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This is to certify that the

thesis entitled

RHEOLOGICAL ANALYSIS OF STARCH-THICKENED, STRAINED

APRICOTS USING MIXER VISCOMETRY TECHNIQUES

presented by

Eugene William Ford

has been accepted towards fulfillment
of the requirements for

M.S. degree 1n Agricultural
Engineering

 

7%

Major professo/l

Date November 7, 1984

0-7639 MSU is an Allirmaiive Action/Equal Opportunity Institution

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RETURNING MATERIALS:

Place in book drop to
remove this checkout from
your record. FINES will
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stamped below.

‘-

RHEOLOGICAL ANALYSIS OF STARCH-THICKENED, STRAINED

APRICOTS USING MIXER VISCOMETRY TECHNIQUES

by

Eugene William Ford

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1984

ABSTRACT
RHEOLOGICAL ANALYSIS OF STARCH-THICKENED, STRAINED

APRICOTS USING MIXER VISCOMETRY TECHNIQUES

by

Eugene William Ford

Three major problems were considered in performing a
complete analysis on a starch—thickened, strained apricot
puree: irreversible breakdown (thixotropy), loading shear
breakdown and wall effects (slippage). Shear stress and
shear rate were estimated from mixer viscometer data. A
structural parameter, yield stress, flow behavior index and
a consistency coefficient were defined to quantify the rate
of breakdown and equilibrium structure of the product. The
techniques developed in this study are useful in describing
the time-dependent behavior of suspensions because the wall

effect--due to slip--is minimized.

To:

Emily, thanks for putting up with me through all of this,
what an angel

William and Wanda Ford, my parents

Earnest and Jean Jones, my new parents

Roy, my brother

Tina, my sister

Lydia, my sister

thanks, all of you, for the support

ii

ACKNOWLEDGMENTS

The author wishes to express his deepest gratitude to
Dr. James F. Steffe, a teacher, advisor, and friend, for his
moral and technical support.

The author is thankful to Dr. John B. Gerrish and Dr.
Kris A. Berglund for serving on the guidance committee.

Thankful acknowledgments go to the Gerber Products
Company which graciously supplied us with the funding,
apricot puree and use of their pilot plant facilities
necessary to complete this study.

A very special thanks goes to Marnie and Emily who made
this all readable from my often unreadable manuscripts.

Special thanks goes to the faculty, staff and students
of Michigan State University Departments of Agricultural
Engineering and Food Science who made every step of the way

enjoyable.

iii

TABLE OF CONTENTS

Chapter

1.

I NTRODUCT I ON I O O O O O O O O O O O O O O O O O O

1.1. Theory of Starch Swelling and Use of Starch
as a Thickening Agent . . . . . . . . . . .

1.2. Overview of Efforts . . . . . . . . . . . .
1.3. Reasons for Study . . . . . . . . . . . . .
1.4. Objectives . . . . . . . . . . . . . . . . .
LITERATURE REVIEW . . . . . . . . . . . . . . . .
2.1. Properties of Starch and Fruit Purees . . .

2.1.1. Starch Solutions . . . . . . . . . .

2.1.2. Fruit Purees . . . . . . . . . . . .

2.1.3. Starch-Thickened Fruit Purees . . .
2.2. Thixotropy Characterization Methods . . . .
2.3. Mixer Viscometry . . . . . . . . . . . . . .
2.4. Wall Effects . . . . . . . . . . . . . . . .
THEORETICAL DEVELOPMENT . . . . . . . . . . . . .
3.1. Mixer Viscometry . . . . . . . . . . . . . .

3.2. Modified Tiu and Roger Method of Breakdown
Characterization . . . . . . . . . . . . . .

3.2.1. Assumption of No Recovery and Basis
of Model . . . . . . . . . . . . . .

3.2.2. Use of Approximate Shear Rate and
Approximate Shear Stress . . . . . .

3.3. Krieger Analysis for Concentric Cylinder
Viscometers . . . . . . . . . . . . . . . .

EXPERIMENTAL EQUIPMENT . . . . . . . . . . . . . .

PREPARATION OF THE STARCH-THICKENED, STRAINED
APRI COTS O O I O O O O O O O O I I C O O O O O O 0

iv

14
15
19

19

21

21

24

25

27

30

DATA COLLECTION AND ANALYSIS . . . . . . . . . . .
6.1. Yield Stress Data Collection and Analysis .

6.1.1. Yield Stress at Initial Point of
Breakdown (Time Zero) . . . . . . .

6.1.2. Yield Stress at Equilibrium . . . .

6.2. Recovery Data Collection and Analysis . . .

6.3. Paddle Mixer Constant (k') Data Collection
and Anaysis . . . . . . .

6.4. Thixotropic Breakdown Data Collection and

Analysis . . . . . . . . .

6.5. Wall Effect Data Collection and Analysis

Equilibrium . . . . . . .

6.6. Paddle Mixer Rheological Parameters

Estimation . . . . . . . . . . . . . . . . .
RESULTS AND DISCUSSION . . . . . . . . . . . . . .
7.1. Discussion of . . . . . . . . . . . . . . .

7.1.1. Results of the Recovery Test . . . .

7.1.2. Results of the Breakdown Analysis .

7.1.3. Results of the Wall Effect Analysis

7.1.4. Results of the Paddle Mixer Test . .

7.1.5. Relationship Between Phenomenological

CONCLUSIONS .

Relationship and Equilibrium

Rheogram . . . . .

SUGGESTIONS FOR FURTHER STUDY

REFERENCES . .

APPENDICES . .

A. ANALYSIS OF STABILITIY OF STARCH

B. FLOW CHART OF ANALYSIS

C. OUTLINE OF DATA COLLECTION

at

38

39

41

44
45
45
45
45
59
63

66
68
69
7O

73

LIST OF TABLES

Table Page
1. Models used to characterize thixotropy . . . . 9
2. Dimensions of the MV sensors and the MV paddle

mixer O O O O O O O O O O O O O O O O O I I O 28

3. List of ingredients per 1000kg of finished
prOdUCt O C O O O O O O O O O O O O O C O O O 31

4. Outline of statistics model used to check for
wall effects I O O O O O O O O C O O O O I O I 43

5. Data used to evaluate the mixer constant (k')
for the MV paddle mixer . . . . . . . . . . . 46

6. Experimental values of a1 and 1/(n o-ne) data
obtained using the modified Tiu and Boger
methOd O I O O O I O I O O O O O O O O O O I O 54

7. Torque at time zero and structural parameter
data obtained using the modified Tiu and
Boger methOd O O O O O O I O O O O O O O O O O 55

8. Series of data and calculations used to
determine yield stress at time zero . . . . . 56

9. The B constants determined using the

‘ statistical model . . . . . . . . . . . . . . 60
10. Rheological data for Karo light corn syrup . . 51
ll. Rheological parameters of starch-thickened,

strained apricots obtained using various MV
sensors and the MV paddle mixer . . . . . . . 52

vi

LIST OF FIGURES

Figure Page
1. Rheological classification of fluids . . . . . 5
2. Paddle mixer schematic . . . . . . . . . . . . 35
3. Yield stress determination using stress to

initiate flow . . . . . . . . . . . . . . . . 37
4. Plot used to evaluate the mixer viscometer

constant (k') for the MV paddle mixer . . . . 47
5. Recovery after a) 10 minutes b) 60 minutes . 43
6. l/(na-ne) versus time at various shear rates . 50
7. al versus shear rate . . . . . . . .'. . . . . 52
8. Rheogram obtained at time zero from modified

Tiu and Boger analysis using the MV paddle
mixer O O O O O O O O O O O O I O O O O O O O 53

9. Rheograms obtained using various MV sensors
and the paddle mixer . . . . . . . . . . . . . 54

10. Apparent viscosity versus shear rate obtained
using various MV sensors and the MV paddle
mixer O O I O I O O O O O I O O O O O O O O O 65

ll. Apparent viscosity versus shear rate obtained

from phenomenological relationship at
equilibrium and equilibrium rheogram . . . . . 57

vii

NOMENCLATURE

constant, which depends on mixer system geometry,
defined by Equation 12

constant in Tiu and Boger's method defined by
Equation 18

diameter of paddle mixer (m)
equivalent height of bob or sensor (m)
the null hypothesis

dummy variables used in t-test for three linear
equations

consistency coefficient (Pa-s“)

paddle mixer constant needed for K approximation and
shear rate approximation defined by Equation 13

initial consistency coefficient defined by Equation
15 (Pa-s“)

rate constant, which is a function of shear rate,
defined by Equation 16

torque (N-m)

initial torque defined by Equation 31 (N-m)
torque to initiate flow (N-m)

flow behavior index, dimensionless

initial flow behavior index defined by Equation 15,
dimensionless
power (J-s'l)

power number for mixing vessels defined by Equation
10, dimensionless

radius of bob or sensor (m)
radius of cup (m)
Reynolds number, dimensionless

ratio of cup to bob radius defined by Equations 2,
3 and 4, dimensionless

Krieger's analysis variable defined by Equation 24

viii

Krieger's analysis variable defined by Equation 24
Student's t-distribution
slip velocity (m-s'l)

