737 30 150
3H 2.580 0.3175 6 37.7 53.8 0.0190 1999 49 150
3H 0.370 0.3175 6 39.6 42.7 0.0196 861 31 150
RECT 3.180 0.4210 2 41.8 51.6 0.0190 1792 47 150
RECT 0.200 0.4210 2 40.2 47.7 0.0195 792 34 150
8TH 2.600 0.3175 2 41.5 52.2 0.0151 2551 61 150
8TH 0.400 0.3175 2 41.4 46.1 0.0149 1172 37 150
FF 2.670 0.3175 2 38.7 56.6 0.0155 2551 65 150
FF 0.405 0.3175 2 42.1 43.8 0.0151 1172 34 150
Q 2.620 0.6350 2 43.2 43.8 0.0145 1192 36 150
Q 0.642 0.6350 2 38.5 38.8 0.0151 689 30 150
3H 2.580 0.3175 6 40.8 47.7 0.0155 2102 55 150
3H 0.370 0.3175 6 38.5 41.1 0.0157 896 37 150
RECT 3.180 0.4210 2 37.7 43.3 0.0149 2068 50 150
RECT 0.200 0.4210 2 39.3 41.1 0.0158 723 34 150
8TH 2.600 0.3175 2 38.3 53.8 0.0119 2551 60 100
8TH 0.400 0.3175 2 37.4 48.3 0.0120 1275 40 100
FF 2.670 0.3175 2 38.6 51.1 0.0123 2585 61 100
FF 0.405 0.3175 2 39.3 43.3 0.0114 1206 35 100
Q 2.620 0.6350 2 39.3 45.5 0.0131 1378 45 100
Q 0.642 0.6350 2 40.4 41.6 0.0130 792 32 100
3H 2.580 0.3175 6 38.5 55.0 0.0122 2171 51 100
3H 0.370 0.3175 6 38.6 41.6 0.0128 965 31 100
RECT 3.180 0.4210 2 40.2 48.8 0.0122 1723 50 100
RECT 0.200 0.4210 2 38.2 45.0 0.0128 758 29 100
8TH 2.600 0.3175 2 42.7 47.7 0.0093 1792 41 100
8TH 0.400 0.3175 2 41.3 38.3 0.0113 827 26 100
FF 2.670 0.3175 2 41.9 47.7 0.0092 2033 45 100
FF 0.405 0.3175 2 41.5 92.2 0.0102 827 37 100
Q 2.620 0.6350 2 41.7 37.2 0.0102 896 27 100
Q 0.642 0.6350 2 42.4 35.5 0.0108 517 31 100
3H 2.580 0.3175 6 41.5 42.2 0.0101 827 36 100
3H 0.370 0.3175 6 40.3 45.0 0.0114 1447 28 100
RECT 3.180 0.4210 2 42.8 37.2 0.0101 1378 39 100
RECT 0.200 0.4210 2 39.8 36.1 0.0104 551 22 100
8TH 2.600 0.3175 2 38.0 50.0 0.0172 2620 70 120
8TH 0.400 0.3175 2 37.3 43.3 0.0166 1310 42 120
FF 2.670 0.3175 2 38.0 56.1 0.0173 2757 70 120
FF 0.405 0.3175 2 38.8 45.5 0.0172 1344 45 120
Q 2.620 0.6350 2 36.4 44.4 0.0172 1378 46 120
Q 0.642 0.6350 2 38.9 39.4 0.0167 827 32 120
3H 2.580 0.3175 6 38.4 53.3 0.0172 2137 55 120
3H 0.370 0.3175 6 38.4 42.2 0.0172 1034 38 120
RECT 3.180 0.4210 2 38.5 47.7 0.0166 2068 52 120
RECT 0.200 0.4210 2 39.9 42.7 0.0172 861 36 120

108

APPENDIX M SHEAR RATE AND SHEAR STRESS VALUES FOR EXTRUDED SPS

 

SPS MC- 58.0%. T- 66.6°C

 

 

DIE P_ 1_ r
(S 11 (s 1) (XPal
Q 146 245 732
229 334 645
313 524 539
8th 1169 1959 1044
1837 3079 1234
2506 4200 1195
FF 1169 1959 1130
1838 3079 1267
2506 4200 1168
3H 389 652 705
613 1027 688
835 1399 891
SPS MC-64.3%, T - 59 3°C
Q 146 240 373
229 376 339
313 514 415
8th 1169 1920 702
1838 3020 669(1)
2506 587
FF 1169 1920 704
1837 3020 716(1)
2506 495

 

(1) Values excluded from data analysis because of extreme slip

 

APPENDIX N SHEAR RATE AND SHEAR STRESS VALUES FOR EXTRUDED POTATO

DOUGH

DIE P 1 r

(s'l) (s‘}1 (KPgl

3H 419 437 68
607 633 177
966 1007 255

8th 1257 1311 189
1322 1900 330
2900 3024 479

PP 1322 1900 213
2900 3024 567

 

109

 

APPENDIX P SHEAR RATE AND SHEAR STRESS VALUES FOR EXTRUDED DEFATTED
SOY DOUGH
DIE P 1 rw
(3'11 (s'1 (KPa)
O 187 343 107
224 411 192
275 505 130
308 566 176
345 634 149
8th 1498 2752 202
1797 3301 247
2205 4050 273
2471 4539 219
2766 5081 233
3H 599 1100 266
735 1350 208
823 1512 220
922 1694 263
FF 1797 3301 244
2205 4050 348
2471 4539 297
2766 5081 283

 

110

APPENDIX Q ENTRANCE PRESSURE DROP DATA FROM LITERATURE

 

 

MATL(1) p 3 P _1AP nt m n n A(2) D Dc a

Kg/m sec KEQ Egg-s sec m m deg

Data Rem e a d a R 1978
S3250 1000 3.00 10679 57.30 0.36 0.000 0.0012 0.009500 90
$3250 1000 7.50 12740 57.30 0.36 0.000 0.0012 0.009500 90
83250 1000 15.00 11959 57.30 0.36 0.000 0.0012 0.009500 90
83250 1000 30.00 13146 57.30 0.36 0.000 0.0012 0.009500 90
$3250 1000 75.00 15019 57.30 0.36 0.000 0.0012 0.009500 90
S3250 1000 150.00 16112 57.30 0.36 0.000 0.0012 0.009500 90
at o J r e a 1981
830120 1000 300.00 3530 7.45 0.43 0.000 0.0020 0.019050 180
830120 1000 500.00 3470 7.45 0.43 0.000 0.0020 0.019050 180
830120 1000 1000.00 4570 7.45 0.43 0.000 0.0020 0.019050 180
830120 1000 3000.00 4970 7.45 0.43 0.000 0.0020 0.019050 180
830120 1000 100.00 5100 1.45 0.63 0.000 0.0020 0.019050 180
830120 1000 300.00 6280 1.45 0.63 0.000 0.0020 0.019050 180
830120 1000 500.00 6880 1.45 0.63 0.000 0.0010 0.019050 180
830120 1000 1000.00 7650 1.45 0.63 0.000 0.0010 0.019050 180
830120 1000 500.00 6570 6.60 0.39 0.000 0.0010 0.019050 180
830120 1000 1000.00 7650 6.60 0.39 0.000 0.0010 0.019050 180
830120 1000 2000.00 9120 6.60 0.39 0.000 0.0010 0.019050 180
S3424 1400 0.95 4070 189.00 0.22 0.000 0.0032 0.015000 90
$3424 1400 1.90 4907 189.00 0.22 0.000 0.0032 0.015000 90
S3424 1400 4.74 5965 189.00 0.22 0.000 0.0032 0.015000 90
S3424 1400 9.48 7289 189.00 0.22 0.000 0.0032 0.015000 90
S3424 1400 19.00 7077 189.00 0.22 0.000 0.0032 0.015000 90
8347160 1400 47.40 3550 28.00 0.26 0.000 0.0032 0.015000 90
8347160 1400 94.80 4610 28.00 0.26 0.000 0.0032 0.015000 90
8347160 1400 190.00 4520 28.00 0.26 0.000 0.0032 0.015000 90
8347160 1400 948.00 6130 28.00 0.26 0.000 0.0032 0.015000 90
0 ate a cu 984

