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RSITY LIBRA

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3 1293 010206

                       

 

 

 

This is to certify that the

thesis entitled
RHEOLOGICAL BEHAVIOR

OF
CALCIUM CARBONATE-CORN SYRUP MIXTURES

presented by

Misael L. Miranda-Maldonado

has been accepted towards fulfillment

of the requirements for
Agricultural

MLS . degree in Engineering

EMF

Major professor

Date July 22, 1994

 

0-7 639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

LIBRARY
Mlchlgan State
Unlverslty

 

 

 

PLACE ll RETURN Boxwmwowmuflunmm
TO AVOID FINES Mum on or More mm.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU IoAn Nflnndlvo ActloNEqnl Opporumlly lmwon
W1

RHEOLOGICAL BEHAVIOR
OF

CALCIUM CARBONATE-CORN SYRUP MIXTURES

by

Misael L. Miranda-Maldonado

A THESIS

Submitted to

Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

in
Agricultural Engineering

Department of Agricultural Engineering

1994

ABSTRACT

RHEOLOGICAL BEHAVIOR or
CALCIUM CARBONATE-CORN SYRUP MIXTURES
by

Misael L. Miranda-Maldonado

The rheological behavior of calcium carbonate-corn syrup mixtures was studied
using mixing viscometry techniques. Materials are found to exhibit power law behavior.
Changes in the flow index behavior and consistency coefficient were evaluated as
functions of temperature and concentration. Decreases in the consistency coefficient (K)
with temperature increases, at a constant concentration, were explained by an Arrhenius
model. Temperature had little effect on the flow behavior index. Several exponential
models were used to demonstrate the influence of temperature and concentration, both

separately and combined, on shear stress-shear rate relationships.

ACKNOWLEDGEMENTS

Sincere thanks to Dr. James Stefi‘e, my advisor and major professor for his
guidance, comments, suggestions, support, encouragement, enthusiasm, friendship,
patience and for helping me to go with the flow in the different stages of this study.

Thanks to the Chilean government for their financial support that made this work
possible.

Thanks to my mother Adriana who gave me the reason to further my education.

Thanks to my aunt Ita and brother Mario for their support.

Thanks to Gloria Bateman, Valerie Geyer and to all the secretaries of the
Department of Agricultural Engineering and all the persons that helped me more than
once to complete my studies and related activities.

Thanks to my friends: Neba Ambe, Habib Chowdhury, Danny Campos, Chris
Daubert, Andy Fogiel, Armando Fuji, Mario Fusco, Phil Gerrish, Kevin Kalmbach,
George Mungai, Carlos Semidei, James Schaper, Rick Stowell, Wee Tan, Muluken
Tilahun and, Andy Wedel. Thanks for making my stay more pleasant here at Michigan
State University.

Special Thanks to Romelia & Irvin Widders, and to the families Crouch, Mungai,
Hudy, and Roberts for they help and friendship.

Thanks to Lorena for her support, encouragement and tolerance.

And overall, thanks to GOD, who made this accident a reality.

iii

TABLE OF CONTENTS

Chapter Page
LIST OF TABLES .............................................. vi
LIST OF FIGURES ............................................ vii
NOMENCLATURE ............................................ viii
I. INTRODUCTION ............................................ 1
II. REVIEW OF LITERATURE .................................... 4
2.1. Rheology Definition and Applications ........................ 4

2.1.1. Fluids, Newtonian and non-Newtonian Fluids ............ 5

2.1.2. Time-dependency ................................ 6

2.2. Types of Measurements and Common Instruments ............... 7

2.3. Mixer Viscometry ...................................... 7

2.3.1. Previous Research in Mixer Viscometry ................ 9

2.4. Properties of Suspensions, Dispersions and Multiphase Systems ...... 9

III. MATERIALS AND METHODS ................................ 14
3.1. Materials ........................................... 14

3.1.1. Sample Preparation .............................. 14

3.1.2. Viscometer Calibration ........................... 14

3.2. Methods ............................................ 15

3.2.1. Equipment Preparation ........................... 15

3.2.2. Data Collection ................................ 15

iv

3.2.3. Analytical Models Used in this Study ................. 15

3.2.4. Shear Stress and Shear Rate Calculations .............. 17

3.2.5. Concentration and Temperature ..................... 18

3.2.6. Temperature Effect .............................. 18

3.2.7. Concentration Effect ............................. 19

3.2.8. Combined Effect of Temperature and Concentration ....... 20

IV. RESULTS AND DISCUSSION ................................. 21
4.1. Temperature Effect at Each Concentration .................... 21

4.2. Concentration Effect on Each Temperature .................... 31

4.3. Effect of Temperature and Concentration ..................... 36

4.4. Summary of Effects .................................... 37

4.5. Use of Calcium Carbonate-Com Syrup Mixture ................ 41

V. CONCLUSIONS ........................................... 43
VI. FUTURE RESEARCH ....................................... 44
BIBLIOGRAPHY ......................................... 45

VII. APPENDIX 1. Prediction of Average Apparent Viscosity at 59.905 1/s ..... 47
VIII. APPENDIX 2. Measurements Performed at 25°C ................... 48
IX. APPENDD( 3. Calculations at 25°C to Fit the Global Model ............ 67
X. APPENDIX 4. Measurements Performed at 40°C ..................... 70
XI. APPENDIX 5. Calculations at 40°C to Fit the Global Model ............ 86
XII. APPENDIX 6. Measurements Performed at 55°C .................... 89
XIII. APPENDIX 7. Calculations at 55°C to Fit the Global Model .......... 108

V

LIST OF TABLES

1. Values of flow index behavior, consistency coefficient, and determination
coefficient at 25°C .......................................... 22

2. Values of flow behavior index, consistency coefficient, and determination
coefficient at 40°C .......................................... 23

3. Values of flow behavior index, consistency coefficient, and determination
coefficient at 55°C .......................................... 24

4. Summary of constants obtained from the three main effects under study ...... 40

vi

LIST OF FIGURES

1. Haake MV paddle sensor ...................................... 16
2. Influence of temperature on shear stress at 0% ....................... 26
3. Influence of temperature on shear stress at 5% ....................... 27
4. Influence of temperature on shear stress at 15% ....................... 28
5. Influence of temperature on shear stress at 25% ....................... 29
6. Influence of temperature on shear stress at 35% ....................... 3O
7. Influence of concentration on shear stress at 25°C ..................... 33
8. Influence of concentration on shear stress at 40°C ..................... 34
9. Influence of concentration on shear stress at 55°C ..................... 35
10. Effect of temperature and concentration on K ....................... 38
11. Effect of temperature and concentration on n ........................ 39

12. Effect of temperature and concentration on average apparent

viscosity at 59.905 1/s ....................................... 42

vii

NOMENCLATURE

b = impeller blade height, m

C = concentration, weight percent CaC03 in corn syrup
d = impeller diameter, m

E a = flow activation energy, cal/g mole

K = consistency coeflicient, Pa s "

KC = constant depending on concentration

K<

£0 = constant depending on Tand C

K0 = frequency factor, Pa s

Kr = constant depending on temperature

k’ = constant for a particular impeller, 1/rad
M = torque, N m

n 2 flow behavior index, dimensionless

n- = average flow behavior index, dimensionless
p = power, N m/s

P a = power number, dimensionless

R = gas constant, cal/K g-mole

R2 = determination coefi‘icient, dimensionless

T = absolute temperature, K

viii

a = constant depending on temperature and concentration, dimensionless
a0 = fitctor determined by the shape and dimensions, dimensionless

7 = shear rate, s "

70 = average shear rate, 3’1

u = viscosity of Newtonian fluids, Pa s

pm or = average apparent viscosity, Pa s

“app = apparent viscosity, Pa s

u, -- relative viscosity, ratio of the viscosity of suspension
to viscosity of suspending liquid, dimensionless

p = fluid density. 13/»!3

a = shear stress, Pa

00 = yield stress, Pa
00 = average shear stress, Pa
tb = volume concentration, dimensionless

0 = rotational speed of the impeller, rad/s

ix

CHAPTER I
INTRODUCTION

Calibration is a basic procedure required to ensure that an analytical method can
give accurate results. This process is based on the use of some pre-defined standards
which can be oils, solutions, pure substances and basically any system with a well known
property that remains constant under certain conditions. It is impossible to calibrate an
instrument to an accuracy greater than that of the standard with which it is compared.
A rule often followed is that the calibration standard should be about ten times as
accurate as the instrument being calibrated (Doebelin, 1983).

In flow measurements for example, a flow-rate calibration depends on standards
of volume (length) and time, or mass and time. A primary calibration is based on the
establishment of steady flow through the flowmeter to be calibrated and subsequent
measurement of the volume or mass of flowing fluid that passes through in an accurately
timed interval. Any stable and precise flowmeter calibrated by such primary method, then
itself becomes a secondary flow-rate standard against which other (less accurate)
flowmeters may be calibrated conveniently (Doebelin, 1983).

A significant deviation in any calibration from the conditions in which the
calibration was performed will invalidate the measurements that can be obtained with
such a calibrated instrument. Possible sources of error for example in flowmeters include

variations in fluid properties such as density, viscosity and temperature.

2

Green (1949) mentioned that commercial rotational viscometers are calibrated
using liquids of known viscosity. These liquids of known properties (Green, 1949) should
be Newtonian and not to have a very high viscosity, at the same time the shear rate of
the calibrating liquids should be within the shear rate range where the fluid still behaves
as a Newtonian substance. These fluids can be oils and, if they present constant
properties, can become standard materials.

Calibration can be done using established standard oils, however, some polymers,
petroleum oils, butene polymers and silicone oils have been used as well. Another
potential group of standards is represented by pure compounds and solutions. Also, Rao
and Vitali (1974) have noted that calibration of a coaxial cylinder viscometer can be done
using constant suspending weights.

Pure substances that can be used as standards were mentioned by Hull and Steffe
(1992). Some of these fluids are difficult to purify. Others have inherent difficulties.
Glycerin, for example, can become hygroscopic at room temperature. There are some
certified fluids that are formed by making solutions of different pure fluids.

When dealing with a sucrose-water solution at high concentration, a 1% change
in sucrose can produce up to 25% in change in the viscosity. This fact means that this
solution is inconvenient due to potential error. Corn syrups exhibit a constant viscosity
both in steady and dynamic shear conditions that makes them useful as Newtonian
calibration fluids when some of the reference standard oils are not suitable (Hull and
Steffe, 1992). Corn syrup can present a tendency to dry due to mass transfer with

exposure to air. Aging may also create changes. If corn syrups do not suffer these

3

problems they can become useful for different food engineering problems where
calibration and process standardization are needed.

Some oils and polymers are commonly used to perform day-to-day calibration of
rheometers. These standards are based on a well known constant viscosity at a certain
temperature and pressure, and these fluids emulate water which is the primary material
used as a reference in viscosity calculations (Hull and Steffe, 1992).

The suspending weight method to calibrate coaxial viscometers is based on
suspending some constant weights from the axis of the sensor and, when the drive is in
constant low speed movement, recording the torque readings with increasing weights.
Based on these measurements it is possible to compute with confidence the maximum
axial torque. This can then be used to compute some rheological properties that depend
directly on the axial torque (Castro et al., 1990).

A suitable shear-thinning standard fluid, for the food industry does not exist. To
address this need, the following objectives were formulated for the current work:

1) Study the shear—thinning behavior of suspensions formed from mixtures of calcium
carbonate and corn syrup.
2) Evaluate the influence of temperature and concentration on the behavior of calcium

carbonate-corn syrup mixtures.

CHAPTER II

REVIEW OF LITERATURE

2.1. Rheology Definition and Applications.
Definition of Rheology.

The term "rheology" was invented by Eugene C. Bingham in 1929 and has since
been defined as "the study of the deformation and flow of matter" (Friedrickson, 1964;
Tanner, 1985), or as "the study of the manner in which materials respond to applied stress
and strain" (Steffe, 1992). All materials have rheological properties and the area is
relevant in many fields of study, such as geology and mining (Cristescu, 1989), concrete
technology (Tattersal and Banfill, 1983), soil mechanics (Vyalov, 1986; Haghighi et al.,
1987), plastics processing (Dealy and Wissbum, 1990), and tribology (study of

lubrication, friction and wear).

Appflgtions of Rheology.

Rheology is useful in the food area for different purposes such as to improve
product development, processing methodology and final product quality. Specifically,
there are numerous reasons why rheological data are needed in the food industry (Escher,
1983; Steffe, 1992):

a. Process engineering calculations for a wide range of equipment such as pipelines,
pumps, extruders, mixers, coaters, heat exchangers, homogenizers, calenders, and

on-line viscometers.

5

b. Determination of ingredient functionality in product development.
c. Regulation of on-process and final product quality control.

d. Shelf life correlation.

e. Evaluation of food texture by correlation to sensory data.

f. Analysis of rheological constitutive equations.

Many factors influence rheological properties. Examples include temperature and soluble
solids as well as the chemical and biochemical reactions which occur in food products.
A knowledge of fluid properties allows one to make economic improvements in a wide

variety of processes (Osorio, 1985).

2.1.1. Fluids, Newtonian and non-Newtonian Fluids.

Fluids are groups of molecules that exhibit the property of deformation without
any change of volume under the action of a force (Sherman, 1990). Fluids are Newtonian
if they follow Newton’s law (Equation 1), otherwise they are non-Newtonian and the
viscosity coefficient is called apparent viscosity. There are numerous models which
represent the behavior of the different fluid systems, however some of the most important
models are the Bingham model (Equation 2) and the Herschel-Bulkley model (Equation

3):

o=ui (1)

o=oo+Ky (2)

o=oo+Kw (3)

Newtonian fluids possess low concentrations of solids while non-Newtonian fluids
generally have a high concentration of solids and may also contain lipids, proteins,
carbohydrates and fibers which interact with the flow and produce deviations from
Newtonian behavior (Osorio, 1985). Non-Newtonian fluids are characteristically food
slurries, pharmaceutical products, gums, biological fluids and oils. (Skelland, 1967).
Emulsion and dispersions, especially those encountered in the food industry, are complex
systems that exhibit a wide variety range of rheological behavior (Peleg and Bagley,

1983).

2.1.2. Time-Dependency.

Fluids whose behavior depends on the time of application of a stress are called
time-dependent fluids, otherwise they are time-independent. Time-dependent fluids are
thixotropic if apparent viscosity decreases with time or rheopectic if apparent viscosity

increases with time (Tanner, 1985; Doublier and Lefevre, 1989).

7

2.2. Types of Measurements and Common Instruments.

Fundamental properties are independent of the instrument on which they are
measured, so different instruments will yield the same results. This is an ideal concept
and different instruments rarely yield identical results. Some examples of instruments
which give subjective results include the following (Bourne, 1982); Farinograph,

Mixograph, Extensograph, Viscoamylograph and the Bostwick Consistometer.

Common Rheological Instruments.

Common instruments capable of measuring fundamental rheological properties,
may be placed into two categories (Steffe, 1992):
- rotational type (parallel plate, concentric cylinder, cone and plate, mixer),
- and tube type (glass capillary, pipe).
Rotational viscometers may be operated in the steady shear (constant angular velocity)

or dynamic (oscillatory) mode.