1n (shear rate)

80,%382.83.B4.85 = constants in the t—tests for three linear

equations defined in Equation 32
effective slip coefficient

shear rate (s'l)

apparent shear rate (5'1)
fluid viscosity (assumes Newtonian fluid), (Pa-s)
apparent viscosity (Pa-s)

apparent viscosity at equilibrium (Pa-s)

initial apparent viscosity (Pa's)

structural parameter defined by Equation 17
structural parameter at equilibrium

density (kg.m'3)
apparent shear stress (Pa)

shear stress at bob (Pa)

apparent shear stress at equilibrium (Pa)

yield stess (Pa)

initial yield stress defined by Equation 15 (Pa)

angular velocity (5'1)

ix

INTRODUCTION

1.1. Theory of Starch Swelling and Use of Starch as a
Thickening Agent

Starch is a polysaccharide consisting of amylose
(linear fraction) and amylopectin (branched fraction). It
occurs naturally as discrete bundles or granules. When
starch is mixed with water and the solution is heated to 60-
75°C, gelatinization occurs. During gelatinization, starch
granules imbibe water until they break apart. Partial
gelatinization leaves the starch in a very swollen state
since the structure is only partially broken down.
Gelatinization is caused by the hydrophilic groups in the
starch molecule taking up moisture in proportion to the
relative humidity of the atmosphere. An increase in
temperature furnishes the energy required to break some of
the intermolecular hydrogen bonds present in a starch
system. This allows for paths of water entry and more
pockets for water storage. Swelling occurs due to an
increased amount of water being held in the starch
structure. This swelling, in turn, thickens the water-
starch solution because of the increased granule size, and
thus increases the viscosity (Fennema, 1976).

Partially gelatinized starch solutions are often used

to thicken products which are thinner than the consumer

prefers, e.g. apricot baby food manufactured by the Gerber
Products Company and used in this study. It is the study of

these products on which this paper will focus.

1.2. Overview of Efforts

This study includes four general areas of
experimentation. First, apricot puree samples were
mechanically degraded with a mixer driven at a constant
angular velocity until consistencies reached equilibrium.
After a 10 or 60 minutes recovery period, a second
mechanical degradation curve was obtained. The degree of
recovery of the initial structure was determined by
comparing the second degradation curve with the first for
each sample. The extent of recovery dictated the nature of
the apricot puree breakdown, i.e. reversible, partially
reversible or irreversible.

Following the recovery analysis, the breakdown and
build-up (if applicable) curves were characterized using a
model developed by Tiu and Boger (1974). The model was
modified to account for the completely irreversible
breakdown which apricot puree seems to undergo. (See Figure
l for rheological classification of fluids.)

Next, the problem of wall effects, which can occur in
suspensions, was investigated using samples which had been
mechanically degraded to their equilibrium structures. Wall
effects can be caused by localized separation (thinning) at

the sensor, or by an even settling of solids within the

entire sample. Wall effects may be a problem particularly
with narrow gap viscometers, such as the one used in this
study.

Finally, the possibility of using a mixer viscometer
instead of a narrow gap concentric cylinder viscometer was
investigated. The value of the mixer is that it would keep
product solids suspended, thereby minimizing product
thinning near the sensor. In addition, a sample type mixer
would tend to minimize sample degradation while loading the

cup into the viscometer.

1.3. Reasons for Study

To date, there has not been a complete characterization
of a starch-thickened fruit puree presented in the
literature. A complete anlysis includes characterization of
recovery, breakdown and build-up (if applicable) curves,
wall effects and the equilibrium rheogram. Secondly, it has
not yet been determined if wall effects are a problem when
using concentric cylinder viscometers, and if wall effects
are present, how to minimize them when testing food
suspensions. Finally, the results of this study will be
invaluable in formulating rheologically based quality

control tests for starch-thickened products.

1.4. Objectives
The major objective of this study was to conduct a
complete rheological analysis of starch-thickened apricot

puree. A secondary objective was to determine whether or

4

not a paddle mixer viscometer could be used to overcome
problems which concentric cylinder viscometers have with
suspended solids. These problems included loading shear
breakdown in the mechanical degradation tests and separation

of sample near the bob (wall effects) in the equilibrium

tests.

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L I TERATURE REV I EW

2.1. Properties of Starch and Fruit Purees

2.1.1. Starch Solutions

Pure starch solutions have been shown to have partially
reversible breakdown at a constant shear rate by Evans and
Haisman (1979), Howling (1980), and Lang and Rha (1981).
The extent of swelling (percent gelatinization) can be
correlated with viscosity behavior (Schoch, 1969).
Specifically, a large amount of swelling results in fragile
granules which are readily fragmented (from the breaking of
intermolecular hydrogen bonds) upon stirring, thereby
resulting in a substantial thinning of the starch solution.
This fact contributes to the irreversible component of the
partially reversible breakdown exhibited by starch
solutions.

It is possible that the corresponding reversible
component is, in part, due to slip, i.e. the formation of a
thinner solution layer near the bob (sensor) during
shearing. Specifically, the redistribution of the sample to
homogeneity (reversal of slip) during the recovery period
could result in a torque pattern which erroneously suggests
reversibility. Traditional theories used to quantify
thixotropy (Cheng and Evans, 1965; Hahn et al., 1959 and
Harris, 1972) ignore the possible presence of slip in the
sample. Van Wazer et a1. (1963), Figoni and Shoemaker
(1981) and Rao (1975) suggested that there may be slip in

the starch suspensions when using contemporary coaxial and

cone-and-plate viscometers, but no remedy was offered.
Evans and Haisman (1979) measured sedimentation rates but
never studied the possibility of sedimentation causing a
thinner liquid to be near the bob, thus resulting in

erroneous data.

2.1.2. Fruit Purees

Apricot puree was studied by Harper (1960) and Watson
(1968). These authors reported the material to be shear-
thinning, at various solids contents and over a wide range
of ripeness. Other data can be found for apple sauce
(Charm, 1962; Haugen and Tung, 1976; Saravacos and Moyer,
1967; Saravacos, 1968; Steffe et al., 1984) tropical fruit
purees--banana, guava, mango, papaya--(Rao, et al., 1974),
peach puree (Harper, 1960; Saravacos and Moyer, 1967) and
plum puree (Saravacos and Moyer, 1967). Data from the above
and other related articles have been summarized in a recent
paper by Steffe et a1. (1983). Also, it should be noted
that all of the fruit products mentioned above were modelled
as power-law fluids, meaning no significant yield stress was
observed.

Duran and Costell (1982) observed thixotropy, i.e.
time-dependent flow, in four varieties of apricot puree.
Canovas and Peleg (1983) observed similar behavior in
commercial semi-liquid food products, such as apple sauce,
banana puree and peach puree. Both of these studies used

the Herschel-Bulkley model to describe equilibrium

8

structure. (Some of the products tested by Canovas and

Peleg were starch—thickened.)

2.1.3. Starch-Thickened Fruit Purees

To date, there has not been a complete analysis of
starch-thickened fruit puree in the literature. Although
Canovas and Peleg (1983) tested some starch-thickened
products, they did not discuss the possibility of wall
effects, i.e. product separation, causing time-dependent

flow, nor did they quantify the breakdown curve.

2.2. Thixotropy Characterization Methods

As stated earlier, thixotropy has been observed in
starch-thickened fruit products. Table 1 presents an
outline of methods used to characterize this phenomenon.

The first two methods listed are based on a hysteresis
loop, which is obtained in the following manner:

1. Angular velocity of the bob of a rotational
viscometer is steadily increased from zero to a
chosen maximum angular velocity in a specific time,
t.

2. Angular velocity is then steadily decreased back to
zero in the same time, t.

Steps 1 and 2 can be carried out with a speed
programmer or with periodic changes in angular velocity by
manual manipulation. The data can be plotted in two ways:
a) shear stress can be plotted against time on an x-t

plotter (then, since shear rate varies linearly with time,

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shear rate at any t can be determined), b) shear stress can
be plotted against shear rate on an x-y plotter.

Hysteresis loops are presently used for quick
qualitative analysis of a thixotropic material. By
measuring the area under the hysteresis loop, the relative
thixotropic behavior of a group of samples can be determined
(Heywood, 1981). It should be noted that the surface area
of the hysteresis loop depends on the previous history of
the sample, the maximum shear rate and the acceleration.

Too fast an acceleration may induce hysteresis in a non-
thixotropic material, since kinetic energy on the
deceleration side of the loop may decrease the torque needed
to turn the bob.