PET96265 1360 137.00 410 5.78 0.67 0.004 0.0010 0.009525 45
PET96265 1360 285.00 900 5.78 0.67 0.002 0.0010 0.009525 45
PET96265 1360 150.00 290 5.78 0.67 0.004 0.0010 0.009525 180
PET96265 1360 570.00 1000 5.78 0.67 0.001 0.0010 0.009525 180
PET96265 1360 850.00 1700 5.78 0.67 0.000 0.0010 0.009525 180
PET96265 1360 1000.00 2000 5.78 0.67 0.000 0.0010 0.009525 180
PET72285 1360 150.00 220 5.78 0.67 0.004 0.0010 0.009525 45
PET72285 1360 420.00 660 0.54 0.87 0.009 0.0010 0.009525 45
PET72285 1360 750.00 1500 0.54 0.87 0.005 0.0010 0.009525 45
PET72285 1360 1000.00 1750 0.54 0.87 0.004 0.0010 0.009525 45
PET72285 1360 1250.00 2000 0.54 0.87 0.003 0.0010 0.009525 45
PET72285 1360 300.00 15 0.54 0.87 0.012 0.0010 0.009525 180
PET72285 1360 475.00 35 0.54 0.87 0.008 0.0010 0.009525 180
PET72285 1360 775.00 200 0.54 0.87 0.005 0.0010 0.009525 180
PET72285 1360 1000.00 300 0.54 0.87 0.004 0.0010 0.009525 180
PET72285 1360 1500.00 780 0.54 0.87 0.002 0.0010 0.009525 180
PET72265 1360 150.00 20 2.05 0.71 0.035 0.0010 0.009525 45
PET72265 1360 420.00 250 2.05 0.71 0.017 0.0010 0.009525 45
PET72265 1360 750.00 900 2.05 0.71 0.011 0.0010 0.009525 45
PET72265 1360 1000.00 1300 2.05 0.71 0.009 0.0010 0.009525 45

111

APPENDIX Q (Cont'd)

 

MATL(1) p 3 P 1AP m n A(2) D D a
- nt n c
e a a- sec m m, deg
PET72265 1360 1250.00 1500 2.05 0.71 0.007 0.0010 0.009525 45
PET72265 1360 150.00 137 2.05 0.71 0.035 0.0010 0.009525 180
PET72265 1360 475.00 375 2.05 0.71 0.015 0.0010 0.009525 180
PET72265 1360 775.00 490 2.05 0.71 0.011 0.0010 0.009525 180
PET72265 1360 1000.00 790 2.05 0.71 0.009 0.0010 0.009525 180
PET72265 1360 1500.00 1100 2.05 0.71 0.006 0.0010 0.009525 180
PET96285 1360 300.00 280 2.32 0.76 0.019 0.0010 0.009525 180
PET96285 1360 570 550 2.32 0.76 0.001 0.0010 0.009525 180
PET96285 1360 850 1000 2.32 0.76 0.001 0.0010 0.009525 180
PET96285 1360 1250 1700 2.32 0.76 0.000 0.0010 0.009525 180
PET96285 1360 1600 2350 2.32 0.76 0.000 0.0010 0.009525 180
PET96285 1360 285 300 2.12 0.75 0.002 0.0010 0.009525 45
PET96285 1360 855 1100 2.12 0.75 0.000 0.0010 0.009525 45
PET96285 1360 1100 1300 2.12 0.75 0.000 0.0010 0.009525 45
Dat o J a 98
PE 915 500 667 11.00 0.33 0.033 0.0010 0.019050 180
PE 915 1000 1260 11.00 0.33 0.026 0.0010 0.019050 180
PE 915 2000 2190 11.00 0.33 0.021 0.0010 0.019050 180
PE 915 3000 2670 11.00 0.33 0.018 0.0020 0.019050 180
PE 915 5000 2770 11.00 0.33 0.015 0.0020 0.019050 180
PE 915 . 200 314 4.05 0.47 0.071 0.0020 0.019050 180
PE 915 300 412 4.05 0.47 0.058 0.0020 0.019050 180
PE 915 500 494 4.05 0.47 0.046 0.0020 0.019050 180
PE 915 1000 912 4.05 0.47 0.033 0.0020 0.019050 180
Data of flan (1923)
HDPE 980 125 1034 19.60 0.33 0.044 0.0031 0.019050 15
HDPE 980 180 1268 19.60 0.33 0.039 0.0031 0.019050 15
HDPE 980 260 1495 19.60 0.33 0.034 0.0031 0.019050 15
HDPE 980 340 1630 19.60 0.33 0.031 0.0031 0.019050 15
HDPE 980 430 1767 19.60 0.33 0.029 0.0031 0.019050 15
HDPE 980 490 1950 19.60 0.33 0.028 0.0031 0.019050 15
HDPE 980 575 2007 19.60 0.33 0.026 0.0031 0.019050 15
HDPE 980 150 693 19.60 0.33 0.041 0.0031 0.019050 30
HDPE 980 230 787 19.60 0.33 0.036 0.0031 0.019050 30
HDPE 980 280 863 19.60 0.33 0.033 0.0031 0.019050 30
HDPE 980 370 920 19.60 0.33 0.030 0.0031 0.019050 30
HDPE 980 466 1271 19.60 0.33 0.028 0.0031 0.019050 30
HDPE 980 590 1339 19.60 0.33 0.026 0.0031 0.019050 30
HDPE 980 190 675 19.60 0.33 0.038 0.0031 0.019050 - 60
HDPE 980 270 765 19.60 0.33 0.034 0.0031 0.019050 60
HDPE 980 340 796 19.60 0.33 0.031 0.0031 0.019050 60
HDPE 980 430 863 19.60 0.33 0.029 0.0031 0.019050 60
HDPE 980 540 878 19.60 0.33 0.027 0.0031 0.019050 60
HDPE 980 625 920 19.60 0.33 0.025 0.0031 0.019050 60
HDPE 980 195 641 19.60 0.33 0.038 0.0031 0.019050 90
HDPE .980 280 701 19.60 0.33 0.033 0.0031 0.019050 90
HDPE 980 360 765 19.60 0.33 0.031 0.0031 0.019050 90
HDPE 980 450 839 19.60 0.33 0.028 0.0031 0.019050 90
HDPE 980 550 839 19.60 0.33 0.026 0.0031 0.019050 90
HDPE 980 650 920 19.60 0.33 0.025 0.0031 0.019050 90
HDPE 980 156 641 19.60 0.33 0.041 0.0031 0.019050 120
HDPE 980 230 730 19.60 0.33 0.036 0.0031 0.019050 120
HDPE 980 295 751 19.60 0.33 0.033 0.0031 0.019050 120

 

APPENDIX Q (Cont'd)

112

 