2.3 Mixer Viscometry.

The general principle of measurement used in mixer viscometry is based on the
determination of the torque on the shaft of the impeller as a function of its rotational
speed (Castell-Perez and Steffe, 1992). This application is based on the power
consumption in a vessel for a Newtonian fluid and can be expressed in terms of a power

number, P0 = (p/d593p) in the laminar flow region, such as:

(4)
or

dflp (dflp)

 

where:

P0 = power number, dimensionless

R, = mixing Reynolds number, dimensionless
p = power, N m/s

(1 = impeller diameter, m

(2 = rotational speed of the impeller, rad/s

p = density, kg/m3

p = Newtonian viscosity, Pa 5

A = constant depending on system geometry, dimensionless

Equation (5) can be used for power law fluids if u is replaced by an apparent viscosity,

pm, evaluated at an average rate of shear, 70, which is defined as

i, = k’ 0 (6)
where

7 = shear rate, s'1
a

9

k / = constant for a particular impeller (Steffe, 1992), 1/rad

2.3.1. Previous Research in Mixer Viscometry.
Castell-Perez and Steffe (1990) evaluated established mixer viscometry methods,
such as the viscosity matching method and the slope method for average shear rate

calculations by agitation of time-independent, non-Newtonian fluids. Their final results
showed that the mixer constant, k’ , is not a constant for all ranges of fluid rheological

properties, system geometries (cup and impeller) and impeller rotational speeds.

Castell-Perez et a1. (1991) were studying a simple and accurate procedure to determine
the flow properties of power-law fluids using a paddle type mixer viscometer. They
considered the mixer as analogous to a concentric cylinder system and incorporated the
end effect in modeling. Data collection is reduced according to these authors because
calibration with stande fluids is not necessary to estimate average shear stress and shear

rate values.

2.4. Properties of Suspensions, Dispersions and Multiphase Systems.
Suspension_s of Paflcles in Newtonian Fluids.
a) Generalities.

Particles suspended in Newtonian fluids cause additional viscous dissipation during
flow and higher viscosities compared to the suspending fluid itself. Also, suspensions of
particles in Newtonian fluids usually exhibit one or more of the following properties:

i) an unbounded viscosity at low shear rates (shear stress),

10

ii) time and/ or strain dependent properties and shear-thinning (pseudoplasticity),

iii) shear-thickening (dilatancy), and

iv) normal stresses.

These effects are the reflections of the structures generated by particle interactions causing
redistribution of particles and their orientations and the net effects of these redistribution
processes on the bulk rheological behavior of the system.

Dilute suspensions of small particles in Newtonian fluids usually behave as a
Newtonian fluid. However, at moderate and high concentrations, the viscosity of the
suspension becomes a function of the strain rate applied. Non-Newtonian behavior
exhibited by suspensions of particles in Newtonian fluids can be a result of several factors

influencing the suspension (Kamal and Mutel, 1985).

Non-midrodanamic Forces:

The most important forces are brownian forces, electrical forces which arise from
the charges on particles, London-van der Waals forces. Non-hydrodynamic forces are
dominant in concentrated suspensions of colloidal particles (particles smaller than 1 pm)
and the rheological behavior of the suspension is determined by the competition between
non-hydrodynamic and hydrodynamic forces. Thus viscosity is a function of the bulk
rheological properties of colloidal dispersions in the microstructure. The relevant theories
have been reviewed by Mewis (1980). The importance of non-hydrodynamic forces
diminishes with increasing size. Generally, for suspensions of particles greater than 10

pm the rheological behavior is mainly determined by the hydrodynamic forces.

11

Particle Interactions:

i) Hydrodynamic interactions of particles, cause a change in the velocity distribution in
the vicinity of other particles.

ii) Direct particle-particle interactions are a significant energy sink and may allow the
formation of aggregates and produce the inhibition or promotion of structures by the
flow and change in particle orientation distribution with the flow strength as well as

anisotropic distribution of particles in some flows.

The relative importance of these factors on the bulk rheological properties of a
suspension, and hence the value of the particle concentration up to which the suspension
behaves as a Newtonian fluid, depends on the nature, shape and dimensions of the solid
particles and to a certain extent on the properties of the suspending fluid (Kamal and

Mutel, 1985).

b) Concentration - Relative Viscosity Relations.
Dilute Susmnsions.

Hydrodynamic theories for the concentration dependence on relative viscosity of
dilute suspensions of particles in a Newtonian matrix have been developed by Einstein
(1906 and 1911) (A. Einstein, Ann. Physik., 19, 289, 1906; A. Einstein, Ann. Physik., 34,
591, 1911) for spherical particles, by Jeffrey (G. B. Jeffrey. Proc. Roy. Soc. (London),
A102, 161, 1923) for ellipsoids, and by Burgers for cylindrical rods. These theories can

be summarized by the following relationship:

12

ur=1+ao¢ (7)

where:

p, = relative viscosity, defined as the ratio of the viscosity of the suspension to the
viscosity of suspending fluid, at volume concentration,

o, and 00 = dimensionless factors determined by the shape, dimensions and orientation

of the suspended particles.

Non-dilute Suspensions.

As the concentration is increased above that of the hydrodynamically dilute
concentration range, the concentration-relative viscosity relation becomes non-linear, due
to particle interactions and non-hydrodynamic forces. Non-linearity has been incorporated
into dilute suspension theories in several ways. Some of them have a theoretical basis,

while some are totally empirical (Kamal and Mutel, 1985).

Maximum packing fraction.

This concept can explain the influence of particle concentration on the viscosity
of the concentrated suspensions using the so-called maximum packing density. There
must come a time, as particles are being added when suspensions "jam up", producing a
continuous three-dimensional contact throughout the suspension, thus making flow
impossible, i.e., the viscosity tends to infinity. The particle phase volume at which this

happens is the maximum packing fraction, and its value will depend on the arrangement

13
of the particles (Barnes et al., 1989).

Multiphase Systems.

Suspensions, emulsions and pastes are the single most important area of
rheological research. These three types of multiphase systems have much in common,
although in suspensions the dispersed phase is solid, in emulsions it is another liquid and
in pastes the particles are in physical contact. All these systems may have one of the
following conditions:

a) dilute with no particle interaction (with the exception of pastes),
b) stable, as in sterically stabilized paints,

c) flocculated with structure fully foamed,

d) partially stable with some structure forming and

e) sedimenting.

CHAPTER III
MATERIALS AND METHODS.
3.1 Materials.
3.1.1. Sample Preparation.

Corn syrup and calcium carbonate were used as raw materials to prepare different
mixtures from which rheological characterization was performed. Calcium carbonate,
obtained from Mallinckrodt Co., had a mean particle size of 7-9 pm. Corn syrup was
obtained from A.E. Staley. It was a high fructose corn syrup (Isosweet 5500) with a

nominal viscosity equal to 0.8 Pa 5 at 25°C.

3.1.2. Viscometer Calibration.

A coaxial cylinder viscometer (Haake RV-12) using a M 150 torque sensor, a MV
cup, and a MV paddle impeller with a NESLAB RTE-9 refi'igerated circulating bath was
used to determine rheological properties of the mixtures over a wide range of
concentrations and temperatures. The viscometer was equipped with a built—in water
circulator to maintain samples at a constant temperature.

In this study the torque sensor was not calibrated using standard oil. The
suspending weight calibrating system (Castro et al., 1990) was used to determine the
maximum axial torque that the drive produced. The deviation of maximum torque from
the value reported by the manufacturer was 2.8 % which is permissible in engineering
calculations. Based on this value, all calculations of shear stress and shear rate were

performed.

14

1 5
3.2 Methods.

3.2.1. Equipment Preparation.

For the preliminary data collection, a traditional concentric cylinder system (MV I
sensor and cup) was used. There was no thixotropy in any sample but the existence of
settling was found. This settling effect made the resulting data unacceptable; hence new
measuring system was needed and the best option for this purpose was mixer viscometry.
At this point in the study, an MV paddle impeller (Figure l) and cup were selected to
perform the measurements, thus avoiding any influence of settling on measurements to

be performed. All subsequent measurements were made using this system.

3.2.2. Data Collection.

Eight data points were taken at each of the following impeller speeds (rpm): 1, 2,
4, 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, 4, 2, 1. From these, the average reading
was obtained. Using the maximum axial torque attained by the weight suspension
calibration, the torque value was obtained, and from the rpm at which the readings were

taken, the angular velocity for each measurement was calculated.

3.2.3. Analytical Models Used in this Study.
In this study three models were considered: Newtonian, Power-law, and Herschel-
Bulkley. The power law model best represented the rheological behavior of calcium

carbonate-corn syrup mixtures.

 

 

0.127m

 

| 15° pitch blade

 

 

 

 

 

 

 

Figure l. Haake MV paddle sensor.

17
3.2.4. Shear Stress and Shear Rate Calculations.

With the values of the angular velocity and the impeller constant kl, taken from
the literature as k’ = 4.47 1/rad; (Steffe, 1992), using the Equation (6) the average shear

rate values were obtained.

The average shear stress values were calculated as:

o = —————2M (3)

a 1: d3 —b-+—l-]
d 3

where :
k’= impeller proportionality constant, 1/rad
M = torque, N m
d = impeller blade diameter, m
b = impeller blade height, m
The corresponding n and K values were obtained from the linear regression analysis

between the shear stress-shear rate values, for each condition studied.

18

3.2.5. Concentrations and Temperature.

This study was performed using 5 different concentrations (0, 5, 15, 25 and 35
weight percent) of calcium carbonate. Three different temperatures (25, 40 and 55°C)
were used to get measurements of torque at ten different speeds of rotation. Three
replications were done for each data set. Angular velocity and the corresponding torque
value at each condition was computed and from these numbers the respective flow
behavior index and consistency coefficient values were calculated by a regression analysis
between the natural log of the angular velocity and torque. Each data set was obtained
for each one of the different conditions of temperature and concentration.

The different exponential models were fitted for shear-stress and shear-rate, and
all the values were combined in a non-linear fitting procedure to get a model which could
collectively explain the behavior of shear stress in terms of shear rate, concentration and

temperature.

3.2.6. Temperature Effect at Each Concentration.
The literature mentions that an Arrhenius-type equation is commonly used to
quantify the effect of the temperature on the rheological behavior of fluids (Ibarz, 1993).

So, for power-law fluids, the consistency coefficient can be expressed as:

K = K. exp [1%] (9)

where:

19

K0 = frequency factor, Pa 3

Ba = flow activation energy, cal/g-mole

R = universal gas constant, cal/K g-mole

T = absolute temperature, K

The general analytical model that explains the temperature effect at each concentration

has the general expression:

a,=f( T. t.) =KTexp[—E1] "

R T Y. (10)

where:

,7 = average of n values for all temperatures and concentrations.

comes from a regression analysis of all the K values at each concentration.

 

Ea
KT exp [-R—T'

3.2.7. Concentration Effect at Each Temperature.
The proposed model which takes into account the effect of concentration has the

following form:

a, =f( c. 7,) = K. exp (BC) if (11)
where:
C = % CaCO3 concentration by weight.

,7 = average of n values for all temperatures and concentrations.

 

20

and KC exp (BC) comes from a regression analysis from all the K values at each

temperature.

3.2.8. Combined Effect of Temperature and Concentration.
The general expression for the variation of shear stress as a function of

temperature, concentration and shear rate has the form:

a, =f(T. c. i) = K.1m exp 7% BCJiZ (12)

 

where the term

K( n 0 exp [7% + BC ] (13)

is obtained from all the K values, and or either comes from the average of all the n values

or may be determined separately as a function of temperature and concentration.

CHAPTER IV

RESULTS AND DISCUSSION

Results of modeling all flow curves using the power law equation are presented
in Tables 1, 2 and 3. The average value of n (r? = 0.9101) at all temperatures and

concentrations was used in determining the independent effects of temperature and

concentration.
4.1. Temperature Effect at Each Concentration.

According to the regression analysis from the different values of K at different
temperatures and concentrations (Tables 1 to 3) the following prediction equations for K.r
have been obtained at different calcium-carbonate concentrations:

0%: 1n KT = -19.53 + 5751.7 (1/T) R2 = 0.7935, number of observations = 9

5%: 1n KT = -14.74 + 4317.4 (1/T) R2 = 0.5287, number of observations =10

15%: In KT

-25.75 + 7894.30 (1/T) R2 = 0.9084, number of observations = 9
25%: 1n KT = -25.32 + 7981.6 (l/T) R2 = 0.9151, number of observations =18

35%: In KT = -16.19 + 5544.3 (III) R2 = 0.9706, number of observations = 9

The predictions for the values of KT are as follows:
0%: KT = 3.0E-09 exp(5751.7 IT)
5%: KT = 4.0E-07 exp(43l7.4 IT)
15%: KT = 7.0E-12 exp(7894.3 IT)

25%: KT = 1.0E-11 exp(7981.6 m

35%: KT = 9.0E-08 exp(5544.3 IT), and r? = 0.9101

21

22

Table 1. Values of flow behavior index, consistency coefficient and R2 at 25°C.

 

 

 

 

 

 

 

Flow Index Consistency R2
Behavior Coefficient

Concentration dimensionless Pa s”

(weight %)

0 0.9560 0.9224 0.9990
1.0032 0.7852 0.9999
1 .0568 0.6547 0.9986

5 0.9581 1.1114 0.9993
0.9662 1.1015 0.9992
1.1338 0.6461 0.9899

15 0.8045 2.3145 0.9491
0.7653 2.3482 0.9479
0.8237 2.0665 0.9523

25 0.9067 4.2554 0.9994
0.9085 4.2800 0.9993
0.8673 4.1873 0.9982
0.8848 4.3843 0.9990
0.9520 3.7893 0.9999

35 0.8479 9.3804 0.9997
0.8152 1 1.2379 0.9994
0.6993 7.5629 0.9623

 

23

Table 2. Values of flow behavior index, consistency coefficient and R2 at 40°C.

 

 

 

 

 

 

 

Flow Index Consistency R2
Behavior Coefficient

Concentration dimensionless Pa sll

(weight %)

0 0.9394 0.3071 0.9902
1.164 0.1311 0.9917
0.9737 0.2798 0.9965

5 1 .0205 0.2745 0.9999
0.9911 0.4502 0.9574
1.1581 0.1453 0.9976

15 1.0136 0.4123 0.9988
1.0567 0.3532 0.9977
0.8416 0.8491 0.9883

25 0.8516 1.0246 0.9558
0.9147 0.7961 0.9552
0.8166 1.2540 0.9610
0.8516 1.0246 0.9558

35 0.5421 5.9571 0.81 19
0.5670 4.6503 0.8121
0.5616 4.9264 0.8140

 

24

Table 3. Values of flow behavior index, consistency coefficient and R2 at 55°C.