Green and Weltman (1943) attempted to use loops
quantitatively by relating the area of the hysteresis curve
to the degree of thixotropy, using two coefficients: a
coefficient of thixotropic breakdown with time and a
coefficient of thixotropic breakdown due to increasing shear
rate. Heywood (1981) stated that because Green and Weltman
carried out their analysis on the first loop obtained,
reproducibility was poor since the condition of the material
prior to shear testing was critical. If an "equilibrium
loop", obtained after repeated cyclings of the hysteresis
loop until the loops superimposed, were used,
reproducibility would be greatly improved. However, the
equilibrium method can not be used with irreversible

thixotropic materials, since the acceleration and

12

deceleration sides of the loop coincide at equilibrium,
making determination of the two coefficients impossible.

Cheng (1956) presented a method of obtaining
quantitative information on thixotropic behavior above yield
stress, using a Bingham Plastic model as the basis and
adding a structural parameter, A. Time-dependence was
assumed to be due to changes in A. A phenomenological
relationship (Bingham Plastic model with x) and a rate
equation (change in A with respect to time) were used to
describe thixotropic behavior. Cheng used an equilibrium
flow curve to determine the constants for the two equations.
After breaking down the sample structure, torque readings
were taken over a range of shear rates and the equilibrium
flow curve was drawn, i.e. shear stress was plotted against
shear rate. It should be noted that the final step in this
method requires complete recovery making this method invalid
for irreversible products.

Kemblowski and Petera (1979) presented a model for
describing thixotropic behavior based on a structural
parameter different from that presented by Cheng, which was
introduced in a phenomenological manner without reference to
its physical meaning. Two starting assumptions were made:
a) A thixotropic fluid's equilibrium behavior can be
described using the power-law model, b) Under isothermal
conditions, the influence of all variables except shear rate
may be described by one scalar value, the structural

parameter. Like Cheng, Kemblowski and Petera developed a

13

phenomenological relationship and a rate equation based on a
structural parameter.

Experiments, designed to find the constants required in
the phenomenological relationship and rate equation, of the
"step-change in shear rate" type were used. (In step-change
in shear rate tests, a sample is sheared at a particular
shear rate to equilibrium, after which the shear rate is
abruptly lowered. The build-up of sample structure is then
monitored. Finally, the original shear rate is employed and
sample structure breakdown is followed.) Using the build—up
and breakdown curves, the appropriate constants were
calculated and the thixotropic phenomenon could be
completely described mathematically. Kemblowski and
Petera's original method (1979) is very complex, although
the rate of structure build-up is assumed to be equal to the
rate of structure breakdown. In a follow—up paper,
Kemblowski and Petera (1980) outlined a slightly more
involved method of description, which included yield stress
determination and techniques for independently determining
build-up and breakdown rates, instead of assuming them
equal.

Tiu and Boger (1974), basing their work on the model by
Petrellis and Flummerfelt (1973), started with the Herschel-
Bulkley equation. To account for time-dependent effects, a
structural parameter,x , similar to Cheng's was added. As
in the previously mentioned methods, a phenomenological

relationship and a rate equation based on the structural

14

parameter were used to describe thixotropy. The balance of
Tiu and Boger's paper was devoted to developing experiments
and deriving equations for the determination of the
necessary constants. Specifically, a series of breakdown
curves run at various shear rates were used. (A breakdown
curve is the change in torque with time at consant shear
rate.) It is important to note that Tiu and Boger's model
was only applied in the non-destructive range of shear rate,
i.e. they assumed total recovery.

Certain other methods are worth noting since they are
based on assumptions different from those underlying the
previously mentioned methods. Harris (1967) used a
relaxation spectrum and an associated memory function to
describe reversible thixotropy. A method which uses the
Bird-Leider equation, which mathematically takes into
account the viscous and elastic properties of the samples,
was presented by Dickie and Kokini (1982, 1983). Most of
the other methods reviewed by the author were based on
similar or the same assumptions underlying the methods
previously listed in this study or were empirical in nature

and apply only to the product used in the study.

2.3. Mixer Viscometry

Metzner and Otto (1957) presented a method of
approximating power-law parameters for non-Newtonian fluids
using apparent viscosity calculated from data obtained with
a mixing vessel. Rieger and Novak (1973) outlined a method

to determine whether or not shear rate is a linear function

15

of angular velocity for a given paddle mixer and, if linear,
how to determine the paddle mixer's proportionality
constant.

Rao (1975) presented a method, based on the
aforementioned techniques, of approximating power-law
parameters for food suspensions, such as starch-thickened
products. These products could not be characterized with
narrow gap viscometers due to the size and possible
separation and settling of particles, i.e. formation of a
dilute phase near the bob. The Rao method (1975) is an
approximation since only an average shear rate can be
determined due to varying shear rate from point to point on

the paddle mixer.

2.4. Wall Effects

According to Whorlow (1980), apparent slippage due to
material properties changing near walls can be detected by
using two or more sensors (bobs) with sensor radii
different, sensor heights equal and a similar cup radius.
If the same shear stress/shear rate flow curve is generated
by all the sensors, no wall effects are present; but if
different flow curves are drawn for each sensor, a wall
effect is present. In this study, the above consideration
was used in testing for the presence of wall effects.

Wall effects in concentric cylinder viscometers can be
characterized using slip velocities (Oldroyd, 1956) or by

using an effective slip coefficient (Mooney, 1931). The

16
method by Oldroyd (1956, not seen, cited by Whorlow, 1980)
assumes that the slip velocity, v, depends only on the shear
stress at the wall. The total angular velocity, 0, of the
bob with respect to the stationary cup is given by:

Tb - v(r ) v(r )
Q - lJ' .1111 at + b + C (1)
T R
r b C

 

 

Rb = radius of bob (m)

RC = radius of cup (m)

v = slip velocity (m-s'l)
r = shear stress (N-m'z)
§ = shear rate (5-1)

If Rb is varied, and RC and TC are kept constant,

(2+0 as Rb+RC
but due to slip,
2V(rc)
Q + ——§;—— as Rb + RC

Mooney's method (1931) as presented in Skelland
(1967), defines S as the ratio of cup to bob radius. Then,

R

_ .3
sa - R1 (2)
R
3
s = —— (3)
b R2
R
- .2
SC - R1 (4)

where,

17

R1 < R2 < R3

The angular velocities required to yield the same
torque, M, with Sa' Sb and SC are then measured as Qa' 9b

and 9 respectively. The following equation is used to

CI
calculate the effective slip coefficient, 8', at the

surface, ZNth:
8'=——-—— (Q+Q-Q) (5)

By repeating this procedure at other values of M, the
relationship between 8' and 12 can be determined by linear
regression, after calculating 8' with Equation 5 and 12

using Equation 6 below:

M
Tb = ————-—3— (6)
2n(Rb) h
where,
h = equivalent height of bob (m)
Tb = shear stress at bob (N-m-z)

To determine effective slip corrections, effective slip

velocities at the hob and cup are calculated using:

Vb = 8b Tb (7)
vC = 8C TC (8)
where,
Vb = slip velocity at bob (m-s'l)
vC = slip velocity at cup (m-s'l)

8b = effective slip coefficient at bob

8 = effective slip coefficient at cup

18

shear stress at bob (N-m’zl

Tb

Tc

shear stress at cup (n-m'z)

and ”b and‘rC are calculated using Equations 6 and 9,

respectively.

.C = —-——M——2— <9)
2n(RC) h

The effective slip coefficients, 8b and B are determined

c'
using Tb and TC, respectively, on the 8' versus 12 curve.

The true shear rate corresponding to Tb is estimated by
multiplying the calculated shear rate (section 3.3) by the
ratio of the actual velocity difference (from cup to bob) to
the velocity difference without slip.

The two methods outlined in this section were not used
to characterize wall effects in this study since the
viscometer used did not conform to the geometry required by
Mooney's method, nor could it yield the angular velocities
required to yield the same torque for all three sensors
required by both Oldroyd's and Mooney's methods. First, one
of the geometry requirements of Mooney's method is that one
of the two cup radii must equal one of the two bob radii.
The viscometer used in the present study was equipped with
one cup and three bobs. Second, a constant angular velocity

viscometer was used, while both methods required a constant

torque viscometer.