MATL( p F AP m n A(2) D a
ent c
Kg/m3 §_2;£__JEEQ__KZ§;§n See U .344 deg

HDPE 980 380 778 19.60 0.33 0.030 0.0031 0.019050 120
HDPE 980 450 787 19.60 0.33 0.028 0.0031 0.019050 120
HDPE 980 540 863 19.60 0.33 0.027 0.0031 0.019050 120
HDPE 980 570 878 19.60 0.33 0.026 0.0031 0.019050 120
HDPE 980 170 641 19.60 0.33 0.039 0.0031 0.019050 180
HDPE 980 250 718 19.60 0.33 0.035 0.0031 0.019050 180
HDPE 980 314 765 19.60 0.33 0.032 0.0031 0.019050 180
HDPE 980 400 810 19.60 0.33 0.030 0.0031 0.019050 180
HDPE 980 465 863 19.60 0.33 0.028 0.0031 0.019050 180
HDPE 980 560 904 19.600 0.33 0.026 0.0031 0.01905 180
LDPE 920 80 620 14.765 0.32 0.118 0.0031 0.01905 15
LDPE 920 190 859 14.765 0.32 0.089 0.0031 0.01905 15
LDPE 920 245 995 14.765 0.32 0.082 0.0031 0.01905 15
LDPE 920 330 1330 14.765 0.32 0.075 0.0031 0.01905 15
LDPE 920 590 1340 14.765 0.32 0.062 0.0031 0.01905 15
LDPE 920 640 1395 14.765 0.32 0.061 0.0031 0.01905 15
LDPE 920 145 620 14.765 0.32 0.098 0.0031 0.01905 30
LDPE 920 240 689 14.765 0.32 0.083 0.0031 0.01905 30
LDPE 920 330 798 14.765 0.32 0.075 0.0031 0.01905 30
LDPE 920 390 859 14.765 0.32 0.071 0.0031 0.01905 30
LDPE 920 475 938 14.765 0.32 0.067 0.0031 0.01905 30
LDPE 920 630 1055 14.765 0.32 0.061 0.0031 0.01905 30
LDPE 920 105 482 14.765 0.32 0.108 0.0031 0.01905 60
LDPE 920 180 620 14.765 0.32 0.091 0.0031 0.01905 60
LDPE 920 270 798 14.765 0.32 0.080 0.0031 0.01905 60
LDPE 920 370 891 14.765 0.32 0.072 0.0031 0.01905 60
LDPE 920 440 938 14.765 0.32 0.068 0.0031 0.01905 60
LDPE 920 95 482 14.765 0.32 0.112 0.0031 0.01905 90
LDPE 920 160 689 14.765 0.32 0.095 0.0031 0.01905 90
LDPE 920 590 980 14.765 0.32 0.062 0.0031 0.01905 90

(1) Material Notation

Ngsggign Material (Table 4)

83250 Defatted soy dough 32% MC, 50°C

330120 Defatted soy dough 30% MC, 129°C

S3424 Defatted soy dough 34% MC, 24 C 0

8347160 Defatted soy dough 34.73 MC, 160 C

PET96265 .96 PE Terephthalate 265 C

PET72285 .72 PE Terephthalate 285°C

PET72265 .72 PE Terephthalate 265°C

PET96285 .96 PE Terephthalate 285°C

PE Polyethylene

HDPE High density polyethylene

LDPE Low density polyethylene

(2) A computed by Eqn 18.

11

3

APPENDIX R EXPERIMENTAL DATA USED IN COMPUTING ENTRANCE PRESSURE DROP

PF

PF

PF

PF

PF

PF

PF

PF

PF

PF

PF

PF

PF

PF

SCRl
SCRl
SCRl
SCRl
SCRl
SCRl
SCRl
SCR2
SCR2
SCR2
SCR2
SCR2
SCR2
SCR3
SCR3
SCR3
SCR3
SCR3
SCR3
SCR3
SCR4
SCR4
SCR4
SCR4
SCR4
SCR4
SPSl
SPSl
SPSI
SPSl
SPSl
SPSI
SPSI
SPSl
SPSl
SPSl
SPSl
SPSI
SPSl
SPSI

3

1100
1100
1100
1100
1100
1100
1100
1100
1100
1100
1100
1100
1100
1100
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200

 

 

F AP m n A DIE D D a n F
ent c d
0"1 K23 .KEé;§P Sec .3 E deg
1822 4439 0.501 0.85 0.12 FF 0 0031 0.031750 90 1 1.00
2898 4780 0 501 0.85 0.12 FF 0.0031 0 031750 90 1 1.00
419 1754 0.501 0.85 0.12 3H 0.0031 0.018330 180 3 1.00
607 1979 0 501 0.85 0.12 3H 0.0031 0 018330 180 3 1.00
966 2680 0.501 0.85 0.12 3H 0.0031 0.018330 180 3 1.00
1257 3002 0.501 0.85 0.12 8TH 0.0031 0.031750 180 1 1.00
1822 3624 0.501 0.85 0.12 8TH 0.0031 0.031750 180 1 1.00
2898 5490 0.501 0.85 0.12 8TH 0 0031 0.031750 180 1 1.00
539 1165 0 501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
539 1165 0.501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
781 1669 0 501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
781 1669 0.501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
1243 1927 0.501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
1243 1927 0.501 0.85 0.12 RECT 0.0042 0.031750 180 1 0.45
30 3950 86.000 0.21 0.00 CR 0.0015 0.009525 90 1 1.00
150 3668 86.000 0.21 0.00 CR 0.0015 0.009525 90 1 1.00
902 9876 86.000 0.21 0.00 CR 0.0015 0.009525 90 1 1.00
1503 28218 86.000 0.21 0.00 CR 0.0015 0.009525 90 1 1.00
37 1472 86.000 0.21 0.00 CR 0.0031 0.009525 90 1 1.00
112 2767 86.000 0.21 0.00 CR 0.0031 0.009525 90 1 1.00
187 5207 86 000 0.21 0.00 CR 0.0031 0.009525 90 1 1.00
300 2821 64.400 0.19 0.00 CR 0 0015 0 009525 90 1 1.00
902 4091 64.400 0.19 0.00 CR 0.0015 0.009525 90 1 1.00
1503 7054 64.400 0.19 0.00 CR 0.0015 0 009525 90 1 1.00
37 1345 64.400 0.19 0.00 CR 0.0031 0.009525 90 1 1.00
112 1966 64.400 0.19 0.00 CR 0.0031 0.009525 90 1 1.00
187 503 64.400 0.19 0.00 CR 0.0031 0 009525 90 1 1.00
300 11428 30.400 0.28 0.00 CR 0 0015 0.009525 90 1 1.00
902 846 30.400 0.28 0.00 CR 0.0015 0.009525 90 1 1.00
1503 4938 30.400 0.28 0.00 CR 0.0015 0.009525 90 1 1.00
37 2548 30.400 0.28 0.00 CR 0 0031 0.009525 90 1 1.00
112 1983 30.400 0.28 0.00 CR 0.0031 0.009525 90 1 1.00
187 3298 30.400 0.28 0.00 CR 0.0031 0 009525 90 1 1.00
187 3298 30.400 0.28 0.00 CR 0.0031 0 009525 90 1 1.00
300 2116 32.250 0.25 0.00 CR 0.0015 0.009525 90 1 1.00
902 3104 32.250 0.25 0.00 CR 0.0015 0.009525 90 1 1.00
1503 564 32.250 0.25 0.00 CR 0.0015 0.009525 90 1 1.00
37 851 32.250 0.25 0.00 CR 0 0031 0.009525 90 1 1.00
112 1313 32 250 0.25 0.00 GR 0.0031 0.009525 90 1 1.00
187 2037 32.250 0.25 0.00 CR 0.0031 0.009525 90 1 1.00
501 1206 132.800 0.27 0.00 RECT 0.0042 0.031750 180 1 0.45
788 1282 132.800 0.27 0.00 RECT 0 0042 0.031750 180 1 0.45
1074 1283 132.800 0.27 0.00 RECT 0 0042 0.031750 180 1 0.45
146 900 132.800 0.27 0.00 Q 0.0063 0.031750 180 1 1.00
229 1020 132.800 0.27 0.00 Q 0.0063 0.031750 180 1 1.00
313 1108 132.800 0.27 0.00 Q 0.0063 0.031750 180 1 1.00
1169 1733 132 800 0.27 0.00 8TH 0.0031 0 031750 180 1 1.00
1837 1887 132.800 0.27 0.00 8TH 0.0031 0 031750 180 1 1.00
2506 1774 132 800 0.27 0.00 8TH 0 0031 0.031750 180 1 1.00
389 694 132.8 0.27 0 3H 0.0031 0.01833 180 3 1.00
612 891 132.8 0.27 0 3H 0.0031 0.01833 180 3 1.00
835 560 132.8 0.27 0 3H 0 0031 0.01833 180 3 1.00
1169 1624 132.8 0.27 0 FF 0.0031 0.03175 90 1 1.00
1837 1693 132.8 0.27 0 FF 0 0031 0.03175 90 1 1.00

APPENDIX R (Cont'd)