 

 

 

 

 

 

 

Flow Index Consistency R2
Behavior Coefficient
Concentration dimensionless Pa su
(weight %)

0 0.9672 0.1295 0.9761
0.8910 0.1896 0.9581
0.9092 0.1653 0.9706

5 1.0083 0.1244 0.9857
0.9296 0.2039 0.9768
0.8681 0.2230 0.9499
0.6665 0.5706 0.8924

15 0.9798 0.2065 0.9914
0.8935 0.2954 0.9766
1.1106 0.1322 0.9957

25 1.1952 0.1448 0.9697
1.0069 0.3193 0.9986
1 .0345 0.2951 0.9997
0.9624 0.4165 0.9989
0.8711 0.5625 0.9893
0.8745 0.5557 0.9902
0.9092 0.4692 0.9939

35 0.71 14 2.0496 0.9492
0.7422 1.8315 0.9600
0.7370 1 .8097 0.9596

 

25

and based on these analytical expressions, the following models can be obtained:

am,=3.012-09exp[5751mm,“9°91 (14)
a(S,,=4.OE-07exp[43174/717,“9°“ (15)
0(15,)=7.0E—12exp[7894.311]?a°3°91 (16)
0(25’)=1.OE—11exp[7981.6l7]va°‘9°91 (17)
0(35,,=9.OE—08exp[5544.3mp,“9°" (18)

The data modeled by Equations 14 to 18 are represented in the Figures 2 to 6,
respectively. In each line of these figures the slope which represents the average apparent
viscosity, is higher as the temperature decreases, which agrees with theory, since it is

supposed that at a lower temperature the tendency to flow is lower.

26

 

 

 

 

 

 

 

 

 

 

 

 

 

120 1-
25C
/ £52
a /
2'. /
.2 //
40
/ /
K/
0 50 IN 150 2% 250
Shearrate,lls

Figure 2. Influence of temperature on shear stress at 0% CaCO3

Shear stress, Pa

27

 

 

 

 

 

 

 

 

 

 

 

 

 

120 +
250
10G / 40¢
/ 55¢
80 //
f /'
4c /
/ //
/
0 50 100 150 200 250
Shear rate, 1Is

Figure 3. Influence of temperature on shear stress at 5% CaCO3

Shear stress, Pa

28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

350
+
25 C
300 /
40 C
/ —B-—
25" / 55 c
2.. //
150 /
M
______________._
MM
0 50 100 150 200 250
Shear rate, 1Is

Figure 4. Influence of temperature on shear stress at 15%CaO3

Shear stress, Pa

29

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

700 I
25 C
+
GOG 40 C
+
55 C
soc /
3 //
200 /
//
._.——a—r
0 50 100 150 200 250
Shear rate, 115

Figure 5. Influence of temperature on shear stress at 25% CaCO3

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 +
250
1400 / :0:
12 // :3
g 1000 /
a 5... //
400 I 14/
/
20c //r/ //
o%/
0 50 100 150 200 250

Shear rate, 115
Figure 6. Influence of temperature on shear stress at 35% CaCO3

31
4.2. Concentration Effect at Each Temperature.

From the regression analysis of the different values of K and concentrations at
constant temperatures (Tables 1 to 3) the following prediction equations for Kc have been

obtained:

25°C: In KC = -0.268 + 0.0709 C R2 = 0.9499, number of observations = 19
40°C: In KC = -l.751 + 0.0874 C R2 = 0.8638, number of observations = 16

55°C: In KC = -1.993 + 0.054 C R2 = 0.5616, number of observations = 20

The predictions for the values of KC are as follow:

25°C: KC = 0.7650 exp(0.0709 C)

40°C: KC = 0.1736 exp(0.0874 C)

55°C: KC = 0.1362 exp(0.054 C)
and ii = 0.9101

and the final models are:

om = 0.7650 exp (0.0709 C) 729‘“ (19)

a,“ = 0.1736 exp (0.0874 C) 73"“ (20)

055.6 = 0.1362 exp (0.0540 C) 72"“ (21)

b“

32

The Equations 19 to 21 are represented in the Figures 7 to 9, respectively. For
each case, the slope which represents the average apparent viscosity is higher as the
concentration increases, which again agrees with theory, since it is supposed that at a

higher concentration the resistance to flow is greater.

Shear stress, Pa

1400

33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3‘;
1200
—nt—
// 5%
1000 :53;
2?;
800 / +
35%
600 /
m I
so 100 150 200 250
She-note, 113

Figure7.lnfluericeotcoricermafiononshearsuessat25099raesCelsius.

Shear stress, Pa

34

 

 

 

 

//

 

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/
’K'J/
/
‘-—:a=——.:
so 100 150 200
Stuart-Its, 11s

mamammmmmwmw

lilil

15%

it?”

I!

Shear stress, Pa

35

 

Shear rate. 1Is

Figure 9. Influence of concentration on shear stress at 55 degrees Celsius.

 

36

4.3. Effect of Temperature and Concentration.

A non-linear model was obtained using SAS (1988) (Statistical Analysis System),
by means of the non-linear procedure, NLIN. This procedure was used to get a predictive
model which had all the main variables included. To fit a non-linear model a program
was written, and the Marquardt method was used, where the variables, range and
derivatives of parameters to be estimated must be specified. One of the variables was
allowed to be a floating parameter, 0t. This parameter would then be compared with the

experimental average flow behavior index (,7) to check out the accuracy of this estimation

as a way of validating the obtained model.
The result of this modeling procedure using 512 data points (Appendix 1)

including all the conditions of temperature, concentration and shear rate was:

In a, = -l7.2338 + 391$??— + 0.0550 C + 0.8896 In 70 (22)

obtaining a goodness of fit R2 = 0.9588. From this equation the final prediction equation

was found to be:

0. = 3.354 exp [50784359

+ 0.0550 C J 73“" (23)

Hence, it is possible to obtain a predictive equation for the average apparent viscosity:

5078.4359
m = 3.3E-08 exp [T

p m + 0.0550 C ] y,‘°°“°‘ (24)

37
4.4. Summary of Effects.

A summary of the parameters observed for each effect is presented in Table 4.
It is demonstrated that with calcium carbonate-corn syrup mixtures, the higher the
concentration, the lower the flow index behavior and the higher the consistency
coefficient for the range of temperatures and concentrations under study.

The values of the consistency coefficient from Tables 1, 2 and 3 are represented
in Figure 10. Here it is demonstrated in a three-dimensional plot that there is a very well
known trend for the behavior of the consistency coefficient as concentration and
temperature vary. This trend is fairly reasonable, it is expected that as concentration
increases the value of the consistency coefficient should go up, and also as temperature
increases the value of the consistency coefficient should go down.

The values of the flow behavior index from the Tables 1, 2 and 3 are represented
in Figure 11. The flow behavior index also exhibits a trend, the higher the temperature
the lower the flow behavior index, and the higher the concentration the lower the flow
behavior index. Both trends are present for most of the values of the independent

variables.

0

Pa . s
a. 76 2. 54 4. 92 7. .79 9.68

K.

    

\\ \\ \ \\\:‘\\\\\\\

\ ‘ .
i“‘“‘=‘\i‘ii\‘“““
0 . o“

\\ 85:. \ \\\\\\\\:\§\ e \

38

   

 
  
  
  
    

‘ \\
\ \\\‘t\
‘ \ \

s \ \ \
~:‘.‘~‘.‘ “.~

\
\“

 

. \\\
5.9:‘§i§\i\\\\\\‘\\‘$“

   
   

«as
'9‘ 9. Q53 5‘?
Go

Figure 10. Effect of temperature and concentration on K.

0’ {men s (on /953

I

n
0.56 6.64 8.

0’)

7.? 9.82 9.90 0.99

i
*i
3

d.
:1
.1

39

 

 

Figure 11. Effect of temperature and concentration on n.

 

40

Table 4. Summary of constants obtained from the three main effects under study.

 

 

 

T C K Err/R B I? or (1

(°C) (weight %) (Pa 8) (K) (1/weight %) (dimensionless)
25-55 0 3.0E-9 5751.7 - ,7 = 0,9101
25-55 5 4015-7 4317.4 - ,7 = 0,9101
25-55 15 7.0E-12 7894.3 - ,7 = 0,9101
25-55 25 1.0E-11 7981.6 - ,7 = 0,9101
25-55 35 9.0E-8 5544.3 - ,7 -.- 0,9101

25 0-35 0.765 - 0.0709 ,7 = 0,9101

40 0-35 0.1736 - 0.0874 :7 = 0.9101

55 035 0.1362 - 0.0540 ,7 -_- 0,9101

 

25-55 0-35 3.3E-8 5078.4 0.0550 (1 = 0,8896

 

41

Figure 12 is a representation of the predictive equation for the average apparent
viscosity found for a shear rate value of 59.905 Us, for different values of concentration
and temperature. In this figure a trend is obvious. This is in agreement with the
principle that the higher the concentration, the higher the viscosity at constant
temperature, and the higher the temperature, the lower the average apparent viscosity at

a constant concentration.

4.5. Use of Calcium Carbonate-Corn Syrup Mixture.

The goal of this work was to study calcium carbonate-corn syrup mixtures to
determine if they could be used as shear-thinning standards in the food industry. This
standard material did not present clear shear-thinning behavior. In others words, with the
equipment used, it is not possible to find shear-thinning behavior which was statistically
significant. Hence, this calcium carbonate-corn syrup mixture is not a suitable shear-

thinning standard for the food industry.

. ”fl—7'"!

.n——
—

1L

100.5

Figure 12. Effect of temperature and concentration on apparent viscosity at 59.905 s'l

42

   

  
 

  
 

. 8
x 8
g
V
a. 8
8 w
0)
N a 811‘, .._ _.
3 ,3 \ \\\\§§§\-_..::;‘.‘.
“:::“\
. ..
6, 8‘ v:
S ' \ ‘
0 Q \ \\z} \\\-\\\ “\\\:g
‘0 “\“i\ \“‘
k I" ‘.\:\\\“\‘:\\
s K A ‘ .
Q 0'
as:
a (A 9"” o

rm" a!

 

E

CHAPTER V

CONCLUSIONS

In Figures 2 to 6, which are the graphic representations of the Equations 14 to 18,
it is demonstrated that the temperature effect at each concentration is fairly well
represented with a power law model showing a general trend that the lower the

temperature the higher the viscosity.

The Equations 19 to 21 are represented in the Figures 7 to 9 respectively, and here

it is observed that the higher the concentrations yield higher viscosities.

From the combined effect of temperature and concentration on shear stress (Figure
12), it is possible to say that the average apparent viscosity decreases as the temperature
increases at a constant concentration. On the other hand, at a constant temperature, the

average apparent viscosity decreases as the concentration goes down.

The calcium carbonate-corn syrup mixture does not exhibit shear-thinning trends

with changes in the calcium-carbonate concentration. Also, these mixtures do not show

thixotropic behavior, but do exhibit a problematic settling phenomenon.

43

CHAPTER VI
FUTURE RESEARCH
A future interesting study would be to determine the influence that the particle size
can have on the change of properties, in a system with Newtonian or non-Newtonian
fluids, looking for any important dependency on the type of solid as well. For example,

some kinds of polymers that are not soluble in the fluid could be investigated.

'Ilr“"“'”“ K1

XIV. BIBLIOGRAPHY.

Barnes, H.A., Hutton, J. F. and Walters, K. 1989. An Introduction to Rheology. Elsevier Science
Publishing, Co., New York.

Boume, M. C. 1982. Food Texture Jand Viscosity: Concept and Measurement. Academic Press,
New York.

Burgers, J .M. 1938. "The Second Report on Viscosity and Elasticity", p 113, Nordenman, NY.

Castell-Perez, M. E., and Steffe, J. F. 1990. Evaluating shear rates for power law fluids in mixer
viscometry. J. of Texture Studies 21:439-453.

Castell-Perez, M. E., and Steffe, J. F. 1992. Using mixing to evaluate rheological properties. Ch.
10. In Viscoela§tic Properties of Foods. Rao, MA. and Steffe, J.F. (ed). Elsevier Applied
Sciences, New York.

Castell-Perez, M. E., Steffe, J. F. and Moreira, R. G. 1991. Simple determination of power law
flow curves using a paddle type mixer viscometer. J. of Texture Studies 22:303-316.

Castro, E. S., Miranda, M.L., Rojo, O.A. 1990. Considerations for calibrating a coaxial cylinder
viscometer through suspending weights method. Alimentos 15 (3):19-24.

Cristescu, N. 1989. Rock Rheology. Kluwer Academic Pub., Boston.

Dealy, J. M. and K. F. Wissbum, 1990. Melt Rheology arnd its Role in Pla__stics Processing. Van
Nostrand Reinhold, New York.

Doebelin, E. 1983. Measurement Systems, Application & Design, third edition. Mc Graw-Hill
Book Company.

Doublier, J .L. and Lefevre, J. 1989. Food Properties and Computer Aided Engineering of Food
Processing System; Edited by Singh, RP. and Medina, A.G. Kluwer Academic
Publishers.

Escher, T. 1983. Relevance of rheological data in food processing. Ch. 8. In Physical
Properties of Foods. Jowitt R. (Ed.), p. 104. Applied Science Publishers, England.

Friedrickson, AG, 1964. Principles and Applications of Rheology. Prentice Hall, Inc.
Englewood Cliffs, NJ.

Green, H. 1949. Industrigl Rheology and Rheological Structures. John Wiley & Sons, Inc. New
York.

Haghighi, K., A.K. Srivastava and J .F. Steffe. 1987. The rheological approach to soil modeling.
Trans. ASAE 30:1661-1672.

45

46

Hull, M. and Steffe, J .F. 1992. Practical fluids for food rheology and process engineering
studies. J. of Process Engineering. 15:199-212.

Ibarz, A. 1993. Rheology of salted egg yolk. J. of Texture Studies. 24:63-71.
Mewis, J. 1980. Proc. of the International Congress on Rheology, 8th, 1:149-168.

Kama], M. R. and Mutel, A. 1985. Rheological properties of suspensions in Newtonian and
non-Newtonian Fluids. J. of Polymer Engineering. Vol. 5(4):293-386.

Osorio, FA. 1985. Back extrusion of power law, Bingham plastic and Herschel-Bulldey fluids.
MS. Thesis, East Lansing, Michigan State University, USA.

Peleg, M. and Barley, E.B. (eds). 1983. Physical Prgierties of Food. AVI Publishing, CO.,
Westport, CT.

Rao, M.A. and Vitali, A.A. 1984. Flow properties of low-pulp concentrated orange juice: Effect
of temperature and concentration. J. of Food Science. 49:882-888.

SAS/STAT User’s Guide 1988. Release 6.03. SAS Institute Inc., Cary, NC, USA.
Sherman, F. 1990. Viscous Flow. Mc Graw-Hill, Inc.

Skelland, A.A.P., (1967). Non-Newtonian Flow and Hefiat Transfer. John Wiley and Sons., Inc.,
New York.

Steffe, J. F. 1992. Rheological Methods in Food Process Engineering. Freeman Press. East
Lansing, MI 48823.

Tanner, RI. 1985. Engineering Rheology. Clarendon Press. Oxford.

Vyalov, S. S. 1986. Rheological Fundamentals of Soil Mechgnics. Elsevier Science Publishers,
New York.

VII. APPENDIX 1. PREDICTION OF AVERAGE APPARENT VISCOSITY at

59.905 lls.