THEORETICAL DEVELOPMENT
3.1. Mixer Viscometry
The power consumption in a mixing vessel for Newtonian
fluids can be expressed in terms of a power number (Metzner

and Otto, 1957, cited by Rao, 1975),

P0 = p/(d593o) (10)
and a mixing Reynolds number,
Re = dsflo/n (11)
as
P0 = A/Re (12)
where,
A = constant depending on system geometry
(dimensionless)
d = impellor diameter (m)
p = power (Torque x Angular velocity) (N'm-s'l)
Po = power number (dimensionless)
n = fluid viscosity (Pa's)
o = density (kg‘m-3)
n = angular velocity (s'l)

Metzner and Otto (1957) suggested that Equation 12 could be
used for non-Newtonian fluids if an apparent viscosity were
used. This apparent viscosity was calculated at an average
shear rate, which was determined by the following equation:

§a= k' n (13)
where,

k' paddle mixer constant

I'a = apparent (average) shear rate (s'l)

This relationship was shown to be valid for a

19

20

particular impellor if a plot of log (p/(KRnIld3I) versus
(1-n) was a straight line. The slope of the straight line
was determined as -log k' (Rieger and Novak, 1973). If the
plot were nonlinear, Equation 13 would be invalid since k'
would not exist. The rotation Reynolds number, Re a Qn-Z
de/k, must be less than 10 for the flow conditions to be
laminar as assumed.

For any type of sensor, including the paddle mixer, the
flow behavior index, n, is equal to the slope of the log
(torque in N'm) versus log (angular velocity in s'l). The
consistency coefficient, K, is determined using the

following relationship between test sample, x, and a

standard fluid, 5, having known rheological properties (Rao,

1975):
n
M , s
Kx = Mi . Aߣ_lnx . Ks (14)
s (Qk')
where,
Ks = consistency coefficient for standard fluid
n
(Pa°s )
Kx = consistency coefficient for test sample (Pa-s”)
M5 = torque at chosen angular velocity for standard
fluid (N°m)
Mx = torque at chosen angular velocity for test
sample (N‘m)
ns = flow behavior index for standard fluid
(dimensionless)
nx = flow behavior index for test sample
(dimensionless)

Equation 14 assumes power law fluid (no yield stress).

21

3.2. Modified Tiu and Boger Method of Breakdown Characterization

3.2.1. Assumption of No Recovery and Basis of Model

Most of the literature defines thixotropy as a
completely reversible process (Hahn et al., 1959; Van Wazer
et al., 1963; Cheng and Evans, 1965 and Sheth, 1976) so
researchers who have developed methods to characterize
thixotropy have followed this general consensus and have
assumed complete recovery. (See Literature Review for an
outline of the most pertinent methods.) Herein lies the
major problem in mathematically describing breakdown of
starch-thickened apricot puree. While the available models
assume complete recovery (usually at the same rate as
breakdown), the apricot puree exhibits only partial recovery
at best and usually no recovery at all.

Although all known methods assume complete recovery,
two do not depend on recovery in their derivation. The first
of these two methods, the hysteresis loop area test, was not
used in this study because the test only gives a relative
indication of thixotropic behavior of a group of samples
(Heywood, 1981). The second method, breakdown curve
analysis (Petrellis and Flummerfelt, 1973, as referenced by
Tiu and Boger, 1974), yields absolute data and is therefore
more repeatable than the hysteresis loop area test. For
this reason, breakdown curve analysis.with three
modifications, was the method of choice for this study. The
initial modification was the assumption of complete

irreversibility, i.e. no recovery, for the apricot puree.

22

Changes were also made in the methods of calculating shear
stress and shear rate.
Tiu and Boger (1974) characterized product breakdown

curves with two basic equations. The phenomenological

relationship
n
T=1[T +KYO] (15)
y o
o
where,
KO = consistency coefficient at time zero (Pa'sn)
nO = flow behavior index at time zero (dimensionless)
A = structural parameter (equal to unity at time zero
and to an equilibrium value,lne, at equilibrium)
(dimensionless)
ry = yield stress at time zero (N-m)
o

is basically the Herschel-Bulkley equation with structural

parameter, 1, added. The rate equation is

91 = - k, (A- xe>2 (16)
dt
where,
k1 = rate constant which is a function of shear rate
Xe = equilibrium structural parameter (dimensionless)
%% = change in structural parameter with respect to

time
Since the structural parameter is equal to unity at
zero shear time, Tiu and Boger defined the phenomenological

K and n at

relationship at time zero and calculated TY , o o
0

that point. To determine the other two constants, k1 and
Aer the apparent viscosity was used. By equating shear
stress in the phenomenological relationship with shear

stress in the apparent viscosity equation, the structural

23

parameter is defined as

 

A = a .n (17)
1' + KOY 0
yo
where,
”a = apparent viscosity (na = %)(Pa-s)

By differentiating Equation 17 with respect to time and

d1 . . . .
substituting for a; in the rate equation and substituting
Equation 17 for A where appropriate, the change in apparent

viscosity with respect to time is found to be

(18)

 

dn

dra = -a1 (“a-he)2
where,

n e = apparent viscosity at equilibrium (Fats)
and
. kli
al(y) = 4n (19)
T + KOY O

Y
0
Integrating Equation 18 at constant shear rate from ”a = ”a0 at

t = 0 to Tl =11 at t = t yields

 

o a
1 1
- = ————_ + a t (20)
”a he nao he 1
where,
”a0 = apparent viscosity at time zero (Pa-s)

For a given shear rate, a plot of l/(na-ne) versus t
yields a straight line whose slope is al. Repeating this
procedure at different shear rates gives the relationship
between a1 and shear rate and therefore, by substituting a1

(i) into Equation 19, the relationship between k1 and shear

24

rate.

By cross-plotting the shear stresses at time zero from
breakdown curves at various shear rates against the
corresponding shear rates, the parameters KO, no and TYO can
be determined by linear regression using the Herschel-
Bulkley model.

Finally, the equilibrium structural parameter can be

 

calculated using ”eY
A =
e -n
+
Ty KOY O (21)
0
Then, kl, KO, no, TY and Ae can be substitutued into the

phenomenological relationship and the rate equation to

complete the analysis.

3.2.2. Use of Approximate Shear Rate and Approximate Shear
Stress

Since a paddle mixer was used to minimize loading shear
breakdown and possible wall effects, an approximate shear
rate calculated using Equation 13 was used in the Tiu and
Boger model. Shear stress, like shear rate, can only be
approximated when using a paddle mixer. Shear stress was
estimated using the idea that torque is directly

proportional to stress (Rao, 1975):

Mx Tx
fi— = ¥_ (22)
s 5
meaning that,
'1'
—.JE
Ta - M Mx (23)

25

where,

a
II

a approfiimate shear stress for test sample
X (N-m )
shear stress for standard solution (N-m‘z)

-2)

A
ll

shear stress for test sample (N-m

H
II

Using a standard fluid of known properties (a power-law
fluid whose properties have been determined using a
concentric cylinder viscometer), the value of shear stress, rs,
can be determined from the power-law equation at a given
shear rate calculated using Equation 13. Ms is read by a
mixer viscometer running at the same shear rate at which Ts
is calculated. A series of shear rates could be used to
verify that Ts/Ms is constant for all shear rates. However,
this is not necessary since shear stress is always a linear

function of torque.

3.3. Krieger Analysis for Concentric Cylinder viscometers
Krieger (1968) suggested the following method for

calculating shear rates at the bob of a concentric cylinder

 

 

viscometer:
2/s
R R
- 29 c 2 , 2 c
Y=— 1+SS f(-ln_)] (24)
s [R 2/s_R 2/8] |: s Rb
c b
where,
1 = d(1n Q)
s d(1n Tb)
._ d (1/3)
S ‘ d(1n 1b)
2
s = s-s
t(et(t-2)+t+2)
f(t) =

2(et-l)2

26

In the preliminary studies of this project, the second derivative
term, 5', in Krieger's shear rate approximation (Equation 24) was

found to be insignificant, and thus Equation 24 reduced to
2/s

'--2—Q- RC (2)

Y- s R2/s 2/s 5

c ’Rb

 

For concentric cylinder viscometers, shear stress is

calculated using Equation 6.

EXPER I MENTAL EQU I PMENT
A Haake RV-12 viscometer (measuring head M500) with
MVI, MVII and MVIII sensors (bobs) and MV paddle mixer
sensor was used to generate rheological data. The system
had a concentric cylinder geometry with the MV series
sensors and was a mixing unit with the paddle mixer sensor.

Table 2 shows the dimensions of these sensors.

27

28

Table 2. Dimensions of the MV sensors and the Mv paddle

 

 

 

mixer.
Sensor Rb(m) Equivalent height (h in meters)
+MVI 0.02004 0.06032
+MV11* 0.01840 0.05859
*Mvrrr 0.01520 0.06210
Diameter (d in meters) Height (m)
+paddle mixer 0.04143 0.02692

 

+The radius of the cup (RC) is 0.021 m in all cases.

*The MVII sensor was made at Michigan State University from
an MVI sensor. The length dimension is slightly smaller
than a true MVII sensor.

 

29

A Haake speed programmer and a Haake F3-C temperature-
controlled water circulator were used to set angular
velocity and to maintain isothermal conditions,
respectively. A Hewlett-Packard 85 computer and a Hewlett-
Packard 3497 Data Acquisition/Control Unit were interfaced
to the system to facilitate data collection. All tests were

run with samples maintained at 25C (t .01°C).