MATL(1)p 3 1‘ AP

SPSI
SPS2
SPSZ
SPSZ
SPSZ
SPSZ
SPS2
SPS2
SPS2
SPS2
SPS2
SP82
SPSZ
SPSZ
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF
DSF

(1) Material Notation

Mm

DSF
PF
SPSI
SPS2
SCRl
SCR2
SCR3
SCR4

m n A DIE D D a nd F

sec REE KPa-sn sec m me deg
1200 2506 1789 132.8 0.27 0 FF 0.0031 0.03175 90 1 1.00
1200 501 488 76.7 0.28 0 RECT 0.0042 0.03175 180 1 0.45
1200 788 668 76.7 0.28 0 RECT 0.0042 0.03175 180 1 0.45
1200 1074 592 76.7 0.28 0 RECT 0.0042 0.03175 180 1 0.45
1200 146 628 76.7 0.28 0 Q 0.0063 0.03175 180 1 1.00
1200 229 664 76.7 0.28 0 Q 0.0063 0.03175 180 1 1.00
1200 313 526 76.7 0.28 0 Q 0.0063 0.03175 180 1 1.00
1200 1169 848 76.7 0.28 0 8TH 0.0031 0.03175 180 1 1.00
1200 1837 1115 76.7 0.28 0 8TH 0.0031 0.03175 180 1 1.00
1200 389 610 76.7 0.28 0 3H 0.0031 0.01833 180 3 1.00
1200 612 586 76.7 0.28 0 3H 0.0031 0.01833 180 3 1.00
1200 835 417 76.7 0.28 0 3H 0.0031 0.01833 180 3 1.00
1200 1169 1186 76.7 0.28 0 FF 0.0031 0.03175 90 1 1.00
1200 1837 1171 76.7 0.28 0 FF 0.0031 0.03175 90 1 1.00
1100 642 386 40.8 0.23 0 RECT 0.0042 0.03175 180 1 0.45
1100 770 583 40.8 0.23 0 RECT 0.0042 0.03175 180 1 0.45
1100 945 520 40.8 0.23 0 RECT 0.0042 0.03175 180 1 0.45
1100 1060 573 40.8 0.23 0 RECT 0.0042 0.03175 180 1 0.45
1100 1186 773 40.8 0.23 0 RECT 0.0042 0.03175 180 1 0.45
1100 187 289 40.8 0.23 0 Q 0.0063 0.03175 180 1 1.00
1100 224 414 40.8 0.23 0 Q 0.0063 0.03175 180 1 1.00
1100 275 350 40.8 0.23 0 Q 0.0063 0.03175 180 1 1.00
1100 308 381 40.8 0.23 0 Q 0.0063 0.03175 180 1 1.00
1100 345 567 40.8 0.23 0 Q 0.0063 0.03175 180 1 1.00
1100 1498 448 40.8 0.23 0 8TH 0.0031 0.03175 180 1 1.00
1100 1797 916 40.8 0.23 0 8TH 0.0031 0.03175 180 1 1.00
1100 2205 810 40.8 0.23 0 8TH 0.0031 0.03175 180 1 1.00
1100 2471 737 40.8 0.23 0 8TH 0.0031 0.03175 180 1 1.00
1100 2766 753 40.8 0.23 0 8TH 0.0031 0.03175 180 l 1.00
1100 499 1672 40.8 0.23 0 3H 0.0031 0.01833 180 3 1.00
1100 599 431 40.8 0.23 0 3H 0.0031 0.01833 180 3 1.00
1100 735 505 40.8 0.23 0 3H 0.0031 0.01833 180 3 1.00
1100 823 513 40.8 0.23 0 3H 0.0031 0.01833 180 3 1.00
1100 922 481 40.8 0.23 0 3H 0.0031 0.01833 180 3 1.00
1100 1797 669 40.8 0.23 0 FF 0.0031 0.03175 90 1 1.00
1100 2205 633 40.8 0.23 0 FF 0.0031 0.03175 90 1 1.00
1100 2471 742 40.8 0.23 0 FF 0.0031 0.03175 90 1 1.00
1100 2766 932 40.8 0.23 0 FF 0.0031 0.03175 90 1 1.00

Material

Defatted soy dough

Potato dough

Extruded SPS 58% MC

Extruded SPS 64.3% MC 0

SPS from capillary rheometer 50% MC, 25 C

SPS from capillary rheometer 50% MC, 502C

SPS from capillary rheometer 50% MC, 70°C

SPS from capillary rheometer 60% MC, 25 C

114

 

115

APPENDIX S SAS PROGRAM FOR COMPUTING ENTRANCE PRESSURE

OPTIONS LS -72;

DATA

A;

INFILE SETl;
INPUT OBS DIE $ D ND F DSUBC ALPHA C NC;

*-

INFILE SETZ;
INPUT OBS MATL $ RHO GAMMA PENT M N LAMDA;

*-

* SETTING TYPE;

*0

IF MATL-'A' THEN TYPE-'BIO';
IF MATLP'B' THEN TYPE-'BIO';
IF MATL-'0' THEN TYPE-'BIO';
IF MATL-'D’ THEN TYPE-'BIO';
IF MATLP'I' THEN TYPE-'POLY';
IF MATLP'J' THEN TYPE-'POLY';
IF MATLP'K' THEN TYPE-'POLY';
IF MATLP'L' THEN TYPE-'POLY';
IF MATLP'M' THEN TYPE-'POLY';
IF MATLP'N' THEN TYPE-'POLY';
IF MATLP'O' THEN TYPE-'POLY';
IF MATL - 'SCRl' THEN TYPE - 'CR';
IF MATL - 'SCR2' THEN TYPE - 'CR';
IF MATL - 'SCR3' THEN TYPE - 'CR';
IF MATL - 'SCR4' THEN TYPE - 'CR';
IF MATL - 'DSF' THEN TYPE - 'TSE';
IF MATL - 'SPSl' THEN TYPE - 'TSE';
IF MATL - 'SPSZ' THEN TYPE - 'TSE';
IF MATL - 'PF' THEN TYPE - 'TSE';
*0
* SETTING GROUP, BY POLYMER AND BIO AND LITERATURE;
*-

* CALCULATING PI TERMS;
*.
PROC SORT; BY TYPE;
DATA C; SET A;
PI - 3.1415926;
RH - D/4;
Q—2*ND*PI*(RH**3)*GAMMA;
PIl-((16*ND**2*(RH**4)*PENT)/(Q**2))/RHO;
P12-((RHO*Q)/(RH*ND*PI*M*((GAMMA*(3*N+1)/(4*N))**(N-1))));
PI3-ND;
PI4-F;
PIS-(3*N+1)/(4*N);
PI6-(16*ND*(RH**2))/(DSUBC**2);
PI7-ALPHA;
PI8 - 1+((LAMDA*Q)/(16*ND*(RH**3)*PI));
LNPIl-LOG(PI1);
LNPI2-LOG(PIZ);
LNPIB-LOG(PI3);
LNPI4-LOG(PI4);
LNPIS-LOG(PIS);
LNPI6-LOG(P16);
LNPI7-LOG(PI7);
LNPIB-LOG(PI8);

116

APPENDIX S (Cont'd)

REGEN-RHO*(D**N)*(Q/(4*PI*RH**2))**(2-N)/(8**(N-1)*M*((3*N+1)/
(4*N))**N);
DPEBOGER-(2*M*((3*N+1)/(4*N)*GAMMA)**N)*(REGEN*(C+1)/32+NC);
ERBOGER - INT(DPEBOGER-PENT)/PENT*100;
BOGER2 - (2*M*((3*N+1)/(4*N)*GAMMA)**N)*(PI2*(C+l)/32+NC);
ERBOG2 - INT(BOGER2-PENT)/PENT*100;

*.

* RESULTS;
*.