Predicted average apparent viscosity using the predictive equation, Equation (24)
Apparent average
average shear

Temperature Concentration K n viscosity stress

°C % CaCO3 Pa sn dimensionless Pa 3 Pa

25 0 0.9224 0.9560 0.5244 0.0216
25 0 1.2729 1.0032 0.5244 0.0216
25 0 0.6547 1.0568 0.5244 0.0216
25 5 1.1114 0.9581 0.6904 0.0285
25 5 1.1015 0.9662 0.6904 0.0285
25 5 0.6461 1.1338 0.6904 0.0285
25 15 2.3145 0.8045 1.1967 0.0493
25 15 2.3482 0.7653 1.1967 0.0493
25 15 2.0665 0.8237 1.1967 0.0493
25 25 3.7893 0.9520 2.0742 0.0854
25 25 4.2800 0.9085 2.0742 0.0854
25 25 4.2554 0.9067 2.0742 0.0854
25 25 4.3843 0.8848 2.0742 0.0854
25 25 4.1873 0.8673 2.0742 0.0854
25 35 4.2907 0.8479 2.0742 0.0854
25 35 9.3804 0.8152 3.5951 0.1482
25 35 11.2379 0.8283 3.5951 0.1482
25 35 10.7634 0.9022 3.5951 0.1482
40 0 0.3071 0.9394 0.2319 0.0096
40 0 0.1311 1.1640 0.2319 0.0096
40 0 0.2798 0.9737 0.2319 0.0096
40 5 0.2745 1.0205 0.3053 0.0125
40 5 0.4502 0.9911 0.3053 0.0125
40 5 0.1453 1.1581 0.3053 0.0125
40 15 0.4123 1.0136 0.5292 0.0218
40 15 0.3532 1.0567 0.5292 0.0218
40 15 0.8491 0.8416 0.5292 0.0218
40 25 2.2041 0.7528 0.9173 0.0378
40 25 0.7961 0.9147 0.9173 0.0378
40 25 1.254 0.8166 0.9173 0.0378
40 25 1.0246 0.8516 0.9173 0.0378
40 35 5.9571 0.5421 1.5899 0.0655
40 35 4.6503 0.5670 1.5899 0.0655
40 35 4.9264 0.5616 1.5899 0.0655
55 0 0.1295 0.9672 0.1105 0.0046
55 0 0.1896 0.8910 0.1105 0.0046
55 0 0.1653 0.9092 0.1105 0.0046
55 5 0.5706 0.6665 0.1455 0.0060
55 5 0.1244 1.0083 0.1455 0.0060
55 5 0.2039 0.9296 0.1455 0.0060
55 5 0.223 0.8681 0.1455 0.0060
55 15 0.2065 0.9798 0.2522 0.0104
55 15 0.2954 0.8935 0.2522 0.0104
55 15 0.1322 1.1106 0.2522 0.0104
55 25 0.4165 0.9624 0.4370 0.0180
55 25 0.1448 1.1952 0.4370 0.0180
55 25 0.3193 1.0069 0.4370 0.0180
55 25 0.5623 0.8711 0.4370 0.0180
55 25 0.5557 0.8745 0.4370 0.0180
55 25 0.2951 1.0345 0.4370 0.0180
55 25 0.4692 0.9092 0.4370 0.0180
55 35 2.0496 0.7114 0.7576 0.0312
55 35 1.8315 0.7422 0.7576 0.0312
55 35 1.8097 0.7370 0.7576 0.0312

47

VIII. APPENDIX 2. MEASUREMENTS PERFORMED AT 25°C.

This appendix contains all the raw data and a summary of the basic calculations done based on
the average of the measurements. keeping in mind that the maximum torque value was equal to 1.428716915
N cm.

1.- Mixer viscometry, 0%, 0 9 corn syrup
rpm readings Average
1 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
2 0.7 0.7 0.7 0.7 0.7 0.6 0.7 0.7 0.6875
4 1.3 1.2 1.3 1.2 1.3 1.2 1.2 1.3 1.25
8 2.5 2.4 2.5 2.4 2.6 2.4 2.5 2.4 2.4625
16 4.9 4.8 4.7 4.6 S 4.8 4.8 4.7 4.7875
32 9.6 9.6 9.5 9.6 9.6 9.5 9.6 9.5 9.5625
64 19.1 19 19 19.1 19 19.1 19 19 19.0375
128 37.9 37.9 37.9 37.9 37 9 37.8 37.8 37.8 37.8625
256 74.9 74.9 75 74.9 75 74.9 74.9 74 9 74.925
128 32.9 32.9 32.9 32.9 32.9 32.8 32.9 32.9 32.8875
64 18 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.0875
32 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5 9.5
16 5 5 5 4.9 5 4.9 S 4.9 4.9625
8 2.6 2.7 2.7 2.6 2.6 2.6 2.6 2.6 2.625
4 1.4 1.5 1.4 1.4 1.4 1.4 1.4 1.5 1.425
2 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
1 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.5 0.5125
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.00571 68-05 -0.9801 -4.243
2 0.2094 0.00982 18-04 -0.679 -4.008
4 0.4188 0.01786 0.0002 -0.378 —3.748
8 0.8376 0.03518 0.0004 -0.077 -3.454
16 1.6752 0.0684 0.0007 0.22407 -3.165
32 3.3504 0.13662 0.0014 0.5251 -2.864
64 6.7008 0.27199 0.0027 0.82613 -2.565
128 13.402 0.54095 0.0054 1.12716 -2.267
256 26.803 1.07047 0.0107 1.42819 -1.97
128 13.402 0.46987 0.0047 1.12716 -2.328
64 6.7008 0.25842 0.0026 0.82613 -2.588
32 3.3504 0.13573 0.0014 0.5251 -2.867
16 1.6752 0.0709 0.0007 0.22407 -3.149
8 0.8376 0.0375 0.0004 -0.077 -3.426
4 0.4188 0.02036 0.0002 -0.378 —3.691
2 0.2094 0.01143 0.0001 -0.679 -3.942
1 0.1047 0.00732 78—05 -0.9801 -4.135
Determination of average shear rate
shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate “ (n-l) d = 0.04143 m
K: consistency coefficient
k'=4.47
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG‘in—l) X Gamma 1/3 1/3
angular average average average averag average average
velocit viscosi shear shear Lnshear Lnshear viscos shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 1.1675 0.46801 0.7874 -0.2391 -0.759 1.682 0.50297 -0.6872
2 0.2094 1.1063 0.93602 1.3533 0.30255 -0.066 1.446 0.86448 —0.1456
4 0.4188 1.0483 1.87204 2.4605 0.90038 0.627 1.314 1.57178 0.45221
8 0.8376 0.9933 3.74407 4.8473 1.57842 1.3202 1.295 3.0964 1.13024
16 1.6752 0.9412 7.48814 9.4239 2.24325 2.0133 1.259 6.01991 1.79507
32 3.3504 0.8919 14.9763 18.823 2.93509 2.7065 1.257 12.0241 2.48691
64 6.7008 0.8451 29.9526 37.474 3.62365 3.3996 1.251 23.9382 3.17547
128 13.402 0.8008 59.9052 74.53 4.3112 4.0928 1.244 47.6091 3.86302
256 26.803 0.7588 119.81 147.49 4.99373 4.7859 1.231 94.2123 4.54555
1/3 term included
Regression Output: K
Constant -0.0786 0.9244
Std Err of Y Est 0.06282
R Square 0.99895
Observations 9
Degrees of Freedom 7
x Coefficien 0.956
Std Err of C 0.0117
Model : Ln 3. stress -0.079 + 0.956 s.rate R‘2 = 0.99895

s.stress = 0.9244. s.rate “ 0.956

48

Mixer Viscometry,

256
128
64
32

H
Haas-ac»

Determination of
shear rate

0 U1QIOF‘mtd

#ChUJM\Dh)W

rad/s

omega

.1047
.2094
.4188
.8376
.6752
.3504
.7008
.402

.803

.402

.7008
.3504
.6752
.8376
.4188
.2094
.1047

GLDF‘OCDCDO

rauchna\¢1001w

U~JRJOCD£5

(N cm)
M

.0042
.0080
.0166
.0334
.0678
.1369
.2727
.5416
.0706
.4709
.2564
.1335
.0687
.035
.0178
.0098
.005

O<DC>O<DC>O<DP‘OC3C>O(DC>O<D

9
4
1

6
8
1
6
4
4
S
9
6

6
2

a~qaim~quamxorewrea\mtnarmtu

(N m)
M
4E-05
8E-05
.0002
.0003
.0007
.0014
.0027
.0054
.0107
.0047
.0026
.0013
.0007
.0004
.0002
lE-04
58-05

O<DC>O<DC>O<3C>O<DC>C

KDHLDNJbFJO\U

UJQLHJDGDQ

0%, 0 9 corn syrup

0 dadthMLd

0
0
1
2
4
9
19
37
75
33
18
9
4
2
1
0
0

U~JUJ#CDUJ

Log Om
-0.
—0.679
.378
.077
.22407
.5251
.82613
.12716
.42819
.12716
.82613
.5251
.22407
.077
.378
.679
.9801

II I l I
OCDCDOCDCDHIHP‘CDOCDCDO

-0

average shear rate

4.47 angular velocity

K shear rate A(n—l)

choef oof consist
2 M / pi b d“2

viscosity =
k'=4.47
average shear stress
(b/d + 1/3)
angular
velocit
rpm rad/s
1 0.1047
2 0.2094
4 0.4188
8 0.8376
16 1.6752
32 3.3504
64 6.7008
128 13.402
256 26.803 1

Regression Statistics
R Square
Observations

K =1.2729 Interce

x1

0.9831
d“2b
average average
shear shear
rate stress
0.468 0.59053
0.936 1.10725
1.872 2.28831
3.7441 4.60122
7.4881 9.35007
14.976 18.8724
29.953 37.5725
59.905 74.6283
19.81 147.51
0.9999
9

Coeffici Standar
0.24127
0.99669 0.0038 261.245

0.0096

KG“(n-1)
average
viscosi
Pa.s
.9318
.9172
.9028
.8886
.8747
.861
.8475
.8342
.8211

CJOCDCDOCDCDOCD

Log
—4.
-4.
—3
—3
-3.
-2.
-2
-2.
-1.
—2.
-2.
-2.
-3.
—3
-3
—4.
—4.

Ln
st

-0.
0.

F*W~JUJH
O‘DP‘R’b\O~J&JfihQ\OHDDJOFIOCD
w~aatwcna-w\o~au>w~aarhr4oxw

49

M
368
095

.78
.476

168
863

.564

266
97

327
591
874
163

.456
.748

008
301

shear
ress
5267
10188

0.82781

fibfiLJRJND‘

.52632
.23538
.9377
.62627
.31252
.99389
Y

#~Jh)h\OhHD m th\DUHVO\w

Lnshear

rate

-0

fiuthNIOP‘O

7E-O9

58-17

.759
-0.
.627

.3202
.0133
.7065
.3996
.0928
.7859

066

0.218
0.988

HIJ~JUJH
CDOrJh)h\DGDNd>~JW\OU1NFJC>O
a~qtuuwaah. U3GHOF‘O‘ ithU‘U

Sigma/
Gamma 1/3
average average

viscos shear
Pa.s stress
1.262 0.37723
1.183 0.7073
1.222 1.46175
1.229 2.93922
1.249 5.97275
1.26 12.0555
1.254 24.001
1.246 47.672
1.231 94.228

x

t Statis P-value Lower 95% Upper 95%
25.0269

0.26406
1.00571

Ln

1/3
average
shear
stress
-0.9749
-0.3463
.37964
.07815
.78721
.48952
.1781
.86434
.54572

btthNbflF‘C

50

Mixer Viscometry, 0%, 0 9 corn syrup

rpm readings Average
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
4 1.1 1.1 1 1.1 1.1 1.1 1 1 1.0625
8 2.3 2.3 2.2 2.3 2.3 2.2 2.2 2.2 2.25
16 4.6 4.7 4.6 4.7 4.8 4.8 4.6 4.7 4.6875
32 9.5 9.4 9.6 9.5 9.4 9.4 9.6 9.5 9.4875
64 19.1 19.1 19 19 19 19 19 19.1 19.0375
128 38 38 38 38 38 38.1 38 38.1 38.025
256 75.5 75.8 75.9 75.8 75.8 75.8 75.7 75.7 75.75
128 38.2 38.1 38.1 38.1 38.1 38.1 38.1 38.2 38.125
64 19.1 19 19.1 19.1 19.1 19 19.1 19 19.0625
32 9.5 9.5 9.6 9.4 9.5 9.4 9.5 9.5 9.4875
16 4.6 4.7 4.7 4.8 4.7 4.7 4.6 4.7 4.6875
8 2.3 2.3 2.2 2.3 2.3 2.3 2.3 2.3 2.2875
4 1.1 1 1 1.1 1.1 1.1 1 1.1 1.0625
2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.00286 38-05 -0.9801 -4.544
2 0.2094 0.00714 78-05 -0.679 -4.146
4 0.4188 0.01518 0.0002 -0.378 -3.819
8 0.8376 0.03215 0.0003 -0.077 -3.493
16 1.6752 0.06697 0.0007 0.22407 -3.174
32 3.3504 0.13555 0.0014 0.5251 -2.868
64 6.7008 0.27199 0.0027 0.82613 —2.565
128 13.402 0.54327 0.0054 1.12716 -2.265
256 26.803 1.08225 0.0108 1.42819 -1.966
128 13.402 0.5447 0.0054 1.12716 -2.264
64 6.7008 0.27235 0.0027 0.82613 -2.565
32 3.3504 0.13555 0.0014 0.5251 -2.868
16 1.6752 0.06697 0.0007 0.22407 -3.174
8 0.8376 0.03268 0.0003 -0.077 ~3.486
4 0.4188 0.01518 0.0002 ~0.378 -3.819
2 0.2094 0.00714 7E~05 -0.679 -4.146
1 0.1047 0.00286 3E-05 -0.9801 -4.544
Determination of average shear rate
average shear rate = 4.47 angular velocity
viscosity = K shear rate ‘ (n-1) b = 0.02692 m
k'=4.47 d = 0.04143 m
K: consistency coefficient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/
KG‘(n-1) Gamma 1/3
angular average average average average average
velocit shear viscosi shear Lnshear Lnshear viscosi shear
rpm rad/s rate Pa.s stress stress rate Pa.s stress
1 0.1047 0.468 0.68023 0.3937 —0.9322 -0.759 0.841 0.25148
2 0.2094 0.936 0.71108 0.9842 —0.0159 -0.066 1.051 0.62871
4 0.4188 1.872 0.74334 2.0915 0.73786 0.627 1.117 1.33601
8 0.8376 3.7441 0.77706 4.429 1.48817 1.3202 1.183 2.8292
16 1.6752 7.4881 0.8123 9.227 2.22214 2.0133 1.232 5.89416
32 3.3504 14.976 0.84915 18.676 2.92721 2.7065 1.247 11.9298
64 6.7008 29.953 0.88767 37.474 3.62365 3.3996 1.251 3.9382
128 13.402 59.905 0.92793 74.85 4.31548 4.0928 1.249 47.8135
256 26.803 119.81 0.97002 149.11 5.00468 4.7859 1.245 95.2497
x

Regression Statistics
R Square
Observations

K =0.6547 Interce
x1

0.99858

Coeffici Standar
-0.4236 0.0406
1.05683 0.0151

-10.428

68-06

70.0891 2E-12

-O.52

1.021

t Statis P-value Lower 95% Upper 95%

-0.3275

1.09248

Ln
1/3

average
shear
stress

-1.
-0.