PREPARATION OF THE STARCH-THICKENED, STRAINED APRICOTS

A batch of strained apricots thickened with tapioca
starch (Table 3) was made in the pilot plant of the Gerber
Products Company located in Fremont, Michigan. The
ingredients were mixed, and the product was cooked by steam
infusion, which caused starch gelatinization and subsequent
thickening. After cooking, the product was sealed in 4.5
oz. (1289) jars and was cooled to room temperature in
preparation for storage.

The tapioca starch investigated was on acetylated di-
starch phosphate. The starch is a cross-linked product made
by reacting the starch with sodium trimetaphosphate: the
cross-bond is achieved through a phosphate ester linkage.
The starch is also stabilized, against gel formation, by

acetylation.

30

31

Table 3. List of ingredients per 1000kg of finished

 

 

 

product.

Ingredients kg/1000kg of finished product
*Apricot Concentrate 32 Brix 181.00

Sugar (white, granulated) 70.00

Tapioca Starch 44.00

Vitamin C .28

Citric Acid to pH 4.0

**Water 704.72

 

 

*Fruit is strained through a .020 in. (.051 cm) screen.

**Small quantity of water is added by steam infusion.

32

The tapioca starch has approximately 1.7% acetyl groups, as

determined by the following analysis:

1.

5.09 of predried, modified starch was weighted and
placed in a 250ml Erlenmeyer flask. (A sample of
unmodified starch was used as a blank.)

50ml distilled water was added and the mixture was
swirled to suspend the starch.

10 drops of phenolphthalein indicator was added.

.lN Sodium Hydroxide was used to titrate to a pink
endpoint.

25.0ml of 0.45N Sodium Hydroxide was added, taking
care not to wet the neck of the flask.

The flask was then sealed tightly with a rubber
stopper and was shaken vigorously for 30 minutes on
a mechanical shaker.

The stopper was carefully removed and washed down
together with the walls of the flask, with a fine
stream of distilled water.

0.500N HCl was used to titrate to the disappearance
of the phenolphthalein color.

%Acetyl Groups = (ml needed for blank - ml needed
for sample)

X normality of the HCl X 0.043 X 100 /
Sample Weight in Grams (dry basis)

Stabilizing the starch by acetylation allowed testing

of the samples over a several month period without

significant changes occuring in sample structure. (Appendix

1 presents starch stability as a function of elapsed time

after processing.)

DATA COLLECT I ON AND ANALYS I S

6.1. Yield Stress Data Collection and Analysis

Both methods of yield stress determination mentioned in
this section are only approximations. Special equipment,
which was unavailable, is required for more accurate
determination of yield stress (DeKee, et a1. 1980 and
Vocadlo and Charles, 1971). Yet, even the methods using
special equipment can only approximate yield stress. Thus,
due to the approximation needed to determine yield stress,
great error in the low range of yield stress is possible.

(Apricot puree has a very small or no yield stress.)

6.1.1. Yield Stress at Initial Point of Breakdown
(Time Zero)

The method used in this study was the extrapolation of
shear stress/shear rate data (20-120 rpm) to the shear
stress (y) intercept, i.e. the yield stress. Data at time
zero were gathered by using torque-versus-time curves from
breakdown (thixotropic) analysis at different angular
velocities. The initial torque reading of each breakdown
curve was defined as the torque at time zero at that angular
velocity. Then, a plot of torque at time zero versus shear
rate was made and extrapolated to determine yield stress,
which was the y-intercept.

In this study, the paddle mixer was used to minimize
loading shear degradation. With a narrow gap viscometer,
significant degradation of the sample can be caused when the

sample is forced through the narrow gap between the inside

33

34

and outside cylinders during loading. With the paddle
mixer, loading degradation is kept to a minimum due to the
paddle geometry (Figure 2).

Since the paddle mixer was used, approximate shear
rates and aproximate initial shear stresses (the latter
calculated from torque at time zero data) were calculated

using Equations 13 and 23, respectively. The linear

regression model, y axb + c (transformed as 1n (y-c) = 1n
a + blnx before use), was used to find the shear stress
intercept that gave the best fit, i.e. the curve with lowest
standard deviation. The variable, c, was defined as the

yield stress at time zero, 1y .
o

6.1.2. Yield Stress at Equilibrium

Two ways of yield stress determination were used at
equilibrium: 1) extrapolation of shear stress/shear rate
data (10-120 rpm) and 2) "torque-to-initiate-flow". The
extrapolation procedure used at equilibrium was identical to
that used in section 6.1.1., but data were collected in a
slightly different manner. Specifically, since the product
was at equilibrium, there was no concern over degradation,
so the MVI sensor was used. (Equilibrium was reached by
shearing the sample for 10 minutes at 60 rpm, using the
paddle mixer.) Then, Equations 25 and 6 were used to
calculate shear rate and shear stress, respectively.

The torque-to-initiate-flow test was performed at

equilibrium, but not at the initital point of breakdown,

35

 

/ .Olm dia

 

 

 

0. 127m

’5 ........

15° pitch blade

 

 

o o L.
l .1

 

 

 

 

 

 

1.. W... _.

Figure 2. MV paddle sensor.

36

because at breakdown the yield point, B, would be lowered
due to degradation of the sample while the torque was
approaching the yield point (Figure 3). After the sample
was degraded for 10 minutes at 60rpm using the paddle

mixer, the paddle was exchanged for the MVI sensor. The
angular velocity was set at the lowest possible speed which
would allow yield stress to be reached before the completion
of the data collection cycle (less than three seconds). A
torque versus time plot was drawn by the HP 85, and the
maximum, B, was defined as the torque at yield, which is

related to yield stress by Equation 6 (Figure 3).

6.2. Recovery Data Collection and Analysis

To determine the extent of reversibility, the sample
was first sheared for 10 minutes at 60 rpm with the paddle
mixer, which was used instead of the MVI concentric cylinder
to minimize loading shear and to maintain the sample
suspension. After the 10 minute breakdown period, one set
of samples was allowed to recover for 10 minutes while a
second set was allowed to recover for 60 minutes. (The
viscometer was turned off during the recovery period.) 10
and 60 minute recovery periods were chosen. With both
sample sets, a second 10 minutes breakdown was performed
following the recovery period. If the sample exhibited
complete recovery, i.e. complete reversibility, presumeably at
the same rate as initial breakdown, then the sample would
build-up to the original structure by the end of the 10

minute recovery period. Thus, if superimposed, the second

37

 

Torque
(N°m)

 

 

 

 

Time (sec)

Figure 3. Yield stress determination
using stress to initiate flow.

38

breakdown curve would retrace the first. A 60 minute
recovery period was used with a second set of samples in
case the rate of recovery was slower than the rate of
breakdown. If no recovery was observed after either

recovery period, irreversibility was assumed.

6.3. Paddle Mixer Costant (k') Data Collection and Analysis

The mixer constant, k', defined in Equation 13, was
determined using standard solutions of hydroxypropyl
methylcellulose, guar gum and corn syrup. The behavior of
the standard fluids was evaluated using data acquired from
the Haake RV-12 (measuring head M500 and sensor MVI) and
using Equations 25 and 6 to calculate shear rate and shear
stress, respectively. Power-law parameters, K and n, were
calculated by linear regression analysis of the standard
fluid shear stress/shear rate data (Table 5). A relatively
slow angular velocity range (10-120 rpm) was chosen for the
paddle mixer rheological parameter estimation test to
simulate the rate of stirring of the apricot puree by the
consumer. This, in turn, dictated that angular velocities
within these limits be chosen for the determination of the
standard fluids' flow curves.

In preliminary studies, the constant k' was shown not
to be a function of angular velocity, but this will not be
definite until further studies are completed. Therefore,
the value of k' will be stated as "calculated at 60 rpm".

Torque readings were taken with the Haake RV-12 and paddle

39

mixer sensor at 60 rpm for all standard solutions.

To check the validity of Equation 13, a plot of log
(p/Knn+ld3)) versus (l-n) was prepared and found to be a
straight line (Figure 4). The variable, p, was determined
by multiplying 6.28 s.1 (60 rpm) by the torque reading
generated by the paddle mixer. The slope of this plot is -
log k'; therefore k' = 4.46. The actual data used to plot

the curve are listed in Table 5.

6.4. Thixotropic Breakdown Data Collection and Analysis

As mentioned previously, a modified version of Tiu and
Boger's method was used to characterize breakdown. Since
the paddle mixer was used, only apparent shear stress and
apparent shear rate could be calculated. Shear rate was

4.46, and shear

calculated using Equation 13, where k'
stress was approximated using Equation 23, where Ts/Ms was
estimated as follows:

1) Using data from tests run on a standard fluid (Table 5),

the value of r was determined as:

5
fs = Ks Ins
r = 4.93 (6.28-4.46)°292

5

rs = 13.056 n-m‘z

where,
Ks, ns and k' are taken from Table 5 (data on

standard fluids)

2) M5 = 0.001327 N'm at angular velocity, 6.28 5'1 (Table

5).