DP - INT(10000*D)/10000;
MP - INT(10*M)/10;
NP - INT(100*N)/100;
DSUBCP - INT(10000*DSUBC)/10000;
CP - INT(100*C)/100;
NCP - INT(100*NC)/100;
* PROC PRINT VAR DIE MATL MP NP GAMMA PENT DSUBCP
PIl PI2 PI3 P14 P15 P16 P17 PI8;
* PROC SORT BY TYPE;
* PROC PRINT NOOBS VAR PENT DPEBOGER; BY TYPE;
*-
* PROC SORT BY MATL;
* PROC STEPWISE;
* MODEL LNPIl - LNPIZ LNPI3 LNPI4 LNPIS LNPI6 LNPI7 LNPI8 / FORWARD;
* BY MATL;
PROC STEPWISE;
MODEL LNPIl - LNPI2 LNPI3 LNPI4 LNPIS LNPI6 LNPI7 LNPI8 / FORWARD;
DATA D; SET C;
IF TYPE - 'BIO' OR TYPE - 'POL';
PROC STEPWISE;
MODEL LNPIl - LNPIZ LNPI3 LNPI4 LNPIS LNPI6 LNPI7 LNPI8/ FORWARD;
DATA E; SET C;
IF TYPE - 'POL';
PROC STEPWISE;
MODEL LNPIl - LNPIZ LNPI3 LNPI4 LNPIS LNPI6 LNPI7 LNPIS/ FORWARD;
DATA F; SET C;
IF TYPE - 'BIO';
PROC STEPWISE;
MODEL LNPIl - LNPI2 LNPI3 LNPI4 LNPIS LNPI6 LNPI7 LNPI8/ FORWARD;
DATA G; SET C;
IF TYPE - 'BIO' OR TYPE - 'TSE' OR TYPE - 'CR';
PROC STEPWISE;
MODEL LNPIl - LNPI2 LNPIB LNPI4 LNPIS LNPI6 LNPI7 LNPI8/ FORWARD;
DATA H; SET C;
IF TYPE - 'TSE' OR TYPE - 'CR';
PROC STEPWISE;
MODEL LNPIl - LNPI2 LNPIB LNPI4 LNPIS LNPI6 LNPI7 LNPIB/ FORWARD;

117

.__.._.

dun—2

APPENDIX T ANOVA TABLES FOR STEPWISE FORWARD REGRESSION OF EQN. 27
ALL—MIA R SQUARE - 0.88396866
C(P) - 6.20601691
DF SUM OF SQUARES MEAN SQUARE F PROB>F
REGRESSION 6 1847.32066661 307.88677777 269.18 0.0001
ERROR 212 242.48268767 1.14378626
TOTAL 218 2089.80335428
B VALUE STD ERROR TYPE 11 SS F PROB>F
INTERCEPT -1.15291711
LNPI2 -l.18510846 0.03445667 1353.05166763 1182.96 0.0001
LNPI3 -0.63247944 0.27702512 5.96210200 5.21 0.0234
LNPI4 0.65345676 0.35453874 3.88553834 3.40 0.0667
LNPIS 2.58675358 0.52345861 27.93124478 24.42 0.0001
LNPI6 -0.14334317 0.12635054 1.47212506 1.29 0.2579
LNPIB 0.58449073 0.11498918 29.55195233 25.84 0.0001
BOUNDS ON CONDITION NUMBER: 2.075972, 53.89638

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY

SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPIl

STEP

O‘U‘IJ-‘WNH

VARIABLE NUMBER
ENTERED IN

LNPI2
LNPIS
LNPI8
LNPI3
INPI4
LNPI6

O‘Ul-PWNH

PARTIAL

000000

R**2

.8595
.0052
.0136
.0030
.0019
.0007

000000

MODEL
R**2

.8595
.8648
.8784
.8813
.8833
.8840

40.
33.
10

C(P)

6669
1423
.4135
6.9733
5.4883
6.2060

F

1327.9560
8.3583
24.0124
5.3906
3.4934
1.2871

PROB>F

.0001
.0042
.0001
.0212
.0630
.2579

000000

118

APPENDIX T (Cont'd)

W R SQUARE - 0-92795738
C(P) - 6.00000000
DF SUM OF SQUARES MEAN SQUARE F
REGRESSION 5 1125.86994782 225.17398956 311.71
ERROR 121 87.40769636 0.72237766
TOTAL 126 1213.27764418
B VALUE STD ERROR TYPE II SS F
INTERCEPT -2.62087454
LNPIZ -0.96834290 0.03779762 474.12595877 656.34
LNPIS 7.74400372 0.63844103 106.28055773 147.13
LNP16 -1.00395201 0.15834837 29.03775237 40.20
LNPI7 -0.20085608 0.10642614 2.57298736 3.56
LNPI8 -0.95693069 0.18975320 18.37160278 25.43
BOUNDS ON CONDITION NUMBER: 2.0053, 44.42087

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY

PROB>F

0.0001

PROB>F

0.0001
0.0001
0.0001
0.0615
0.0001

SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPII

VARIABLE NUMBER PARTIAL MODEL

STEP ENTERED IN R**2 R**2 C(P) F
1 LNPIZ 1 0.8387 0.8387 147.956 649.8326
2 LNPIS 2 0.0493 0.8880 67.188 54.5367
3 LNPI6 3 0.0244 0.9124 28.150 34.3030
4 LNPI8 4 0.0134 0.9258 7.562 22.1237
5 LNPI7 5 0.0021 0.9280 6.000 3.5618

PROB>F

0.0001
0.0001
0.0001
0.0001
0.0615

119

APPENDIX T (Cont'd)

R SQUARE - 0.81814085

 

C(P) - 6.00000000

DF SUM OF SQUARES MEAN SQUARE F PROB>F
REGRESSION 5 96.20570016 19.24114003 85.48 0.0001
ERROR 95 21.38493250 0.22510455
TOTAL 100 117.59063266

B VALUE STD ERROR TYPE II 83 F PROB>F

INTERCEPT 1.62856536
LNPI2 -0.76301681 0.06124559 34.93839022 155.21 0.0001
LNPIS 4.30005273 0.59462695 11.77179430 52.29 0.0001
LNPI6 -0.49140581 0.13720729 2.88742366 12.83 0.0005
LNPI7 -0.32227736 0.06304277 5.88265388 26.13 0.0001
LNPI8 -0.22787577 0.20811843 0.26987305 1.20 0.2763
BOUNDS ON CONDITION NUMBER: 4.6443, 77.87777

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY
SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPIl

VARIABLE NUMBER PARTIAL MODEL

STEP ENTERED IN R**2 R**2 C(P) F PROB>F
1 LNPI2 1 0.5777 0.5777 123.595 135.4384 0.0001
2 LNPIS 2 0.1831 0.7608 29.968 74.9902 0.0001
3 LNPI7 3 0.0320 0.7928 15.242 14.9894 0.0002
4 LNPI6 4 0.0231 0.8158 5.199 12.0179 0.0008
5 LNPI8 5 0.0023 0.8181 6.000 1.1989 0.2763

APPENDIX T (Cont'd)

W

REGRESSION

ERROR
TOTAL

INTERCEPT

LNPI2
LNPIS
LNPI6
LNPI7

BOUNDS ON CONDITION NUMBER:

9.
-1.
-2.
-0.
-1.