<fiwUNHHC

3804
4641

.28969
.03999
.77396
.47904
.17547
.86731
.5565

51

Mixer Viscometry, 5%, 4.99%. 60.11 g corn syrup, 3 g CaCO3

rpm readings Average
1 0.4 0.5 0.4 0.5 0.4 0.4 0.4 0.4 .425
2 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
4 1.6 1.6 1.6 1.6 1.7 1.6 1.6 1.6 1.6125
8 3.2 3.1 3.2 3.1 3.2 3.1 3.2 3.1 3.15
16 6.2 6.1 6.1 6.1 6.1 6.1 6.1 6.2 6.125
32 12.2 12.2 12.1 12.2 12.1 12.2 12.1 12.1 12.15
64 24 24.1 24.1 24 24.1 24 24 24.1 24.05
128 47.2 47.3 47.2 47.2 47.2 47 2 47.2 47.1 47.2
256 78 77.9 78 78.1 78.3 78.3 78.4 78.5 78.1875
128 43 42.9 43 42.9 42.9 42.9 42.9 42.8 42 9125
64 22.6 22.5 22.5 22.5 22.5 22.6 22.5 22.6 22.5375
32 11.8 11.9 11.8 11.8 11.8 11.9 11.9 11.8 11.8375
16 6.1 6.1 6 6.1 6 6 6 6.1 6.05
8 3.1 3.1 3 3.1 3.1 3.1 3 3.1 3.075
4 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.5 1.475
2 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.00607 68-05 -0.9801 -4.217
2 0.2094 0.01143 0.0001 -0.679 -3.942
4 0.4188 0.02304 0.0002 -0.378 -3.638
8 0.8376 0.045 0.0005 -0.077 -3.347
16 1.6752 0.08751 0.0009 0.22407 -3.058
32 3.3504 0.17359 0.0017 0.5251 -2.76
64 6.7008 0.34361 0.0034 0.82613 -2.464
128 13.402 0.67435 0.0067 1.12716 -2.171
256 26.803 1.11708 0.0112 1.42819 -1.952
128 13.402 0.6131 0.0061 1.12716 -2.212
64 6.7008 0.322 0.0032 0.82613 -2.492
32 3.3504 0.16912 0.0017 0.5251 -2.772
16 1.6752 0.08644 0.0009 0.22407 -3.063
8 0.8376 0.04393 0.0004 —0.077 -3.357
4 0.4188 0.02107 0.0002 -0.378 —3.676
2 0.2094 0.01 0.0001 -0.679 -4
1 0.1047 0.00429 48-05 -0.9801 -4.368
Determination of average shear rate
average shear rate = 4.47 k' b = 0.02692 m
viscosity = K shear rate A(n 1) d = 0.04143 m
K = consistency coefficient
k'=4.47
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG“(n-1) Gamma 1/3 1/3
angular average average average average average average
velocit viscisi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 1.1281 0.46801 0.8366 0.1784 -0.7593 1.7875 0.534 ~0.6266
2 0.2094 1.1151 0.93602 1.5747 0.4541 -0.0661 1.6824 1.006 0.00592
4 0.4188 1.1023 1.87204 3.1741 1.15503 0.62703 1.6955 2.028 0.70685
8 0.8376 1.0896 3.74407 6.2006 1.82464 1.32017 1.6561 3.961 1.37647
16 1.6752 1.0771 7.48814 12.057 2.48962 2.01332 1.6101 7.702 2.04144
32 3.3504 1.0647 14.9763 23.917 3.17457 2.70647 1.59? 15.28 2.72639
64 6.7008 1.0524 29.9526 47.341 3.85737 3.39962 1.5805 30.24 3.4092
128 13.402 1.0403 59.9052 92.91 4.53163 4.09276 1.551 59.35 4.08346
256 26.803 1.0283 119.81 153.91 5.03635 4.78591 1.2846 98.31 4.58817
X Y
Regression Statistics
R Square 0.99932
Observations 9

Coeffici Standar t Statis P-value Lower 95% Upper 95%
K =1.1114 Interce 0.10562 0.0255 4.13761 0.0033 0.045 0.16598
x1 0.9581 0.0095 101.105 18—13 0.936 0.98051

52

Mixer Viscometry, 5%, 5%, 60.84 g corn syrup, 3.04 g CaCO3

rpm readings Average
1 0 4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
2 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8125
4 1.6 1.6 1.7 1.6 1.6 1.7 1.6 1.6 1.625
8 3 3 3.1 3.2 3.1 3.1 3.1 3.2 3.2 3.1625
16 6.3 6.3 6.4 6.2 6.3 6.3 6.3 6.3 6.3
32 12.5 12.4 12.4 12.5 12.5 12.5 12.4 12.4 12.45
64 24.7 24.7 24.7 24.7 24.7 24.7 24.6 24.7 24.6875
128 47.2 47.3 47.2 47.2 47.3 47.3 47.3 47.3 47.2625
256 79.3 79.2 79.6 79.6 80.1 80.4 80.1 79 8 79.7625
128 42.9 42.9 42.8 42.8 42.9 42.9 42.8 42 9 42.8625
64 22.9 22.9 22.9 22.8 22.9 22.8 22.9 22.9 22.875
32 12.2 12.3 12.2 12.2 12.2 12.2 12.3 12.2 12.225
16 6.4 6.4 6.4 6.4 6.4 6.5 6.4 6.5 6.425
8 3.3 3.3 3.2 3.3 3.4 3.3 3.4 3.3 3.3125
4 1.7 1.7 1.8 1.8 1.7 1.7 1.8 1.8 1.75
2 0.9 0.9 1 1 1 0.9 0.9 1 0.95
1 0.6 0.5 0.5 0.6 0.5 0.5 0.6 0.6 0.55
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.00571 68-05 -0.9801 -4.243
2 0.2094 0.01161 0.0001 -0.679 -3.935
4 0.4188 0.02322 0.0002 -0.378 -3.634
8 0.8376 0.04518 0.0005 -0.077 -3.345
16 1.6752 0.09001 0.0009 0.22407 -3.046
32 3.3504 0.17788 0.0018 0.5251 -2.75
64 6.7008 0.35271 0.0035 0.82613 -2.453
128 13.402 0.67525 0.0068 1.12716 -2.171
256 26.803 1.13958 0.0114 1.42819 -1.943
128 13.402 0.61238 0.0061 1.12716 -2.213
64 6.7008 0.32682 0.0033 0.82613 -2.486
32 3.3504 0.17466 0.0017 0.5251 -2.758
16 1.6752 0.0918 0.0009 0.22407 -3.037
8 0.8376 0.04733 0.0005 -0.077 -3.325
4 0.4188 0.025 0.0003 -0.378 —3.602
2 0.2094 0.01357 0.0001 -0.679 -3.867
1 0.1047 0.00786 88-05 -0.9801 -4.105
Determination of average shear rate
averageshear rate = 4.47 k' b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47
= consistency coefficient
average shear stress = 2 M / pi b d‘2
(b/d + 1/3) 0.9831
Sigma/
KG“(n-1) Gamma 1/3
angular average average average average average
velocit viscosi shear shear Lnshear Lnshear viscos shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 1.3635 0.46801 0.7874 -0.2391 -0.759 1.682 0.50297
2 0.2094 1.3086 0.93602 1.5994 0.4696 -0.066 1.709 1.02166
4 0.4188 1.2559 1.87204 3.1987 1.16275 0.627 1.709 2.04331
8 0.8376 1.2053 3.74407 6.2252 1.8286 1.3202 1.663 3.9766
16 1.6752 1.1568 7.48814 12.401 2.51779 2.0133 1.656 7.92176
32 3.3504 1.1102 14.9763 24.507 3.19896 2.7065 1.636 15.6549
64 6.7008 1.0655 29.9526 48.596 3.88354 3.3996 1.622 31.0426
128 13.402 1.0226 59.9052 93.033 4.53296 4.0928 1.553 59.4289
256 26.803 0.9814 119.81 157.01 5.05629 4.7859 1.31 100.295
x
Regression Statistics
R Square 0.99919
Observations 9

Coeffici Standar t Statis P-value Lower 95% Upper 95%
K =1.1015 Interce 0.0967 0.0281 3.44444 0.0088 0.03 0.16309
x1 0.96621 0.0104 92.7094 ZE—l3 0.942 0.99085

Ln
1/3

average
shear
stress

-0.
0.

Kbawwwpo

6872
02142

.71457
.38043
.06961
.75078
.43536
.08478
.60812

Mixer Viscometry.

rpm
1
2
4
8

128

Determination of
average shear rate

viscosity
k'=4.47
k:
average shear stress
(b/d + 1/3)
angular
velocit
rpm rad/s
1 0.1047
2 0.2094
4 0.4188
8 0.8376
16 1.6752
32 3.3504
64 6.7008
128 13.402
256 26.803

04th memdfiH‘OQNUIN

rad/s

omega

.1047
.2094
.4188
.8376
.6752
.3504
.7008
.402

.803

.402

.7008
.3504
.6752
.8376
.4188
.2094
.1047

R>H
mumwpoooo

13

(3000me

5%,

Mdfiwm UQOWH \DUU‘IN

(N cm)

.00196
.0075

.01804
.04018
.08483
.17234
.34807
.69561
.3696

.69346
.34718
.17305
.08483
.04161
.02018
.00893
.00375

OOCDCDCDCDC>CDl-‘C>OCDCDC>C>C>O3

Regression Statistics
R Square
Observations

K =0.6461 Interce

x1

me‘ WHNMHQ§ \DQWU‘H

(N m)
M

2E-05
88-05
.0002
.0004
.0008
.0017
.0035
.007

.0137
.0069
.0035
.0017
.0008
.0004
.0002
9E-05
48-05

OOOOOOOOOOOOO

consistency coefficient

wane-tn NUU'U‘QU \DQWO‘H

NO‘UW‘OHDO‘U‘Q‘H \INUIH

Log Om

-0

—0.
-0.

—0

OOOHHHOOO

-0

—O.
-0.
-0.

.9801
679
378
.077
.22407
.5251
.82613
.12716
.42819
.12716
.82613
.5251
.22407
.077
378
679
9801

average shear rate
4.47 angular velocity
K shear rate ‘(n=1)

2 M / pi b d“2

0.9831

KG“(n-1)
average average
viscosi shear
Pa.s rate
0.744 0.46801
0.7981 0.93602
0.8562 1.87204
0.9186 3.74407
0.9855 7.48814
1.0572 14.9763
1.1342 29.9526
1.2168 59.9052
1.3054 119.81

0.98993

9

Coeffici Standar
-0.4368
1.1338

1

average

shears
stress

0
1
2

5.
11.

23
47
95
88

0.1164
0.0432

.2707
.0334
.4852
5362
688
.744
.956
.838
.7

4.5
0.1
0.6
1.3
2.9
5.9
12.1 1
24.4 2
48.7 4
95.5 9
48.5 4
24.3 2
12.1 1
5.9
3
1.4
0.6
0.2
Log M
-4.707
-4.125
-3.744
-3.396
-3.071
-2.764
—2.458
-2.158
-1.863
-2.159
-2.459
-2.762
-3.071
-3.381
-3.695
-4.049
-4.426
b
d
Lnshear
stress
-1.3069
0.03288
0.91033
1.71131
2.45853
3.16734
3.87028
4.56266
5.24015

5%, 90.23 9 corn syrup,

53

1

Ln
1/3
average
shear
stress
-1.7551
-0.4153
0.46216
.26314
.01035
.71916

.11449
.79198

g CaCO3 Sample in storing
Average
2 0.1 0.1375
.5 0.5 0.525
3 1.2 1.2625
8 2.9 2.8125
9 6 5.9375
12.1 12.0625
.3 24.4 24.3625
.7 48.7 48.6875
.5 95.5 95.8625
.6 48.5 48.5375
.3 24.3 24.3
.2 12.1 12.1125
.9 6 5.9375
.9 2.9 2.9125
.5 1.4 1.4125
.6 0.7 0.625
2 0.3 0.2625
= 0.02692 m
= 0.04143 m
Sigma/
Gamma 1/3
average average
Lnshear viscosi shear
rate Pa.s stress
-0.759 0.578 0.1729
-0.066 1.104 0.66015
0.627 1.328 1.5875
1.3202 1.479 3.5365
2.0133 1.561 7.46594
2.7065 1.585 15.1677
3.3996 1.601 30.6339
4.0928 1.6 61.2207
4.7859 1.575 120.54
x

0.0056
5E-09

-0.71
1.032 1

-O

t Statis P-value Lower 95% Upper 95%
—3.7527
26.2387

.1616
.23598

1
2
2
3.42211
4
4
Y

7.

54

Mixer Viscometry, 15%, 60.72 9 corn syrup, 9.11 g CaCO3
rpm readings Average
1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
2 1.6 1.6 1.5 1.5 1.6 1.5 1.6 1.6 1.5625
4 2.8 2.9 2.9 2.8 2.8 2.8 2.8 2.8 2.825
8 5.3 5.3 5.2 5.3 5.3 5.2 5.3 5.2 5.2625
16 10.2 10.2 10.3 10.2 10.2 10.1 10.2 10.2 10.2
32 20.3 20.2 20.1 20.1 20.1 20.1 20.2 20.1 20.15
64 39.6 39.5 39.7 39 5 39.5 39.6 39.9 39.5 39.6
128 77 77 77 77.3 77.1 77 77 77 77.05
64 39.6 39.7 39.6 39.6 39.5 39.5 39.8 39.8 39.6375
32 20.2 20.2 20.2 20.2 20.2 20.2 20.2 20.2 20.2
16 10.3 10.3 10.3 10.5 10.4 10.3 10.3 10.3 10.3375
8 5.4 5.4 5.4 5.3 5.3 5.4 5.4 5.4 5.375
4 2.9 2.9 3 2.9 3 3 2.9 2.9 2.9375
2 1 7 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.625
1 1 1 1 1 1 1 1 1 1
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.01286 0.0001 -0.9801 -3.891
2 0.2094 0.02232 0.0002 —0.679 -3.651
4 0.4188 0.04036 0.0004 -0.378 -3.394
8 0.8376 0.07519 0.0008 -0.077 —3.124
16 1.6752 0.14573 0.0015 0.22407 -2.836
32 3.3504 0.28789 0.0029 0.5251 -2.541
64 6.7008 0.56577 0.0057 0.82613 -2.247
128 13.402 1.10083 0.011 1.12716 -1.958
256 26.803 0.56631 0.0057 1.42819 -2.247
128 13.402 0.2886 0.0029 1.12716 -2.54
64 6.7008 0.14769 0.0015 0.82613 -2.831
32 3.3504 0.07679 0.0008 0.5251 -3.115
16 1.6752 0.04197 0.0004 0.22407 ~3.377
8 0.8376 0.02322 0.0002 -0.077 ~3.634
4 0.4188 0.01429 0.0001 —0.378 -3.845
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n—1) d = 0.04143 m
k'=4.47
K: consistency coefficient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/
KG“(n-1) Gamma 1/3
angular average average average average average
veloc1t viscosi shear shear Lnshear Lnshear viscosi shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 2.0248 0.46801 1.7716 0.57188 -0.759 3.785 1.13168
2 0.2094 1.7434 0.93602 3.0757 1.12353 -0.066 3.286 1.96472
4 0.4188 1.5011 1.87204 5.5608 1.71575 0.627 2.97 3.55222
8 0.8376 1.2925 3.74407 10.359 2.33785 1.3202 2.767 6.61718
16 1.6752 1.1128 7.48814 20.078 2.99963 2.0133 2.681 12.8257
32 3.3504 0.9581 14.9763 39.664 3.68044 2.7065 2.648 25.337
64 6.7008 0.825 29.9526 77.95 4.35607 3.3996 2.602 49.7939
128 13.402 0.7103 59.9052 151.67 5.02169 4.0928 2.532 96.8843
256 26.803 0.6116 119.81 78.024 4.35702 4.7859 0.651 49.8411
x
Regression Statistics
R Square 0.94913
Observations 9