40

3) Then, rs/Ms = 13.056/0.001327 = 9835.
By substituting rs/Ms into Equation 23,

Ta = 9835 Mx (26)

x
The breakdown curves were run at constant velocity (20,

40, 60, 80, 100 and 120 rpm) for 10 minutes, and 51 data
points were recorded for each curve. Only the first five
points (0, 12, 24, 36 and 48 seconds) were used, since the
curve, l/(na-ne) versus t, was nonlinear after this period
of time. (Nonlinearity violates Equation 20.)

A plot of l/(na-ne) versus t, where n = Ta/ia, was made
and linearly regressed for each sample. The linear

regression yielded a1 and (r—Lr“), i.e. the slope and

'ao ne

intercept, respectively (Equation 20). Then, al was plotted
against apparent shear rate, and the curve was linearly
regressed.

The variable, b, was defined as the intercept,

l/(nao-ne), from Equation 20. Since n = Ta/Ya,

b = -—-—-——- (27)
Tao Te
Y Y
where, a a
Tao = approximated shear stress at time zero (N'm-z)
Rearranging,
§
b = .___£L__. (28)
T " T
ao e

By substituting shear rate and shear stress from Equations

13 and 26, respectively,

41

 

 

k'Q
b = _ (29)
9835(MO Me)
where,
Me = torque at equilibrium (N-m)
Mo = torque at time zero (N°m)
Then, since k' = 4.46, as mentioned earlier,
4.460
b = r _ (30)
9835(MO Me)
Solving for Mo yielded:
4. 0
M = L-fM (31)

o 9835 b e

thus, the initital torque, Mo, was estimated using the

equilibrium torque, M in Equation 31. The experimental

e'
torque at time zero taken from each breakdown curve was also
used to estimate M0 for each set of data. The value of Tao
in both cases was calculated using Equation 26. Then, each
Tao was plotted against its respective Ia to yield the values

of K n and T by linear regression (Figure 8).

o' o y

o
The equilibrium structural parameter, Te, was
determined using Equation 21 and was tabulated (Table 7).
The value of k1 was calculated using Equation 19. Finally,

the fluid's thixotropic behavior was characaterized by

substituting the calculated values into Equations 15 and 16.

6.5. Wall Effect Data Collection and Analysis at Equilibrium
Using the MVI, MVII and MVIII sensors, equilibrium

shear stress/shear rate data (10-120 rpm) were collected on

42

samples previously degraded with the paddle mixer (10
minutes at 60 rpm). The three data sets obtained from the
sensors were statistically compared using the student's t-
value test for comparison of three linear equations
(Kleinbaum and Kupper, 1978) (Table 4).

The null hypothesis, H stated that slopes, n,

0!
calculated from MVI, MVII and MVIII data were the same and
that the intercepts, 1n K, were the same for all three data
sets. Following is the model used in the statistical

analysis:

Y = 80 + 8111 + 82I2 + B3X3 + B4I1X3 + 8512X3 (32)

where,
Il,I2 = dummy variables
x3 = 1n (shear rate)
y = 1n (shear stress)
80'81I82'B3IB4I85 = constants

since,
I = Kin 1n 1 = In K + n In i

If the null hypothesiswere true, so = so + 81 = so + 82
and B3 = 83 + 84 = 83 + 85, which imply that 81 = 82 = 0 and
B4 :85 = 0, respectively. Thus, the null hypothesis assumed
all 8 values were equal to zero. It follows that the t-
values (corresponding tof3 values) either validated or
invalidated the null hypothesis. Specifically, an absolute
t—value greater than the tabulated value at the chosen level
of significance implied that the constant,3 i' was

statistically important and not equal to zero. At the

43

Table 4. Outline of statistics model used to check for wall

 

 

effects.*
Ii 12 Equation Data 1 Data 2
0 0 y = so + 83 X3 MVI MVIII
0 1 y = (80+82) + (83+85) X3 MVII MVII
l O y = (80+81) + (83+B4) X3 MVIII MVI

 

 

 

*Two computer runs were required for a complete analysis.

44

chosen level of significance, the three curves were
determined to be the same or different using 8 values

calculated in the statistical analysis.

6.6. Paddle Mixer Rheological Parameters Estimation
Torque/angular velocity data (10-120 rpm) were
collected using the paddle mixer and Haake Rv-12 with
samples previously degraded. These data were linearly
regressed after transformation using y = axb as the model,
where the constant, b, is the flow behavior index, n. The
value of the consistency coefficient, K, was then calculated

using Equation 14 with data taken at 60 rpm.

RESULTS AND DISCUSSION

7.1. Discussion of

7.1.1. Results of the Recovery Test

After running eight 10 minute and eight 60 minute
recovery tests, it was determined that complete
irreversibility was exhibited by the starch-thickened,
strained apricot puree. (See Figure 5 for a representative
sampling of curves.) Partial recovery may have occurred had
the recovery period been extended to a few days. However,
since a major reason for this study was to develop a quick
method of quality control for industry, the storage of a
sample over such a long recovery period seemed impractical.
In addition, spoilage, which would change sample structure,
could occur over an extended recovery period at ambient

temperature.

7.1.2. Results of the Breakdown Analysis

As previously mentioned, a modified version of Tiu and
Boger's (1974) method of breakdown characterization was used,
where complete irreversibility was assumed and a paddle mixer
was used instead of a concentric cylinder viscometer.

Following are the results of this study:

1. Figure 6 shows a plot of l/(na - ”e) versus t for a
representative sample at each angular velocity used in the
breakdown analysis (20, 40, 60, 80, 100 and 120 rpm). The
general trends of increasing slope, a1, and intercept,
l/(rho-rb), with increasing shear rate can be seen on this plot.

The increasing value of a1 with increasing shear rate

45

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d
L L 1 L L L L L 1
1 .2 3 4 5 6 .7 8 9 10
1-n
Figure 4. Plot used to evaluate the mixer

viscometer constant (k) for the
MV paddle.

3)

Torque (N-m x 10

48

 

 

 

 

 

 

 

T 1 l
.
Second
CurveZ
l I I J
2 4 6 8
Time (min.)
Figure 5. Recovery after a) 10 minutes.

10

3)

Torque (N-m x 10

49

I

 

    
 

 

 

 

 

 

In;
First Curve
P c-
l i l I
0 2 4 6 8 10

Time (min.)

Figure 5. Recovery after b) 60 minutes.

50

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51

shows that the rate of product structure breakdown is
greater at higher shear rates. The increasing value of

l/(nao-n ) with increasing shear rate is predictable since

e

-Te) using n - r/i. Specifically,

l/(nao-ne) becomes Y/(Tao

1/(nao-ne) increases with increasing shear rate and decreasing

r the increase in l/(n n is basically due to the

ao’Tei ao' e)

increase in shear rate, while the proximity of the
intercepts at different shear rates is due to the value of
T -Te.

2. Figure 7 presents a1 versus shear rate for each set

of data in Table 6. a1 (i) data was transformed and

b

linearly regressed using y = ax , and the following

relationship was found:

a1 = .0526 i1-443 (33)

3. In Table 8 is the determination of TY , which was
0

found to be 0.0 N-m'z, using the method outlined in section
6.1.1. (Yield Stress at Initial Point of Breakdown).
Basically, Table 8 presents the results of a trial-and—error

determination of TY . The data at time zero from the
o

breakdown curves (Figure 8) were cross-plotted on a shear—
stress-at-time-zero versus shear-rate plot, and linear

regression was performed as follows: a) a value of TY was
0

assumed, b) the data were linearly regressed, after

2

transformation, using the assumed value of T c) r and

Y0'
standard deviation were tabulated, d) steps a through c were

repeated for different assumed values of TY .
o

52

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Table 6. Experimental values of a and l/(n '“e ) data
obtained using the modified Tiu and Boger method.
Sample Slope Intercept Number of Shear sRat;
(rpm) a1 l/(nao’ne) Points ?a
l (20) 1.578 .948 5 9.315
2 (20) 1.122 .864 6 9.315
3 (20) 1.241 .940 5 9.315
1 (40) 4.384 1.719 5 18.675
2 (40) 3.543 1.745 5 18.675
3 (40) 3.747 1.786 6 18.675
1 (60) 6.341 1.614 5 28.000
2 (60) 7.089 2.824 5 28.000
3 (60) 4.819 2.352 5 28.000
4 (60) 6.326 2.859 5 28.000
5 (60) 5.693 2.375 5 28.000
6 (60) 6.585 3.015 5 28.000
7 (60) 5.660 2.753 5 28.000
1 (80) 12.086 3.944 5 37.350
2 (80) 11.285 2.904 6 37.350
3 (80) 9.059 3.457 5 37.350
1(100) 13.540 4.547 5 46.665
2(100) 14.156 4.592 5 46.665
3(100) 14.025 4.720 5 46.665
1(120 19.32 6.092 6 56.024
2(120) 16.23 5.695 6 56.024
3(120) 15.33 5.294 5 56.024

 

 

 

 

 

Table 7. Torque at time zero data and structural parameter
data obtained using the modified Tiu and Boger
method.