DP

4
21
25

B VALUE

86852899
01074225
70569296
23503598
23594343

120

C(P) -

SUM OF SQUARES

490.16839969

3.69162571 0.17579170
493.86002541
STD ERROR TYPE 11 SS
0.02726333 241.61357709
0.88659883 1.63719754
0.16563993 0.35394598
0.54766675 0.89528808
5.202306, 57.76826

MEAN SQUARE

122.54209992

R SQUARE - 0.99252496
5.00000000

697.09

1374.43
9.31
2.01
5.09

PROB>F

0.0001

PROB>F

0.0001
0.0061
0.1706
0.0348

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY

SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPIl

STEP

L‘WNH

VARIABLE NUMBER
ENTERED

LNPI2
LNPIS
LNPI7
LNPI6

IN

TWIN)!“

PARTIAL MODEL

R**2

0.9850
0.0057
0.0011
0.0007

R**2

0.9850
0.9907
0.9918
0.9925

C(P)

20.1788

6.1481
5.0134
5.0000

F

1574.5365
14.1007

2.9966
2.0134

PROB>F

0.0001
0.0010
0.0974
0.1706

APPENDIX T (Cont'd)

   

1". . 14 a : .T__ -,_

A!!! 7 FROM THIS m,

DF

REGRESSION 6

ERROR 111

TOTAL 117
B VALUE
INTERCEPT 10.55962959
LNPIZ ~1.13463792
LNPI3 -O.63629414
LNPI4 0.74751392
LNPIS -4.66337204
LNPI7 -l.38251886
LNPI8 -0.44582534

121

R SQUARE - 0.95124048

C(P) - 6.00108358
SUM OF SQUARES MEAN SQUARE F
1872.01012471 312.00168745 360.91
95.95713623 0.86447870
1967.96726094
STD ERROR TYPE 11 SS F
0.03237008 1062.13903934 1228.65
0.27282291 4.70227992 5.44
0.35972045 3.73303974 4.32
0.77472304 31.32286511 36.23
0.35535902 13.08463879 15.14
0.16107995 6.62217724 7.66
3.16159, 74.59625

BOUNDS ON CONDITION NUMBER:

PROB>F

0.0001

PROB>F

0.0001
0.0215
0.0400
0.0001
0.0002
0.0066

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY

SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPII

STEP

0U4>UNH

VARIABLE NUMBER
ENTERED IN
LNPI2 1
LNPIS 2
LNPI7 3
LNPI8 4
LNPI3 5
LNPI4 6

PARTIAL

000000

R**2

.9194
.0107
.0122
.0056
.0013
.0019

000000

MODEL
R**2

.9194
.9301
.9424
.9480
.9493
.9512

67
45.
19.

C(P)

.8299
5978
9986
.3080
.2805
.0011

1323.
17.
24.
12.

2303
6823
2026
2245

.9672
.3183

PROB>F

000000

.0001
.0001
.0001
.0007
.0877
.0400

122

APPENDIX T (Cont'd)

W R SQUARE - 0-92245772

C(P) - 6.02234466

DF SUM OF SQUARES MEAN SQUARE F PROB>F
REGRESSION 6 554.75600765 92.45933461 168.53 0.0001
ERROR 85 46.63307856 0.54862445
TOTAL 91 601.38908621

B VALUE STD ERROR TYPE II SS F PROB>F
INTERCEPT 9.29396825
LNPIZ -1.03148925 0.06433050 141.04921679 257.10 0.0001
LNPI3 -0.17633655 0.21540245 0.36767030 0.67 0.4153
LNPIS 1.99315994 1.12223617 1.73057702 3.15 0.0793
LNPI6 0.44738397 0.15906953 4.33972287 7.91 0.0061
LNPI7 -1.50476378 0.27897226 15.96209124 29.09 0.0001
LNPIB 0.78177762 0.21072830 7.55085074 13 76 0.0004
BOUNDS ON CONDITION NUMBER: 8.406162, 146.2706

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY

SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPIl

VARIABLE NUMBER PARTIAL MODEL
STEP ENTERED IN R**2 R**2 C(P) F PROB>F
1 LNPIZ 1 0.8450 0.8450 79.9200 490.7595 0.0001
2 LNPI7 2 0.0398 0.8848 38.7807 30.7692 0.0001
3 LNPI8 3 0.0259 0.9108 12.6768 25.5815 0.0001
4 LNPI6 4 0.0079 0.9187 6.1344 8.4324 0.0047
5 LNPIS 5 0.0032 0.9218 4.6848 3.5032 0.0646
6 LNPI3 6 0.0006 0.9225 6.0223 0.6702 0.4153

123

APPENDIX T (Cont'd)

Li I ' ’ _-.p ‘1 - SQUARE - 0.88067270
$192!, C(P) - 2.43212636

 

DF SUM OF SQUARES MEAN SQUARE F PROB>F
REGRESSION 4 72.89368395 18.22342099 112.55 0.0001
ERROR 61 9.87677552 0.16191435
TOTAL 65 82.77045947

B VALUE STD ERROR TYPE II SS F PROB>F

INTERCEPT 4.35474983
LNPI2 -0.69619258 0.05759814 23.65523535 146.10 0.0001
LNPI4 0.15010593 0.14527829 0.17285406 1.07 0.3056
LNPI6 0.46141609 0.13043597 2.02617077 12.51 0.0008
INPI8 0.42889568 0.04323441 15.93417582 98.41 0.0001
BOUNDS ON CONDITION NUMBER: 2.037436, 24.53229

NO OTHER VARIABLES MET THE 0.5000 SIGNIFICANCE LEVEL FOR ENTRY
SUMMARY OF FORWARD SELECTION PROCEDURE FOR DEPENDENT VARIABLE LNPIl

VARIABLE NUMBER PARTIAL MODEL

STEP ENTERED IN R**2 R**2 C(P) F PROB>F
1 LNPIZ 1 0.6679 0.6679 100.641 128.6906 0.0001
2 LNPI8 2 0.1866 0.8545 11.267 80.7752 0.0001
3 LNPI6 3 0.0241 0.8786 1.455 12.3178 0.0008
4 LNPI4 4 0.0021 0.8807 2.432 1.0676 0.3056

124

APPENDIX U ANOVA TABLES FOR LINEAR REGRESSION
1. Regression of Eqn. 27 fbr published polymer data.

ANALYSIS OF VARIANCE

SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 5 96.20570016 19.24114003 85.476 0.0001
ERROR 95 21.38493250 0.22510455
C TOTAL 100 117.59063
ROOT MSE 0.4744518 R-SQUARE 0.8181
DEP MEAN 8.719047 ADJ R-SQ 0.8086
C.V. 5.441556
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
INTERCEP 1 1.62856536 0.72915465 2.233 0.0279
LNPIZ 1 -0.76301681 0.06124559 -12.458 0.0001
LNPI3 0 0
LNPI4 0 0 . . .
LNPIS 1 4.30005273 0.59462695 7.232 0.0001
LNPI6 1 -0.49140581 0.13720729 ~3.581 0.0005
LNPI7 1 -0.32227736 0.06304277 -5.112 0.0001
LNPI8 1 -0.22787577 0.20811843 -1.095 0.2763
2. Regression of predicted vs. o'bservedAPent (intercept - 0).
ANALYSIS OF VARIANCE
SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 1 1.02154E+14 1.02154E+14 1310.994 0.0001
ERROR 100 7.79213E+12 77921282947
U TOTAL 101 1.09946E+14
ROOT MSE 279143.8 R-SQUARE 0.9291
DEP MEAN 905353.4 ADJ R-SQ 0.9284
C.V. 30.83258
NOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
PENT 1 0.92588020 0.02557140 36.208 0.0001

125

APPENDIX U (Cont'd)
1. Regression of Eqn. 27 fer pdblished defatted soy dough data.

ANALYSIS OF VARIANCE

SUM OF MEAN

SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 4 490.16840 122.54210 697.087 0.0001
ERROR 21 3.69162571 0.17579170
C TOTAL 25 493.86003

ROOT MSE 0.4192752 .R-SQUARE 0.9925

DEP MEAN 14.11403 ADJ R-SQ 0.9911

C.V. 2.970626

PARAMETER ESTIMATES

PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETERFO PROB > |T|
INTERCEP 1 9.86852899 2.66071388 3.709 0.0013
LNPIZ 1 -1.01074225 0.02726333 -37.073 0.0001
LNPI3 0 0 . . .
LNPI4 0 0 . . .
LNPIS 1 -2.70569296 0.88659883 -3.052 0.0061
LNPI6 1 -0.23503598 0.16563993 -1.419 0.1706
LNPI7 1 -1.23594343 0.54766675 -2.257 0.0348
LNPI8 0 0 . . .

2. Regression of predicted vs. o'bservedAPent (intercept - 0).

ANALYSIS OF VARIANCE

SUM OF MEAN

SOURCE DF SQUARES SQUARE F VALUE . PROB>F
MODEL 1 2.41589E+15 2.41589E+15 213.294 0.0001
ERROR 25 2.83164E+14 1.13266E+13
U TOTAL 26 2.69906E+15

ROOT MSE 3365498 R-SQUARE 0.8951

DEP MEAN 8234025 ADJ R-SQ 0.8909

C.V. 40.87306 '

NOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.