Coeffici Standar t Statis P—value Lower 95% Upper 95%
K =2.314S Interce 0.8392 0.1896 4.4253 0.0022 0.391 1.28762
x1 0.8045 0.0704 11.428 38-06 0.638 0.97097

Ln

1/3
average
shear
stress
.1237
.67535
.26757
.88967
.55145
.2322?
.90789
.57352
.90884

K UfiUWNl-‘HOO

55

Ln

1/3
average
shear
stress
.22906
.69907
.23153
.82339
.45233
.10826
.77796
.45114
.77796

KibssunuhiHrac>o

Mixer Viscometry, 15%, 15%, 61.4 9 corn syrup THIS IS THE FIRST WITH THE SAMPLE
9.19 g CaCO3
rpm readings Average
1 1 1 1 1 1 1 1 1 1
2 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
4 2.7 2.7 2.8 2.7 2.7 2.8 2.7 2.7 2.725
8 4.9 4.9 4.9 5 4.9 5 4.9 4.9 4.925
16 9.3 9.2 9.2 9.2 9.3 9.2 9.3 9.2 9.2375
32 17.9 17.8 17.8 17.8 17.7 17.8 17.8 17.8 17.8
64 34.8 34.7 34.7 34.8 34.8 34.8 34.8 34.8 34.775
128 68.2 68.2 68.3 68.1 68.2 68.1 68.2 68.1 68.175
64 34.8 34.8 34.7 34.8 34.7 34.8 34.8 34.8 34.775
32 17.7 17.6 17.7 17.6 17.7 17.6 17.7 17.7 17.6625
16 9 8.9 8.9 8.9 9 8.9 9 8.9 8.9375
8 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6
4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
1 0.7 0.7 0.7 0.8 0.7 0.8 0.7 0.8 0.7375
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.01429 0.0001 -0.9801 -3.845
2 0.2094 0.02286 0.0002 -0.679 -3.641
4 0.4188 0.03893 0.0004 -0.378 -3.41
8 0.8376 0.07036 0.0007 ~0.077 -3.153
16 1.6752 0.13198 0.0013 0.22407 -2.879
32 3.3504 0.25431 0.0025 0.5251 -2.595
64 6.7008 0.49684 0.005 0.82613 -2.304
128 13.402 0.97403 0.0097 1.12716 -2.011
64 6.7008 0.49684 0.005 0.82613 -2.304
32 3.3504 0.25235 0.0025 0.5251 -2.598
16 1.6752 0.12769 0.0013 0.22407 -2.894
8 0.8376 0.06572 0.0007 -0.077 -3.182
4 0.4188 0.03429 0.0003 -0.378 -3.465
2 0.2094 0.01857 0.0002 -0.679 -3.731
1 0.1047 0.01054 0.0001 -0.9801 -3.977
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47
K = consistency coefficient
average shear stress = 2 M / pi b d‘2
(b/d + 1/3) 0.9831
Sigma/
KG“(n-1) Gamma 1/3
angular average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 0.3775 0.46801 1.9684 0.67724 -0.759 4.206 1.25742
2 0.2094 0.3534 0.93602 3.1495 1.14724 -0.066 3.365 2.01187
4 0.4188 0.3309 1.87204 5.364 1.67971 0.627 2.865 3.42647
8 0.8376 0.3098 3.74407 9.6945 2.27156 1.3202 2.589 6.1928
16 1.6752 0.29 7.48814 18.183 2.90051 2.0133 2.428 11.6154
32 3.3504 0.2715 14.9763 35.038 3.55644 2.7065 2.34 22.3821
64 6.7008 0.2542 29.9526 68.452 4.22614 3.3996 2.285 43.7268
128 13.402 0.238 59.9052 134.2 4.89932 4.0928 2.24 85.7247
256 26.803 0.2228 119.81 68.452 4.22614 4.7859 0.571 43.7268
x
Regression Statistics
R Square 0.94793
Observations 9
Coeffici Standar t Statis P—value Lower 95% Upper 95%
K =2.3482 Interce 0.85365 0.1826 4.67438 0.0016 0.422 1.28549
x1 0.76534 0.0678 11.2891 38—06 0.605 0.92565

9.

Mixer Viscometry,

rpm
1 0.8
2 1.4
4 2.5
8 4.8
16 9.4
32 18.5
64 36.8
128 76
64 39.2
32 20
16 10.2
8 5.3
4 2.9
2 1.6
1 0.9
rad/s
rpm omega
1 0.1047
2 0.2094
4 0.4188
8 0.8376
16 1.6752
32 3.3504
64 6.7008
128 13.402
64 6.7008
32 3.3504
16 1.6752
8 0.8376
4 0.4188
2 0.2094
1 0.1047

15%.
readings
0.8 0
1.4 1
2.6 2
4.9 4.
9.3 9.

18.7 18
36.8 37
76 76
39.2 39
20 20
10.3 10
5.3 5
2.9 2
1.6 1
1 1
(N cm)
M
0.01143
0.02
0.03625
0.06911
0.13448
0.26592
0.52755
1.08654
0.56006
0.28574
0.14626
0.07572
0.04072
0.02286
0.01375

O’t‘OUN NH O‘DOU‘I‘Q

15.1%.

\DbNi—‘O

NUQUH
OVOO‘O‘Q
01me N «amateur-ha:

H
HHNU‘C

(N m)
M
.0001
.0002
.0004
.0007
.0013
.0027
.0053
.0109
.0056
.0029
.0015
.0008
.0004
.0002
.0001

OOOOOOOOOOOOOOO

56

61.17 g corn syrup.

HNUJQWH
OHMU‘OO‘DO‘QQH’DNHO
\DO‘CDUN NHWGMQG‘Q

Log Om

-0

-0.
.378
-0.
.22407
.5251
.82613
.12716
.82613
.5251
.22407
.077

-0

OOOHOOO

-0

-0.
-0.
-0.

.9801

679
077

378
679
9801

Determination of average shear rate

average shear rate
K

viscosity
k'=4.47

K
average shear

(b/d + 1/3)
angular
velocit

rpm rad/s

1 0.1047
2 0.2094
4 0.4188
8 0.8376
16 1.6752
32 3.3504
64 6.7008

128 13.402

256 26.803

Regression St

R Square

Observations

K =2.0665 Interce

x1

4.

47

shear rate“(n-1)

consistency coeffiicient

stress = 2 M / pi b d“2
0.9831
KG‘(n-1)
average average average
viscosi shear shear
Pa.s rate stress
2.33525 0.468 1.57475
2.21219 0.936 2.75581
2.09562 1.872 4.99491
1.98519 3.7441 9.52231
1.88058 7.4881 18.5279
1.78148 14.976 36.6375
1.68761 29.953 72.6845
1.59868 59.905 149.7
1.51443 119.81 77.1627
atistics
0.95233
9

Coeffici Standar
0.72586
0.82366

0.1876
0.0696

3.86882

Log
-3.
—3.
-3
-3.

-2
-2
-1.
-2
-2.
-2
-3.
-3.
-3
-3.

angular velocity

Lnshear

ra

I I
XbbUNNHOOO

11.8259

Hmouw NHmmhmOhm

M
942
699

.441

.871
.575
.278

964

.252

544

.835

121

.641

862

te
.759
.066
.627
.3202
.0133
.7065
.3996
.0928
.7859

0.0047
2E—06

HNUJQUH
OHMU‘IOOWO‘QQVDth-‘O

9.23 g CaCO3

Average

8 0.8 0.8

4 1.4 1.4

5 2.5 2.5375

9 4.8 4.8375

5 9.4 9.4125

.7 18.6 18.6125

.1 37.1 36.925

76.1 76.05
.2 39.2 39.2
20 20

2 10.2 10.2375

.3 5.3 5.3

8 2.8 2.85

.6 1.6 1.6

.9 1 0.9625
= 0.02692 m

= 0.04143 m
Sigma/ Ln
Gamma 1/3 1/3
average average average
viscosi shear shear
Pa.s stress stress
3.365 1.00594 0.00592
2.944 1.76039 0.56554
2.668 3.19071 1.16024
2.543 6.08278 1.80546
2.474 11.8355 2.4711
2.446 23.4038 3.1529
2.427 46.4303 3.83795
2.499 95.6269 4.56045
0.644 49.2909 3.89774
Y

0.282
0.659

t Statis P—value Lower 95% Upper 95%

1.16951
0.98835

 

57
10.- Mixer Viscometry, 25%, 25%, 65.91 9 corn syrup, 16.47 g CaCO3
rpm readings Average
1 1.5 1.4 1.4 1.5 1.5 1.5 1.4 1.5 1.4625
2 2.9 2.8 2.8 2.9 2.8 2.9 2.8 2.8 2.8375
4 5.5 5.4 5.5 5.5 5.4 5.4 5.4 5.5 5.45
8 10.5 10.5 10.5 10.6 10.5 10.5 10.5 10.5 10.5125
16 20.7 20.7 20.7 20.6 20.7 20.6 20.7 20.7 20.675
32 40 39.9 40 40 40 40 39.9 40 39.975
64 76.2 76.1 76 75.9 76 76 75.9 75.9 76
32 39.7 39.7 39.7 39.7 39.7 39.7 39.6 39.7 39.6875
16 20.7 20.6 20.7 20.6 20.7 20.7 20.6 20.7 20.6625
8 10.8 10.9 10.9 10.8 10.9 10.9 10.8 10.9 10.8625
4 5.8 5.8 5.8 5.8 5.8 5.8 5.9 5.8 5.8125
2 3.2 3.1 3.2 3.1 3.2 3.1 3.2 3.2 3.1625
1 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.02089 0.0002 -0.9801 -3.68
2 0.2094 0.04054 0.0004 -0.679 -3.392
4 0.4188 0.07787 0.0008 -0.378 -3.109
8 0.8376 0.15019 0.0015 -0.077 —2.823
16 1.6752 0.29539 0.003 0.22407 -2.53
32 3.3504 0.57113 0.0057 0.5251 -2.243
64 6.7008 1.08582 0.0109 0.82613 -1.964
32 3.3504 0.56702 0.0057 0.5251 -2.246
16 1.6752 0.29521 0.003 0.22407 -2.53
8 0.8376 0.15519 0.0016 -0.077 -2.809
4 0.4188 0.08304 0.0008 -0.378 -3.081
2 0.2094 0.04518 0.0005 -0.679 -3.345
1 0.1047 0.02572 0.0003 —0.9801 -3.59
Determination of average shear rate
average shear rate = 4.47 angular velocity
viscosity = K shear rate“(n-1) b = 0.02692 m
k’=4.47 d = 0.04143 m
K = consistency coeffiicient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG*(n—1) Gamma 1/3 1/3
angular average average average averae average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 4.6545 0.46801 2.8788 1.05739 -0.759 6.151 1.83898 0.60921
2 0.2094 4.4252 0.93602 5.5854 1.72016 -0.066 5.967 3.56793 1.27199
4 0.4188 4.2071 1.87204 10.728 2.37286 0.627 5.731 6.85295 1.92468
8 0.8376 3.9998 3.74407 20.693 3.0298 1.3202 5.527 13.2186 2.58163
16 1.6752 3.8027 7.48814 40.697 3.70616 2.0133 5.435 25.9972 3.25799
32 3.3504 3.6154 14.9763 78.688 4.36549 2.7065 5.254 50.2654 3.91732
64 6.7008 3.4372 29.9526 149.6 5.00797 3.3996 4.995 95.5641 4.5598
X Y
Regression Statistics
R Square 0.99997
Observations 7

Coeffici Standar t Statit P-value Lower 95% Upper 95%
K =3.7893 Interce 1.33219 0.0041 321.076 68-14 1.322 1.34286
x1 0.95196 0.0022 439.214 98—15 0.946 0.95753

 

58
DUPLICATE AT THIS CONDITIONS TO CHECK SAMPLE RECOVERY, THIS WAS DONE AT 25 % WEIGHT, AFTER 15
MINUTES
10:53 am 11:3 am 12 min
rpm readings Average
1 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.1 3.1875
4 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8
8 10.9 10.8 10.9 10.8 10.9 10.8 10.8 10.8 10.8375
16 20.7 20.6 20.7 20.6 20.6 20.7 20.6 20.6 20.6375
32 39.9 40 40 40 40 40 49.9 40.1 41.2375
64 76.5 76.5 76.4 76.3 76.3 76.2 76.3 76.2 76.3375
32 39.5 39.6 39.6 39.5 39.6 39.5 39.6 39.6 39.5625
16 20.5 20.6 20.5 20.6 20.6 20.6 20.6 20.5 20.5625
8 10.7 10.8 10.8 10.8 10.7 10.8 10.7 10.8 10.7625
4 5.7 5.7 5.8 5.7 5.8 5.7 5.8 5.7 5.7375
2 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1
1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.02572 0.0003 -0.9801 -3.59
2 0.2094 0.04554 0.0005 -0.679 -3.342
4 0.4188 0.08287 0.0008 -0.378 —3.082
8 0.8376 0.15484 0.0015 -0.077 -2.81
16 1.6752 0.29485 0.0029 0.22407 -2.53
32 3.3504 0.58917 0.0059 0.5251 -2.23
64 6.7008 1.09065 0.0109 0.82613 -1.962
32 3.3504 0.56524 0.0057 0.5251 -2.248
16 1.6752 0.29378 0.0029 0.22407 -2.532
8 0.8376 0.15377 0.0015 -0.077 -2.813
4 0.4188 0.08197 0.0008 -0.378 —3.086
2 0.2094 0.04429 0.0004 -0.679 —3.354
1 0.1047 0.02429 0.0002 -0.9801 —3.615
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47
K = consistency coeffiicient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG‘(n-1) Gamma 1/3 1/3
angular average average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 4.9393 0.46801 3.5432 1.26503 -0.759 7.571 2.26336 0.81685
2 0.2094 4.6403 0.93602 6.2744 1.83648 -0.066 6.703 4.00803 1.3883
4 0.4188 4.3593 1.87204 11.417 2.4351 0.627 6.099 7.29305 1.98692
8 0.8376 4.0954 3.74407 21.333 3.06025 1.3202 5.698 13.6273 2.61208
16 1.6752 3.8475 7.48814 40.624 3.70435 2.0133 5.425 25.95 3.25617
32 3.3504 3.6145 14.9763 81.173 4.39659 2.7065 5.42 51.8529 3.94841
64 6.7008 3.3957 29.9526 150.27 5.0124 3.3996 5.017 95.9884 4.56423
x y
Regression Statistics
R Square 0.99925
Observations 7
Coeffici Standar t Statis P—value Lower 95% Upper 95%
K = 4.28 Interce 1.45395 0.0213 68.292 78-10 1.399 1.50868
x1 0.90847 0.0111 81.6859 28-10 0.88 0.93705