Theoretical Data Actual Data

Sample Me ”0 Tao Mo Tao

(rpm) (N-mx103) (N-mx103) (N/mz) (N-mx103) (N/mz) *e

1 (20) 3.22 4.22 41.50 4.24 41.66 .725
2 (20) 3.46 4.56 44.85 4.62 45.42 .779
3 (20) 3.28 4.29 42.19 4.35 42.79 .739
1 (40) 4.20 5.30 52.13 5.24 51.55 .764
2 (40) 4.43 5.52 54.29 5.47 53.82 .806
3 (40) 4.23 5.29 52.03 5.29 52.03 .770
1 (60) 5.31 7.07 69.53 6.30 61.97 .853
2 (60) 5.43 6.44 63.34 6.48 63.70 .872
3 (60) 5.63 6.84 67.27 6.85 67.37 .904
4 (60) 5.31 6.31 62.06 6.36 62.58 .853
5 (60) 5.64 6.84 67.27 6.88 67.66 .906
6 (60) 4.87 5.81 57.14 5.85 57.57 .782
7 (60) 5.12 6.15 60.49 6.20 60.96 .823
l (80) 5.43 6.39 62.85 6.36 62.59 .798
2 (80) 5.65 6.96 68.45 6.81 67.01 .831
3 (80) 5.60 6.70 65.87 6.70 65.90 .823
1(100) 5.97 7.01 68.97 7.04 69.22 .820
2(100) 6.03 7.06 69.44 7.05 69.32 .828
3(100) 6.20 7.21 70.91 7.18 70.64 .851
1(120) 6.52 7.46 73.32 7.53 74.01 .847
2(120) 6.28 7.28 71.60 7.39 72.68 .815
3(120) 6.86 7.94 78.09 7.99 78.57 .891

 

 

 

 

 

56

 

 

 

 

Table 8. Series of data and calculations* used to
determine yield stress at time zero.
Assumed yield stress Kon nO R2 0(std. dev.)
TYO (N'm ) (Pa°s )

20 8.146 0.482 0.9110 0.2831
15 11.26 0.421 0.9119 0.2471
9 15.34 0.366 0.9122 0.2148
8 16.05 8.358 0.9123 0.2103
7 16.77 0.351 0.9123 0.2059
6 17.50 0.344 0.9123 0.2017
5 18.24 0.337 0.9123 0.1977
4 18.98 0.330 0.9123 0.1939
3 19.73 0.324 0.9123 0.1902
2 20.48 0.318 0.9122 0.1866
1 21.24 0.312 0.9122 0.1832
0 22.01 0.307 0.9122 0.1799

 

 

*using the following model for linear regression:

y = axb + c

1n (y-c) = In a + bln X

where y shear stress data

shear rate data

K
II

57

The best approximation of 120 was taken from the curve
with the lowest standard deviation, 0.

4. Figure 8 shows a plot of shear stress/shear rate data
at time zero from Tables 7 and 6, respectively. By linear

regression of the transformed data, shear stress and shear

rate were found to be related by

Tao = 22.01 §a-3°7 (34)
where,
- . n
Ko - 22.01 Pa 5
no = 0.307
T = 0.0 N-m‘2
Yo

This linear regression is the best fitting curve from the TY
o
approximation above (Table 8).

5. By substituting al from Equation 33 and Ko, no and

TYO from Equation 34 into Equation 19, kl (7) was determined

as
k1 = 1.158 76°750 (35)

6. Re was determined for every sample using Equation

21 (Table 7) and the average value was:

*a = 0.822

7. The calculated constants were then substituted into
the phenomenological relationship and the rate equation,

respectively, as

T = 1 (22.01 i-307) (36)

91 = - (1.1587?750

2
at )(A-O.822) (37)

Equations 36 and 37 completely characterize breakdown,

58

although it must be noted that the sample is irreversible.
It can be seen in Equation 37 that dxfldt is a function of ~%
and A. Since 7 is held constant during any given breakdown
in Tiu and Boger's analysis, only 1 changes with time. At
the initital point of breakdown, dx/dt is at its greatest
value. Since A = 1 at time zero and approaches 0.822 at
equilibrium, the value of A-le in Equation 37 decreases with
time, i.e. dA/dt decreases with time. This, in turn,
predicts the actual decrease in rate of breakdown as the
structure approaches equilibrium (Figure 5).

By integrating Equation 37 from 1 = 1 at t = 0 to A = A

at t = t a relationship between A and t may be found as

x (t) = (1.158 i-750 + 5.62)"1 + 0.822 (38)
Thus, by substituting Equation 38 into Equation 36 the
actual shear stress/shear rate relationship at any time, t,
can be determined.

This method of characterization is an excellent way of
mathematically describing irreversible breakdown because it
is simple and complete; there are two areas which need
improvement, however. The simple analysis of yield stress
chosen for this study could yield only an approximate value
and depended greatly on the computer software used to do the
curve fitting. Also, transfer of sample from the jar into
the MV cup resulted in sample breakdown prior to breakdown
under controlled conditions.

The problem of loading shear breakdown during loading

of the cup into the viscometer was minimized by using the

59

paddle mixer. The replacement of the concentric cylinder
viscometer with the paddle mixer also eliminated the
possibility of erroneously assuming a decrease in torque at
constant shear rate due to wall effects, i.e. thinning of
sample near the bob, was thixotropic breakdown. (The mixer

maintained the sample suspension.)

7.1.3. Results of Wall Effect Analysis

Yield stress at equilibrium was found to be zero by both
methods presented in section 6.1.2. (Yield Stress at
Equilibrium). The shear stress/shear rate equations for the

three sensors were

MVI T = 12.34 7°418 (39)
MVII: r = 15.25 i-352 (40)
MVIII: T = 18.80 §°333 (41)

(Table 11).

The three curves were found to be statistically
different at the 99.9% confidence level (Table 9). Table 10
lists the rheological parameters for Karo light corn syrup
obtained using the MVI, MVII and MVIII sensors. Since the
corn syrup, which is considered homogeneous, had nearly
equal rheological parameters for all three sensors, there
was no sign of wall effects occuring. The Karo syrup test
confirmed that the differences in apricot puree rheological
data were due to wall effects and not to inherent problems

with the viscometer.

60

 

 

 

Table 9. The B constants determined using the
statistical model.
Constant Value Standard Error t-value
TEST 1
. on -—————
Apr1cot puree
Bo 2.513 0.180 xlO-l 139.55
81 0.421 0.226 x10- 18.63
32 0.275 0.234 x10-l 11.78
83 0.418 0.376 x10-2 111.10
34 -0.0846 0.536 x10-2 -15.78
85 —0.0554 0.529 x10-2 -10.47
TEST 2
.____. ._____ . on ______
Apr1cot puree
Bo 2.934 0.137 x10—1 214.77
81 -0.421 0.226 xlO-l -18.63
82 -0.146 0.202 x10-l - 7.22
83 0.333' 0.382 x10-2 87.15
84 0.0846 0.536 x10-2 15.78
85 0.0292 0.534 x10-2 5.48

 

 

61

Table 10. Rheological data for Karo light corn syrup.

 

 

 

Sensor n K (Pa-s“)
MVI 1.0 2.46
MVII 1.0 2.31
MVII 1.0 2.39
MV Paddle 1.0 2.47

 

 

62

 

 

 

 

 

 

Table 11. Rheological parameters of starch-thickened,
strained apricots obtained using various MV
sensors and the MV paddle mixer.