PARAMETER ESTIMATES

PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|

PENT 1 1.16667834 0.07988436 14.605 0.0001

126

APPENDIX U (Cont'd)
1. Regression of Eqn. 27 in: twin-screw extruder data.

ANALYSIS OF VARIANCE

SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 7 72.96672622 10.42381803 61.668 0.0001
ERROR 58 9.80373325 0.16902988
C TOTAL 65 82.77045947
ROOT MSE 0.4111324 R-SQUARE 0.8816
DEP MEAN 6.229246 ADJ R-SQ 0.8673
C.V. 6.600035
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETERPO PROB > |T|
INTERCEP 1 4.82881873 1.93533238 2.495 0.0155
LNPI2 1 -0.66693893 0.07417413 -8.992 0.0001
LNPI3 1 -0.01294504 0.13871981 -0.093 0.9260
LNPI4 1 0.19065828 0.17607393 1.083 0.2834
LNPIS 1 -0.67566395 1.04673791 -0.645 0.5212
LNPI6 1 0.48817136 0.16286907 2.997 0.0040
LNPI7 1 0.03216432 0.24319444 0.132 0.8952
LNPI8 1 0.30976205 0.18932755 1.636 0.1072
2. Regression of predicted vs. observedAPent (intercept - 0).
ANALYSIS OF VARIANCE
SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 1 2.24368E+14 2.24368E+14 597.170 0.0001
ERROR 65 2.44217E+13 375718726972
U TOTAL 66 2.48790E+14
ROOT MSE 612959 R-SQUARE 0.9018
DEP MEAN 1317796 ADJ R-SQ 0.9003
C.V. 46.51395
NOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
PENT 1 1.14325345 0.04678359 24.437 0.0001

127

APPENDIX U (Cont'd)
1. Regression of Eqn. 27 fer twin.screw extruded potato dough data.

ANALYSIS OF VARIANCE

SUM OF MEAN

SOURCE OF SQUARES SQUARE F VALUE PROB>F
MODEL 5 8.74900592 1.74980118 232.014 0.0001
ERROR 8 0.06033439 0.007541799
C TOTAL 13 8.80934032

ROOT MSE 0.08684353 R-SQUARE 0.9932

DEP MEAN 6.86524 ADJ R-SQ 0.9889

C.V. 1.264974

NOTE: MODEL IS NOT FULL RANK. LEAST SQUARES SOLUTIONS FOR THE
PARAMETERS ARE NOT UNIQUE. SOME STATISTICS WILL BE MISLEADING. A
REPORTED DF OF 0 OR B MEANS THAT THE ESTIMATE IS BIASED. THE FOLLOWING
PARAMETERS HAVE BEEN SET TO 0, SINCE THE VARIABLES ARE A LINEAR
COMBINATION OF OTHER VARIABLES AS SHOWN.

LNPIS -+.0418519*INTERCEP

LNPI6 --4.60517*INTERCEP+1.00009*LNPI3 -.713909*LNPI4
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
INTERCEP B 2.01025290 18.80823535 0.107 0.9175
LNPIZ 1 -1.20371941 2.24960210 -0.535 0.6071
LNPI3 B 0.009700634 0.09660354 0.100 0.9225
LNPI4 B 0.40792679 1.64483735 0.248 0.8104
LNPIS 0 0 . .
LNPI6 0 0 . . .
LNPI7 1 -0.07077102 0.11879876 -0.596 0.5678
LNPI8 1 -0.04989444 2.76469565~ _ -0.018 0.9860
2. Regression of predicted vs. ObservedAPent (intercept - 0).
ANALYSIS OF VARIANCE
SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 1 1.22635E+14 1.22635E+14 2127.529 0.0001
ERROR 13 749343593639 57641814895
U TOTAL 14 1.23384E+14
ROOT MSE 240087.1 R-SQUARE 0.9939
DEP MEAN 2655886 ADJ R-SQ 0.9935
C.V. 9.039813
NOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|

PENT 1 0.99158004 0.02149760 46.125 0.0001

128

APPENDIX U (Cont'd)

1. Regression of Eqn. 27 fer twin screw extruder defatted soy dough
data.

ANALYSIS OF VARIANCE

SUM OF MEAN

SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 5 26.10774046 5.22154809 44.882 0.0001
ERROR 18 2.09409131 0.11633841
C TOTAL 23 28.20183177

ROOT MSE 0.3410842 R-SQUARE 0.9257

DEP MEAN 5.592433 ADJ R-SQ 0.9051

C.V. 6.09903

NOTE: MODEL IS NOT FULL RANK. LEAST SQUARES SOLUTIONS FOR THE
PARAMETERS ARE NOT UNIQUE. SOME STATISTICS WILL BE MISLEADING. A
REPORTED DF OF 0 OR B MEANS THAT THE ESTIMATE IS BIASED. THE FOLLOWING
PARAMETERS HAVE BEEN SET TO 0, SINCE THE VARIABLES ARE A LINEAR
COMBINATION OF OTHER VARIABLES AS SHOWN.

LNPIS -+0.60811*INTERCEP
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:

VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
INTERCEP B 0.91196859 2.71849594 0.335 0.7412
LNPI2 1 -1.01267016 0.18592286 -5.447 0.0001
LNPI3 1 0.18719735 0.18070384 1.036 0.3140
LNPI4 1 0.01075148 0.23770239 0.045 0.9644
LNPIS 0 0 . . .
LNPI6 1 -0.11061647 0.34529471 -0.320 0.7524
LNPI7 1 -0.01958339 0.33250461 -0.059 0.9537
LNPI8 0 0

2. Regression of predicted vs. observedAPent (intercept - 0).

ANALYSIS OF VARIANCE

SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 1 7.75500E+12 7.75500E+12 150.681 0.0001
ERROR 23 1.18372E+12 51466202543
U TOTAL 24 8.93872E+12
ROOT MSE 226861.6 R-SQUARE 0.8676
DEP MEAN 596944.6 ADJ R-SQ 0.8618
C.V. 38.0038
LNOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|
PIENT l 0. 82719354 0 . 06738720 12 . 275 0 .0001

129

APPENDIX U (Cont'd)
1. Regression of Eqn. 27 for twin-screw extruded SPS data.

ANALYSIS OF VARIANCE

SUM OF MEAN

SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 6 28.33342592 4.72307099 173.484 0.0001
ERROR 21 0 57172090 0 02722480
C TOTAL 27 28.91014682

ROOT MSE 0.1649994 R-SQUARE 0.9802

DEP MEAN 6.457039 ADJ R-SQ 0.9746

C.V. 2.555322

PARAMETER ESTIMATES

PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETERFO PROB > |T|
INTERCEP 1 -0.12425401 1.84586475 -0.067 0.9470
LNPI2 1 -1.15247246 0.05914654 -19.485 0.0001
LNPI3 1 -0.48282691 0.07975095 -6.054 0.0001
LNPI4 1 0.29246896 0.10763972 2.717 0.0129
LNPIS 1 -1.18409473 3.32475756 -0.356 0.7253
LNPI6 1 -0.22026055 0.11409482 -1.931 0.0672
LNPI7 1 -0.06331602 0.15055214 —0.421 0.6783
LNPI8 0 0
2. Regression of predicted vs. o'bservedAPent (intercept - 0).
ANALYSIS OF VARIANCE
SUM OF MEAN
SOURCE DF SQUARES SQUARE F VALUE PROB>F
MODEL 1 3.43189E+13 3.43189E+13 2523.672 0.0001
ERROR 27 367167053531 13598779760
U TOTAL 28 3.46860E+13
ROOT MSE 116613.8 R-SQUARE 0.9894
DEP MEAN 1024732 ADJ R-SQ 0.9890
_C.V. 11.37993
NOTE: NO INTERCEPT TERM IS USED. R-SQUARE IS REDEFINED.
PARAMETER ESTIMATES
PARAMETER STANDARD T FOR H0:
VARIABLE DF ESTIMATE ERROR PARAMETER-0 PROB > |T|

PENT 1 0.98180232 0.01954374 50.236 0.0001

130

APPENDIX V INDUSTRIAL APPLICATIONS OF THE DIE PRESSURE DROP MODEL

The following steps outline the procedure for calculating the

pressure drop in extruder dies for food industry applications.