59

AFTER 35 MINUTES CHECK THESE TWO LINE
rpm readings Average
1 1.8 1.8 1.8 1.8 1.8 1.7 1.8 1.8 1.7875
2 3.2 3.2 3.2 3.1 3.2 3.2 3.1 3.1 3.1625
4 5.8 5.8 5.8 5.8 5.7 5.7 5.8 5.8 5.775
8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8 10.8
16 20.6 20.7 20.7 20.6 20.7 20.7 20.7 20.7 20.675
32 39.9 40 39.9 40 40 40.1 40.1 40 40
64 76 75.9 75.9 76 75.9 75.9 76 75.9 75.9375
32 39.7 39.6 39.6 39.6 39.5 39.6 39.6 39.6 39.6
16 20.5 20.6 20.5 20.5 20.6 20.6 20.5 20.6 20.55
8 10.8 10.7 10.7 10.8 10.7 10.8 10.8 10.7 10.75
4 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7
2 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1
1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.02554 0.0003 -0.9801 -3.593
2 0.2094 0.04518 0.0005 -0.679 -3.345
4 0.4188 0.08251 0.0008 -0.378 -3.084
8 0.8376 0.1543 0.0015 -0.077 -2.812
16 1.6752 0.29539 0.003 0.22407 -2.53
32 3.3504 0.57149 0.0057 0.5251 —2.243
64 6.7008 1.08493 0.0108 0.82613 -1.965
32 3.3504 0.56577 0.0057 0.5251 -2.247
16 1.6752 0.2936 0.0029 0.22407 —2.532
8 0.8376 0.15359 0.0015 -0.077 -2.814
4 0.4188 0.08144 0.0008 ~0.378 -3.089
2 0.2094 0.04429 0.0004 -0.679 -3.354
1 0.1047 0.02429 0.0002 -0.9801 -3.615
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47
K = consistency coeffiicient
average shear stress = 2 M / pi b d‘2
(b/d + 1/3) 0.9831
Sigma/
KG‘(n-1) Gamma 1/3
angular average average average average average
velocit viscos. shear shear Lnshear Lnshear viscosi shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 4.9271 0.46801 3.5186 1.25806 -0.759 7.518 2.24764
2 0.2094 4.6247 0.93602 6.2252 1.8286 —0.066 6.651 3.9766
4 0.4188 4.3408 1.87204 11.368 2.43078 0.627 6.072 7.26161
8 0.8376 4.0743 3.74407 21.259 3.05679 1.3202 5.678 13.5802
16 1.6752 3.8242 7.48814 40.697 3.70616 2.0133 5.435 25.9972
32 3.3504 3.5894 14.9763 78.737 4.36612 2.7065 5.257 50.2969
64 6.7008 3.3691 29.9526 149.48 5.00715 3.3996 4.99 95.4855
x
Regression Statistics
R Square 0.99942
Observations 7

Coeffici Standar
1.44818 0.0186
0.90672 0.0097

t Statis P-value Lower 95% Upper 95%
77.7103 38-10 1.4 1.49608
93.1423 18-10 0.882 0.93174

K =4.2554 Interce
x1

Ln

1/3
average
shear
stress
.80988
.38043
.9826
.60861
.25799
.91794
.55897

wawNHHo

60

11.- Mixer Viscometry. 25%, 25%, 74.08 9 corn syrup, 18.54 g CaCO3
rpm readings Average
1 1.9 .9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
2 3.3 3.3 3.3 3.2 3.2 3.2 3.2 3.3 3.25
4 5.8 5.8 5.9 5.9 5.8 5.8 5.8 5.8 5.825
8 10.7 10.7 10.8 10.7 10.7 10.8 10.6 10.7 10.7125
16 20.2 20.3 20.2 20.4 20.3 20.3 20.3 20.3 20 2875
32 38.7 38.7 38.8 38.9 38.8 38.8 38.8 38.8 38 7875
64 73.7 73.7 73.6 73.5 73.4 73.3 73.3 73.2 73 4625
32 38.3 38.2 38.2 38.1 38.2 38.2 38.1 38.1 38.175
16 19.9 20 19.8 19.9 19.9 19.9 19.9 19.9 19.9
8 10.6 10.5 10.6 10.6 10.5 10.6 10.6 10.5 10.5625
4 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7
2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.2
1 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.02715 0.0003 -0.9801 -3.566
2 0.2094 0.04643 0.0005 -0.679 -3.333
4 0.4188 0.08322 0.0008 -0.378 -3.08
8 0.8376 0.15305 0.0015 -0.077 -2.815
16 1.6752 0.28985 0.0029 0.22407 —2.538
32 3.3504 0.55416 0.0055 0.5251 -2.256
64 6.7008 1.04957 0.0105 0.82613 -1.979
32 3.3504 0.54541 0.0055 0.5251 -2.263
16 1.6752 0.28431 0.0028 0.22407 -2.546
8 0.8376 0.15091 0.0015 -0.077 -2.821
4 0.4188 0.08144 0.0008 -0.378 -3.089
2 0.2094 0.04572 0.0005 -0.679 -3.34
1 0.1047 0.02715 0.0003 -0.9801 -3.566
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47
K = consistency coeffiicient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/
KG‘tn-l) Gamma 1/3
angular average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 5.229 0.46801 3.74 1.31909 -0.7593 7.9914 2.389
2 0.2094 4.8122 0.93602 6.3974 1.85589 -0.0661 6.8347 4.087
4 0.4188 4.4286 1.87204 11.466 2.4394 0.62703 6.125 7.324
8 0.8376 4.0756 3.74407 21.087 3.04865 1.32017 5.6321 13.47
16 1.6752 3.7507 7.48814 39.935 3.68724 2.01332 5.3331 25.51
32 3.3504 3.4518 14.9763 76.351 4.33534 2.70647 5.0981 48.77
64 6.7008 3.1766 29.9526 144.61 4.97401 3.39962 4.8278 92.37
x
Regression Statistics
R Square 0.99902
Observations 7

K =4.3843 Interce

x1

Coeffici Standar t Statis P-value Lower 95% Upper 95%
1.53906
0.91664

1.47802
0.88476

0.0237
0.0124

62.
71.

2507
3354

1E-09
5E-10 0.853

1.417

Ln

1/3
average
shear
stress
0.87092
1.40772
.99122
.60047
.23907
.88716
.52584

K hJJCALJH

12.- Mixer Viscometry,

rpm

HUGUH
HMUI‘OQ‘QU‘QWWWH
wamD-‘QU‘hUIOUID-‘D

rad/s

omega

.1047
.2094
.4188
.8376
.6752
.3504
.7008
.3504
.6752
.8376
.4188
.2094
.1047

0000l—‘UO‘UH0000

25%,
readings
1.9
3.1 3
5.4 5
9.9 9

18.5 18
35.4 35
67.4 67
34.8 34
18.1 18
9.6 9
5.2 5
3 2
1.7 1
(N cm)
M
0.02679
0.04429
0.07787
0.14073
0.26431
0.50523
0.96153
0.49701
0.25878
0.13716
0.07447
0.04161
0.02429

1.

4053014090900me

61

25 %, 65.09 9 corn syrup,

(N m)
M
.0003
.0004
.0008
.0014
.0026
.0051
.0096
.005
.0026
.0014
.0007
.0004
.0002

0000000000000

\JVDUJMHQUDUJGUIHCD

\JKONUINQUhUI‘OUID-‘m

Log Om
-0.9801
-0.679
-0.378
-0.077
0.22407
0.5251
0.82613
0.5251
0.22407
-0.077
-0.378
-0.679
-0.9801

Determination of average shear rate

average shear rate
viscosity

k'=4.47

K

average shear stress
(b/d

16
32
64

+ 1/3)

angular
velocit
rad/s
.1047
.2094
.4188
.8376
.6752
.3504
.7008

Otto-1140000

K

shear rate‘(n-1)

Regression Statistics
R Square
Observations

K =4.1873 Interce

x1

consistency coeffiicient

2 M / pi b d‘2

0.9831
KG‘(n-1)
average average average
viscosi shear shear
Pa.s rate stress
4.8927 0.46801 3.6908
4.4782 0.93602 6.1022
4.0988 1.87204 10.728
3.7516 3.74407 19.389
3.4337 7.48814 36.416
3.1428 14.9763 69.609
2.8766 29.9526 132.48
0.99821
7

QWNQHQNDmmbl—‘W

Log M
-3.572
—3.354
-3.109
—2.852
-2.578
-2.297
—2.017
—2.304
-2.587
-2.863
-3.128
—3.381
-3.615

4.47 angular velocity

Lnshear
stress
1.30585
1.80864
2.37286
2.96471
3.59501
4.24289
4.8864
x

HUGO-1H
Hummmqummmwp

16.27 g CaCO3

Ave
.9 1.9 1.8
.1 3.1 3.1
4 5.4 5.4
8 9.8 9.8
5 18.5 18
.3 35.3 35
.2 67.1 67
.7 34.8 34
.1 18.1 18.
.6 9.6 9.
.2 5.2 5
.9 2.9 2
.7 1.7 1
= 0.02692 m
= 0.04143 m
Sigma/
Gamma
average
Lnshear viscosi
rate Pa.s
—0.759 7.886
-0.066 6.519
0.627 5.731
1.3202 5.179
2.0133 4.863
2.7065 4.648
3.3996 4.423

rage
75

5
5

.5
.3625
.3
.7875

1125
6

.2125
.9125
.7

1/3
average
shear
stress
.35767
.89801
.85295
.3856
.2623
.4656
.6245

Coeffici Standar t Statis P-value Lower 95% Upper 95%

1.43206
0.86728

0.0314
0.0164

45.
52.

5906
8559

7E—09
3E-09

1.351
0.825

1.
0.

5128
90946

Ln

1/3
average
shear
stress
.85767
.36047
.92468
.51653
.14683
.79472
.43822

anwwwwo

62

13.- Mixer Viscometry, 35%, 35%, 76.16 9 corn syrup, 26.67 g CaCO3

rpm readings Average
1 3.9 4 4 4 4.1 4 4 4.1 4.0125
2 7 7 7.1 7 7 7 7.1 7.1 7.0375
4 12.4 12.4 12.3 12.4 12.5 12.3 12.5 12.5 12.4125
8 22.5 22.3 22.3 22.4 22.3 22.5 22.4 22.4 22.3875
16 41.1 41.3 41.1 41 41 41 41.1 41.2 41.1
32 75.8 75.8 75.7 75.8 75.7 75.6 75.5 75.7 75.7
16 41.4 41.6 41.6 41.6 41.6 41.4 41.4 41.6 41.525
8 23.1 23.3 23 23.3 23.1 23.1 23.1 23 23.125
4 13.2 13.1 13.3 13.3 13.2 13.1 13.1 13.3 13.2
2 7.8 7.7 7.8 7.8 7.7 7.8 7.7 7.7 7.75
1 4.8 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7125
rad/s (N cm) (N m)
rpm omega M M Log 0m Log M
1 0.1047 0.05733 0.0006 -0.9801 -3.242
2 0.2094 0.10055 0.001 -0.679 -2.998
4 0.4188 0.17734 0.0018 -0.378 —2.751
8 0.8376 0.31985 0.0032 -0.077 -2.495
16 1.6752 0.5872 0.0059 0.22407 -2.231
32 3.3504 1.08154 0.0108 0.5251 -1.966
16 1.6752 0.59327 0.0059 0.22407 -2.227
8 0.8376 0.33039 0.0033 -0.077 -2.481
4 0.4188 0.18859 0.0019 -0.378 -2.724
2 0.2094 0.11073 0.0011 -0.679 -2.956
1 0.1047 0.06733 0.0007 -0.9801 -3.172
Determination of average shear rate
average shear rate = 4.47 angular velocity
viscosity = K shear rate“(n-1) b = 0.02692 m
k'=4.47 d = 0.04143 m
K = consistency coeffiicient
average shear stress = 2 M / pi b d‘2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG‘(n-1) Gamma 1/3 1/3
angular average average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 12.389 0.46801 7.8984 2.06665 —0.759 16.88 5.0454 1.61848
2 0.2094 10.944 0.93602 13.853 2.62849 -0.066 14.8 8.84911 2.18032
4 0.4188 9.6672 1.87204 24.433 3.19594 0.627 13.05 15.6077 2.74777
8 0.8376 8.5395 3.74407 44.068 3.78574 1.3202 11.77 28.1505 3.33757
16 1.6752 7.5434 7.48814 80.903 4.39325 2.0133 10.8 51.68 3.94507
32 3.3504 6.6635 14.9763 149.01 5.00402 2.7065 9.95 95.1868 4.55584
Regression Statistics
R Square 0.99967
Observations 6

K =9.3805 Interce

x1

Coeffici Standar
2.23863
0.84793

0.0118
0.0077

189.857
110.221

8E—11
1E—09

2.206
0.827

t Statis P—value Lower 95% Upper 95%

2.27137
0.86929

63

14.- Mixer Viscometry, 35%, 35%, 71.35 9 corn syrup, 24.98 g CaCO3
rpm readings Average
1 4.8 5 4.9 4.9 5 4.9 4.9 5 4.925
2 8.4 8.3 8.4 8.3 8.3 8.4 8.4 8.5 8.375
4 14.5 14.7 14.5 14.6 14.5 14.5 14.7 14.5 14.5625
8 25.5 25.8 26 25.6 25.9 26.2 25.9 26.1 25.875
16 46.9 47.2 47 48.9 46.7 47.4 46.8 47.2 47.2625
32 85.5 85.4 85.2 85.4 85.5 85.3 85.4 85.5 85.4
16 47.4 47.4 47.5 47.5 47.3 47.5 47.6 47.4 47.45
8 26.5 26.6 26.6 26.7 26.6 26.6 26.7 26.7 26.625
4 15.5 15.4 15.3 15.2 15.4 15.4 15.3 15.2 15.3375
2 9.1 9 9 9.1 9.1 9.1 9.1 9.1 9.075
1 5.6 5.6 5.6 5.6 5.6 5.6 5.6 5.5 5.5875
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.07036 0.0007 -0.9801 -3.153
2 0.2094 0.11966 0.0012 -0.679 -2.922
4 0.4188 0.20806 0.0021 -0.378 -2.682
8 0.8376 0.36968 0.0037 -0.077 -2.432
16 1.6752 0.67525 0.0068 0.22407 —2.171
32 3.3504 1.22012 0.0122 0.5251 -1.914
16 1.6752 0.67793 0.0068 0.22407 -2.169
8 0.8376 0.3804 0.0038 —0.077 -2.42
4 0.4188 0.21913 0.0022 -0.378 —2.659
2 0.2094 0.12966 0.0013 -0.679 -2.887
1 0.1047 0.07983 0.0008 -0.9801 -3.098
Determination of average shear rate
average shear rate = 4.47 angular velocity
viscosity = K shear rate“(n-1) b = 0.02692 m
k'=4.47 d = 0.04143 m
K = consistency coeffiicient
average shear stress = 2 M / pi b d‘2
(b/d + 1/3) 0.9831
Sigma/
KG“(n—1) Gamma 1/3
angular average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress
1 0.1047 14.87 0.46801 9.6945 2.27156 -0.7593 20.714 6.193
2 0.2094 12.973 0.93602 16.486 2.80249 ~0.0661 17.613 10.53
4 0.4188 11.318 1.87204 28.665 3.35569 0.62017 15.312 18.31
8 0.8376 9.874 3.74407 50.933 3.93052 1.32017 13.604 32.54
16 1.6752 8.6142 7.48814 93.033 4.53296 2.01332 12.424 59.43
x