2 data

Sensor K(Pa-sn) n r points
MVI: Test 1 12.13 .420 .999 13
Test 2 12.15 .422 .999 13
Test 3 12.21 .420 .998 13
Test 4 12.35 .419 .998 13
Test 5 12.41 .424 .998 13
Test 6 12.27 .420 .997 13
Test 7 12.97 .411 .996 12
Test 8 13.44 .403 .998 13
Test 9 12.04 .417 .999 13
Test 1 12.12 .422 .997 13
Pooled Data 12.34 .418 .995 129
NVII: Test 1 15.91 .370 .997 13
Test 2 16.10 .361 .997 13
Test 3 16.75 .366 .997 13
Test 4 17.25 .352 .997 13
Test 5 16.46 .371 .997 13
Test 6 17.28 .362 .997 13
Test 7 16.37 .357 .998 13
Test 8 16.96 .354 .998 13
Test 9 14.69 .368 .998 13
Test 1 14.92 .364 .998 13
Pooled Data 16.25 .362 .980 130
MVIII: Test 1 17.47 .348 .995 12
Test 2 16.31 .370 .984 13
Test 3 19.32 .330 .993 13
Test 4 18.94 .337 .995 12
Test 5 19.23 .329 .993 12
Test 6 19.51 .329 .994 13
Test 7 20.03 .326 .995 13
Test 8 18.98 .335 .993 13
Test 9 17.97 .335 .995 13
Test 1 18.93 .319 .991 13
Pooled Data 18.80 .333 .984 127
Paddle Test 1 14.04 .380 .995 13
Test 2 14.63 .378 .996 13
Test 3 14.08 .381 .998 13
Test 4 14.92 .367 .997 12
Test 5 13.70 .381 .997 13
Test 6 14.76 .371 .998 13
Test 7 13.59 .378 .998 13
Test 8 13.73 .379 .997 13
Pooled Data 14.17 .377 .992 103

 

 

63

The plots of Equations 39, 40 and 41 are shown in
Figure 9. K and n from Equations 39, 40 and 41 were used to
calculate apparent viscosity in "a = Kin-1, and ”a was
plotted as a function of shear rate in Figure 10. In the
basic rheogram (Figure 9), there is a marked difference in
the three curves, while in Figure 10, the three curves seem
to converge at higher shear rates. One would expect Figures
9 and 10 to show the same results. However, K and n are not
independent of each other; thus the rearrangement of
variables in the three equations can alter the relationships
of the latter. Therefore, although the apparent viscosities
were the same, for all practical purposes, the rheograms

were statistically different and therefore, there was a wall

effect.

7.1.4. Results of Paddle Mixer Test

The paddle mixer was used to approximate the
equilibrium structure of the apricot puree, in case wall
effects were indeed occuring with the concentric cylinder
viscometer. The following shear stress/shear rate
relationship was estimated (Table 11):

T = 14.17i-377 (41)

Figures 9 and 10 illustrate the accuracy of the paddle mixer
approximation in comparison to the MVI, MVII and MVIII
curves. Since the paddle mixer keeps the sample suspended,
one would expect the paddle mixer curve to be higher than
the other curves on the plot, due to lack of wall effects.

However, for reasons not yet understood, this is not the

64

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1

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RPP?§£NT VISCOSITY, Hrs

07

1.
1

0.53

65

 

 

\\\Q> MVIII

MVI

  

 

MV Paddle h \

 

 

 

cp.00

.00 80.00 120.00 180.00_ 220.00

Figure 10.

SHEHR RRTE. s1

Apparent viscosity versus shear rate
obtained using various MV sensors and
the MV paddle mixer.

66

case. Note that laminar flow is present since Re = 0.002

using K and n from Equation 41.

7.1.5. Relationship Between Phenomenological Relationship
and Equilibrium Rheogram

The phenomenological relationship used in the breakdown
structure analysis (Equation 36) should be the same as the
equilibrium rheogram (Equation 41) when the equilibrium
structural parameter is substituted into Equation 36.

The structural parameter,k , at equilibrium is equal to
0.822. Thus, Equation 36 becomes

1 = 18.09 ia-307 (42)
and Equation 41, the equilibrium rheogram, is
T = 14.17:,a-377

As previously discussed in Section 7.1.3., K and n are not
independent variables. Thus, even though Equations 42 and
41 are different, their respective apparent viscosities
may be similar enough, especially at higher shear rates, and
the structure characterized by the two equations may be
equal, as expected. Apparent viscosity 013 = Kln'l) versus
shear rate was plotted for each equation (Figure 11). The
two curves show the same basic structure, especially at
higher shear rates, and therefore, satisfy the assumption
that the equilibrium structure can be characterized by both
the breakdown analysis and the equilibrium analysis. Slight

differences may be due to a small, but undetected, yield

stress.

67

 

3.73

3-20

Pa-s

I
l

2.67
1

2-13

1.60

RPPHRENT VISCOSITY

1.07

0.53

 

1']:

14.17 V "623

1')

-.693

18.09 Y

 

 

cp.00

.00 60.00 120.00 180.00 1 210.00

Figure 11.

SHERR RRTE,s'

Apparent viscosity versus shear rate
obtained from phenomenological
relationship at equilibrium and
equilibrium rheogram.

 

CONCLUSIONS

It was shown that a paddle mixer could be used in the

rheological analysis of starch-thickened, strained apricot

puree.

A complete rheological analysis was performed on the

product and the following conclusions are supported:

1.
2.

The product showed completely irreversible breakdown.
The breakdown curve analysis gave the following
relationships:

a. Phenomenological Relationship: r'= (22.01 Ya'307)

b. Rate equation: 3% = -(l.158 §'750) (A-.822)2
Wall effects did occur with the concentric cylinder
viscometer.

The equilibrium structure rheogram of the product was

determined using the paddle mixer as r = 14.17 §a'377

68

SUGGESTIONS FOR FURTHER STUDY
1) One possible way to eliminate breakdown during loading
of sample into the cup is to replace the MV cup with the jar
in which the product is packaged. Further study is
necessary to devise such a system.
2) It would be valuable to determine whether or not k' is a
function of the angular velocity used to calculate it.
3) Further investigation into improving methods of yield
stress determination is greatly encouraged, since only simple
estimates of yield stress could be performed in this study.
4) It was impossible to completely characterize wall
effects in this study. The viscometer used did not conform
to the geoemtry required by Mooney's method, nor could it
yield the angular velocities required to yield the same
torque for all three sensors required by both Oldroyd's and
Mooney's methods. Wall effect characterization studies are
suggested.
5) It would be interesting to do a study on viscous heating
during rotation of the sensor and the possible effects this
heating would have on the highly temperature-dependent
rheological properties.
6) Finally, it would be beneficial to further studies if it

were confirmed the Xe is independent of shear rate.

69

LIST OF REFERENCES

10.

ll.

12.

13.

REFERENCES

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APPENDICES

APPENDIX A

ANALYSIS OF STABILITY OF STARCH

73

APPENDIX A
ANALYSIS OF STABILITY OF STARCH

The plot that follows is a representation of the
stability of the starch used in the analysis. Three
different combinations of starch were used and the speed of
breakdown determined as a slope of the breakdown curve, as
characterized by M = a + b 1n t where M = torque, a =
intercept and b = slope. The product used in the thesis is
Batch 3 on this plot. The slight change in slope seen in
Batch 3 in the first days of the study as opposed to Batches
l and 2 shows the relative stability of the product.
Batches l and 2 also showed synersis problems over time

while Batch 3 did not.

74

 

 

 

 

0.!

 

m

 

o~ x :ME\E.2 .odofim

 

 

-1.l

Time, days

APPENDIX B

FLOW CHART OF ANALYSIS

75

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHECK FOR CHECK SINCE IRREVERSIBLE
THIXOTROPY FOR MUST CHARACTERIZE
USING PADDLE RECOVERY EQUILIBRIUM STRUCTURE
DIFFERENT RESULTS SAME RESULTS
[FIND MODELLING METHOD WITH DIFFERENT WITH DIFFERENT
1 SENSORS SENSORS (CORN
(APRICOTS) SYRUP)
[USE TIU AND ROGER]
1 [WIALL EFFECTS OCCURIé-I
MODIFICATIONS -
APPROXIMATE SHEAR RATE r___L_
APPROXIMATE SHEAR STRESS USE PADDLE

 

 

 

 

 

 

  
  

IRREVERSIBILITY ’
- 1 7 RAO'S METHOD

BREAKDOWN STRUCTURE- l

 

EQUATION OF STATE n+1 3
RATE EQUATION log (p/KQ d ) versus (1-n)
must be a straight line

slope = log k'

J

lié = kln where k1 = 4.46]

EQUILIBRIUM STRUCTURE-
EQUILIBRIUM RHEOGRAM

L C .1

 

 

[COMPLETE ANALYSIS]

APPENDIX C

OUTLINE OF DATA COLLECTION

12.

13.

14.

76
Appendix C. Outline of Data Collection

Turn on equipment

Allow to equilibrate to 25°C

Pour sample into cup

Attach paddle mixer to viscometer

Load cup into viscometer

Allow to equilibrate to 25°C (5 minutes)

Run viscometer at constant shear rate for 10 minutes
and collect torque readings

Have computer print out torque versus time plot
Rest sample for 10 or 60 minutes

Repeat constant shear rate test and plot

Collect torque readings using the angular velocity
range, 10-120 rpm

Have computer determine n from the torque versus
angular velocity curve

Have computer calculate K using Rao's method (1975)

Repeat steps 3413-for each sample used

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