DATA COLLECTION

For the following data collection with two or three circular dies
with the same cross sections but different lengths will be needed. If
a wide range of shear rates is required, it is mormally recommended that
two sets of dies are used, one with twice the diameter of the orher.
This gives an eight fold change in shear rate as well as additional

change in flow rate.

For each material tested, perform the following steps:

1) Accurately calibrate the extruder moisture content and product rate,
and use the calibration program given in Appendix D for predicting
product rates at the same moisture content of the test material.

2) For the appropriate range of processing conditions (MC,temperature,
rpm, etc) collect AP vs. Q data for the long/short die combinations.
Extreme care should be taken to ensure that extrusion conditions
(barrel temperature, work input, etc.) are as similar as possible
for each long/short die combination.

3) Record temperature, pressure, product rate, moisture content, and
density of material. Record the temperature at the die entrance by
inserting a small probe through the die hole to the die cone entry.
To determine density, pre-weigh an empty capillary or die of known
volume, extrude material into the capillary, and weigh the capillary

plus extrudate. Calculate density as follows:

131

APPENDIX V (Cont'd)

4)

5)

p - 1 we t - t d e wei ht

volume of die

If the material exhibits elastic properties by swelling at
temperatures below 100°C, further data collection will be necessary
to estimate the material elastic time constant. For the same
product rate and temperature, photograph the extrudate swell for
three different L/Ds of equal diameter dies.

If the data of step 3 does not have significant variation in
temperature this step can be omitted.

Use a rheometer that maintains constant temperature to determine
viscosity as a function of temperature for temperature-time
histories and moisture contents similar to those for the extrusion
process. For doughs of low viscosity a rotary viscometer is the
simplest kind to use. For most doughs of moderate to high

viscosities a tube or capillary rheometer will be required.

DATA.ANALYSIS

6)

7)

Adjust data to the average extrusion die temperature. At low medium
and high shear rates, use step 5 to collect data required to model n

as a function of temperature according to

_ A e(AEv/RT)

"1-constant

Adjust extrudate pressure data to an average temperature as follows:

132

APPENDIX V (Cont'd)

- l -1
AEanve. meas. ]
APadj - APobse
where AEv/R is the slope of the line in step 6 and T is the mean

Ave.

of all temperatures recorded in step 3.

8)

9)

10)

A)

B)

Extrapolate extruder AP data for each shear rate as

shown in Figure 10 and obtain APent for each long/short die
combination.

Convert extruder AP vs. Q data to shear stress vs. shear rate
data. Plot 7w vs. F on log-log paper. Use linear regression to
obtain the slope and intercept of a line through this data where n

is the slope of this line and m is computed as follows:

m - intercept/((3n+1)/(4n))n

Note, the above relationship assumes a Power-law fluid
approximation.

Elastic time constant calculation

For nonelastic materials, this step can be skipped. For elastic
materials, a method is proposed for determining an elastic time
constant.

Compute a swell ratio, 6, - extrudate diameter/die diameter.

Plot the swell ratio, 8, vs. die residence time (See Figure 21) and

compute A as (Williams, 1977):

133

APPENDIX V (Cont’d)
1n[: - ’99:]
A - o - 3
-t

where t is the die residence time.

 

11) Prediction of entrance pressure drop.

A) Compute «1 and «2 for all data as follows:

2 4
«1 _ 16 nd rh APEB.

p Q2

«2 - .p Q

m drh"

where

_ Q n-1 3 +1 n-l
n (1 ) - m 3 4n
wall 2wn r

If the material is elastic compute "8 as follows:

_1+__1_9__

3
16« ndrh

1r8

If data of more than one material was collected, compute «

follows:

«5 - (3n+1)/(4n)

(8)

(11)

(12)

(13)

58.8

(14)

134

APPENDIX V (Cont'd)

B) Regress 1n1r1 - lna + bzlnar2 + b51n1r5 + b81n1r8 using a rendition of

the SAS program given in appendix 8.

C) Model AP as follows:
ent

2 b2 b5 b8
Arent- _2_0_____ [a<«2> («5) («8) 1 (15)
2 4
16nd rh

12) For predicting APdhole of circular or noncircular holes use the

following approximation:

 

.L.E [ 3021 ] “Qn 1
APdhole - (8t)nrh(3n+l) n fc (16)

where fc is obtained from Figure 3.

13) For prediction total die pressure drop for circular or non circular

dies use the following approximation:

APT - APent + APdhole (17)

135

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temperature, shear rate and moisture on viscosity of defatted soy flour
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Engr. and Sci. 17(4):257-265.

 

October 1987
BIRTHDATE: August 26, 1963
CITIZENSHIP: U.S.
MARITAL STATUS: Single
HOME ADDRESS: 3000 Trilogy wk phone #(201) 797-6800

Milford, MI 48042 hm phone #(313) 685-1542
CURRENT POSITION: Engineering Consultant to Nabisco Brands
PROFESSIONAL.TRAINENG: Passed Engineer-in-Training Exam

EDUCATION:

Dec. '87 M.S. Candidate in Agricultural/Food engineering,
Michigan State University. Thesis topic: Pressure
drop vs. flow rate modeling for extrusion dies.

June '85 B.S. Agricultural Engineering, Michigan State
University. Concentration of study: 1983-85 Agri.
Engr., Michigan State University; 1981-83 Mech.
Engr., University of Michigan.

EXPERIENCE:
1987-present. Engineering Consultant to Nabisco Brands, Inc.
1985-1987. Res. Assis., Agri. Engr., Michigan State University

Project leader of installation of new Baker Perkins 50mm Twin
Screw Extruder, including complete equipment installation,

developing training materials as well as training/certifying
operators.

Project leader of research on food extruder die flow analysis
methods: organizing/operating extrusion tests.

l984/spring. Agricultural Aide, Colombia, South America
Provided farm training for Colombian students.

l979-1986/summers. Equipment operator. Dyrland Farms, Inc, Big
Sandy Montana, and Drever's Dairy, Balzac Alberta. Operated and
maintained heavy farm equipment, assisted in dairy operations.

FOREIGN LANGUAGES:

Spanish; Four years study in high school, three months practice in
Colombia. Able to participate in general communications. Reading
and writing at junior high school level.

Mandarin_ghing§e: Currently studying under private tutor.

139

ACADEMIC HONORS:

Michigan State Dean's Honor list, University of Michigan Dean's Honor
list, National Honor society, Phi Beta Kappa

SOCIETY'MEMBERSHIPS:

American Society of Agricultural Engineers:
Alpha Epsilon (Honor society of Agricultural Engineering)

PUBLICATIONS:

Hawkins, M.D., Morgan, R.G., Steffe,J.F. 1986. Extrusion die swell
phenomena of starch based doughs. ASAE paper No. 86-6523. ASAE, St.
Joseph, MI. Presented at the ASAE 1986 winter mtg, Chicago IL.

Howkins, M.D., Morgan, R.G. 1986. Similitude approach to food extrusion
die flow problems. ASAE paper No. 86-6001. ASAE, St. Joseph, MI.
Presented at the ASAE 1986 summer mtg, Cal-Poly State Univ. San Luis
Abispo.

REFERENCES:

Ronnie G. Morgan, Ph.D., PE.

Mgr Process Research and Development
Grocery Products and Venture Technology
Kraft, Inc.

801 Waukegan Rd Glenview, IL 60025
(312) 998-7440

Rudy Leschke, Mgr. extrusion engineering
Nabisco Brands, R&D Ctr.

2111 Rt. 208

Fairlawn NJ, 07410

(201) 797-6800

Howard A. Dyrland
Dyrland Farms, Inc.

Big Sandy, Montana 59520
(406) 378-2267

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3 1193 03J82

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