Regression Statistics
R Square 0.99939
Observations 5

t Statis P-value Lower 95% Upper 95%
179.206 68-09 2.376 2.46225
70.2701 28—07 0.778 0.85216

Coeffici Standar
K =11.238 Interce 2.41929 0.0135
x1 0.81524 0.0116

Ln

1/3
average
shear
stress
.82339
.35431
.90751
.48234
.08478

<puuup

64

15.- Mixer Viscometry, 35%, 35%, 71.31 9 corn syrup, 24.95 g CaCO3

rpm readings Average
1 4.6 4.6 4.6 4.7 4.7 4.7 4.7 4.7 4.6625
2 8 8.1 8.1 8.1 8.1 8.2 8.1 8.1 8.1
4 14 14.1 14.1 14.1 14.1 14.2 14.1 14.1 14.1
8 24.8 25.1 25 25 25 25.2 24.9 25 25
16 45.3 45.2 45.5 45.2 45.4 45.3 45.3 45.4 45.325
32 82.4 82.3 82.3 82.3 82.4 82.2 82.3 82.3 82.3125
16 45.5 45.5 45.4 45.6 45.6 45.5 45.6 45.6 45.5375
8 25.5 25.5 25.5 25.5 25.6 25.6 25.5 25.6 25.5375
4 14.7 14.7 14.6 14.7 14.7 14.7 14.6 14.7 14.675
2 8.7 8.7 8.6 8.7 8.6 8.7 8.7 8.8 8.6875
1 5.3 5.3 5.3 5.3 5.3 5.3 5.4 5.4 5.325

rad/s (N cm) (N m)
rpm omega M M Log Om Log M

1 0.1047 0.06661 0.0007 -0.9801 -3.176
2 0.2094 0.11573 0.0012 -0.679 -2.937
4 0.4188 0.20145 0.002 -0.378 -2.696
8 0.8376 0.35718 0.0036 -0.077 -2.447
16 1.6752 0.64757 0.0065 0.22407 -2.189
32 3.3504 1.17601 0.0118 0.5251 -1.93
16 1.6752 0.6506 0.0065 0.22407 -2.187
8 0.8376 0.36486 0.0036 -0.077 -2.438
4 0.4188 0.20966 0.0021 -0.378 -2.678
2 0.2094 0.12412 0.0012 -0.679 -2.906
1 0.1047 0.07608 0.0008 -0.9801 -3.119

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
viscosity = K shear rate“(n-1) d = 0.04143 m
k'=4.47

K = consistency coefficient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831

Sigma/ Ln

KG*(n-1) Gamma 1/3 1/3
angular average average average average average average

velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 14.21 0.46801 9.1778 2.21679 -0.7593 19.61 5.863 1.76862
2 0.2094 12.42 0.93602 15.944 2.7691 -0.0661 17.034 10.19 2.32093
4 0.4188 10.856 1.87204 27.755 3.32341 0.62703 14.826 17.73 2.87524
8 0.8376 9.4894 3.74407 49.211 3.89612 1.32017 13.144 31.44 3.44794
16 1.6752 8.2945 7.48814 89.219 4.4911 2.01332 11.915 56.99 4.04292
32 3.3504 7.2501 14.9763 162.03 5.08776 2.70647 10.819 103.5 4.63959
X Y

Regression Statistics
R Square 0.99969
Observations 6

Coeffici Standar t Statis P-value Lower 95% Upper 95%
K =10.763 Interce 2.37615 0.0112 211.35 4E-11 2.345 2.40737
x1 0.82825 0.0073 112.915 1E-09 0.808 0.84862

 

65
DUPLICATE AT THIS CONDITIONS TO CHECK SAMPLE RECOVERY, THIS WAS DONE AT 25% WEIGHT, AFTER 15 MINUTES
10:53 am 11:3 12 min
rpm readings Average
1 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
2 3.2 3.2 3.2 3.2 3.2 3.2 3.2 3.1 3.1875
4 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8
8 10.9 10.8 10.9 10.8 10.9 10.8 10.8 10.8 10.8375
16 20.7 20.6 20.7 20.6 20.6 20.7 20.6 20.6 20.6375
32 39.9 40 40 40 40 40 49.9 40.1 41.2375
64 76.5 76.5 76.4 76.3 76.3 76.2 76.3 76.2 76.3375
32 39.5 39.6 39.6 39.5 39.6 39.5 39.6 39.6 39.5625
16 20.5 20.6 20.5 20.6 20.6 20.6 20.6 20.5 20.5625
8 10.7 10.8 10.8 10.8 10.7 10.8 10.7 10.8 10.7625
4 5.7 5.7 5.8 5.7 5.8 5.7 5.8 5.7 5.7375
2 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.1
1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.02572 0.0003 —0.9801 -3.59
2 0.2094 0.04554 0.0005 —0.679 -3.342
4 0.4188 0.08287 0.0008 -0.378 -3.082
8 0.8376 0.15484 0.0015 -0.077 -2.81
16 1.6752 0.29485 0.0029 0.22407 -2.53
32 3.3504 0.58917 0.0059 0.5251 -2.23
64 6.7008 1.09065 0.0109 0.82613 -1.962
32 3.3504 0.56524 0.0057 0.5251 -2.248
16 1.6752 1.09065 0.0109 0.22407 -1.962
8 0.8376 0.56524 0.0057 -0.077 -2.248
4 0.4188 0.29378 0.0029 -0.378 -2.532
2 0.2094 0.15377 0.0015 -0.679 —2.813
1 0.1047 0.08197 0.0008 -0.9801 -3.086
Determination of average shear rate
average shear rate = 4.47 angular velocity
viscosity = K shear rate‘(n~1) b = 0.02692 m
k'=4.47 d = 0.04143 m
K = consistency coeffiicient
average shear stress = 2 M / pi b d“2
(b/d + 1/3) 0.9831
Sigma/ Ln
KG“(n-1) Gamma 1/3 1/3
angular average average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 10.624 0.46801 3.5432 1.26503 -0.7593 7.5708 2.263 0.81685
2 0.2094 9.0295 0.93602 6.2744 1.83648 -0.0661 6.7033 4.008 1.3883
4 0.4188 7.6743 1.87204 11.417 2.4351 0.62703 6.0987 7.293 1.98692
8 0.8376 6.5226 3.74407 21.333 3.06025 1.32017 5.6978 13.63 2.61208
16 1.6752 5.5437 7.48814 40.624 3.70435 2.01332 5.4251 25.95 3.25617
32 3.3504 4.7117 14.9763 81.173 4.39659 2.70647 5.4201 51.85 3.94841
X Y
Regression Statistics
R Square 0.99892
Observations 6

Coeffici Standar t Statis P-value Lower 95% Upper 95%
K =4.2907 Interce 1.45644 0.0228 63.937 ZE-08 1.393 1.51969
x1 0.90216 0.0149 60.7022 28—08 0.861 0.94343

AFTER 35 MINUTES

rpm
1

2

4

8
16
32
64
32

16
8
4
2
1

H
HNfimm

Determination of
average shear rate =

viscosity = K
k'=4.47
K =
average shear stress
(b/d + 1/3)
angular
velocit
rpm rad/s
1 0.1047
2 0.2094
4 0.4188
8 0.8376
16 1.6752
32 3.3504
64 6.7008

10.
20.
39.

39.
20.
10.

QHQWU'I‘J 0000N0

rad/s
omega

0.

1047

0.2094

0000HUGUH00

.4188
.8376
.6752
.3504
.7008
.3504
.6752
.8376
.4188
.2094
.1047

CHECK
readings
1.8 1.8 1
3.2 3.2 3
5.8 5.8 5
10.8 10.8 10.
20.7 20.7 20.
40 39.9 40
75.9 75.9 76
39.6 39.6 39.
20.6 20.5 20.
10.7 10.7 10.
5.7 5.7 5
3.1 3.1 3
1.7 1.7 1
(N cm) (N m)
M M
0.02554 0.0003
0.04518 0.0005
0.08251 0.0008
0.1543 0.0015
0.29539 0.003
0.57149 0.0057
1.08493 0.0108
0.56577 0.0057
1.08493 0.0108
0.56577 0.0057
0.2936 0.0029
0.15359 0.0015
0.08144 0.0008
average

4.

47

000590

qpqmmm

66

THESE TWO LINE

shear rate‘(n-1)

Regression Statistics
R Square
Observations

K =4.2554 Interce

x1

0.9831
KG“(n-1)
average average average
viscosi shear shear
Pa.s rate stress
10.587 0.46801 3.5186
8.9926 0.93602 6.2252
7.6383 1.87204 11.368
6.4879 3.74407 21.259
5.5107 7.48814 40.697
4.6808 14.9763 78.737
3.9758 29.9526 149.48
0.99942
7

Coeffici Standar
1.44818
0.90672

consistency coeffiicient

10.
20.
40
75.
39.
20.
10.

\IHQQONUIW \JOQNO

Log Om

-0.
-0.
-0.
—0.
.22407
0.
0.
0.
.22407
-0.
-0.
-0.
-0.

0

0

9801
679
378
077

5251
82613
5251

077
378
679
9801

shear rate
angular velocity

2 M / pi b d“2

0.0186
0.0097

10.
20.
40.
75.
39.
20.
10.

\IHQGO‘G‘OH‘JOQN‘J

Log M

-3.
-3.
~3.
-2.
-2.
-2
-1.
-2
-1.
-2
-2
-2.
-3.

593
345
084
812
S3

.243

965

.247

965

.247
.532

814
089

Lnshear

St

uwbtaunupap

77.7103
93.1423

ress

.25806
.8286

.43078
.05679
.70616
.36612
.00715

10.
20.

76

39.
20.
10.

Average
.8 1.8 1.7875
.1 3.1 3.1625
.8 5.8 5.775
8 10.8 10.8
7 20.7 20.675
.1 40 40
75.9 75.9375
6 39.6 39.6
5 20.6 20.55
8 10.7 10.75
.7 5.7 5.7
.1 3.1 3.1
.7 1.7 1.7
= 0.02692 m
= 0.04143 m
Sigma/
Gamma 1/3
average average
Lnshear viscosi shear
rate Pa.s stress
-0.7593 7.5182 2.248
—0.0661 6.6507 3.977
0.62703 6.0724 7.262
1.32017 5.6781 13.58
2.01332 5.4349 26
2.70647 5.2575 50.3
3.39962 4.9905 95.49
x

3E-1O
1E-10 0.882

1.4

t Statis P-value Lower 95% Upper 95%

1.49608
0.93174

Ln

1/3
average
shear
stress
.80988
.38043
.9826
.60861
.25799
.91794
.55897

weuwuwwo

IX. APPENDIX 3. CALCULATIONS AT 25°C TO FIT THE GLOBAL MODEL.

These calculations were done based on the results coming from the appendix 2, and it was used

to fit a model using the values coming from the three different temperatures.

sstress

0.
0.
l.
3.
6.
12.
23.
47.
94.

50297
86448
57178
0964
01991
0241
9382
6091
2123

sstress

0.
0
1.
2.
5.
12.
24.
47.
94.

37723

.7073

46175
93922
97275
0555
001
672
228

sstress

0.
O.
1.
2.
5.
11.
23.
47.
95.

25148
62871
33601
8292
89416
9298
9382
8135
2497

SSCIGSS

0.
1.
2
3
7
15.
30.
59.
98.

5344
00594

.02759
.96088
.70171

2777
241

3503
3147

sstress

0.
1.
2.
3.
7.
15.
31.
59.
100

50297
02166
04331
9766
92176
6549
0426
4289

.295

SStIGBS

.1729
.66015
.5875
.5365
.46594
.1677
.6339
.2207
.54

1n

sstress

—0.
-0.
.45221
.13024
.79507
.48691
.17547
.86302
.54555

fiwWNHf-‘O

In

6872
1456

sstress

-0.
-0.
.37964
.07815
.78721
.48952
.1781

.86434
.54572

fiUWND—‘HO

1n

9749
3463

sstress

-1.
.4641

.28969
.03999
.77396
.47904
.17547
.86731
.5565

—0

buUNHl—‘O

In

3804

SSCICSS

-0.
.00592
.70685
.37647
.04144
.72639
.4092

.08346
.58817

‘thNND-‘OO

In

6266

sstress

-0.
0.

6872
02142

0.71457

bfiUNNH

1n

.38043
.06961
.75078
.43536
.08478
.60812

SSCIGSS

-1
-0

.7551
.4153
0.
1.26314
2.01035
2.
3
4
4

46216

71916

.42211
.11449
.79198

N
U!
0
H

.9244
.9244
.9244
.9244
.9244
.9244
.9244
.9244
.9244

5-0-2

.2729
.2729
.2729
.2729
.2729
.2729
.2729
.2729
.2729

5-0-3

.65471
.65471
.65471
.65471
.65471
.65471
.65471
.65471
.65471

5-5-1

.1114
.1114
.1114
.1114
.1114
.1114
.1114
.1114
.1114

5-5-2

.10153
.10153
.10153
.10153
.10153
.10153
.10153
.10153
.10153

5-5-3

.6461
.6461
.6461
.6461
.6461
.6461
.6461
.6461
.6461

000000000NN HHHHHHHHHNN HHHHHHHHHNN 000000000NN HHHHHHHHHNN 000000000X

1n

-0.
-0.
-0.
-0.

-0
-0
-0

-0.

—0

000000000

-0
-0
-0
-0
-0
-0
-0
-0
-0

000000000

K

0786
0786
0786
0786
.0786
.0786
.0786
0786
.0786

.2413
.2413
.2413
.2413
.2413
.2413
.2413
.2413
.2413

.4236
.4236
.4236
.4236
.4236
.4236
.4236
.4236
.4236

.10562
.10562
.10562
.10562
.10562
.10562
.10562
.10562
.10562

.0967
.0967
.0967
.0967
.0967
.0967
.0967
.0967
.0967

.4368
.4368
.4368
.4368
.4368
.4368
.4368
.4368
.4368

T

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

15

15
15
15
15
15
15
15

15
15
15
15
15
15

15
15

15

15
15
15
15
15
15
15

15
15
15
15

15
15

15

15
15
15

15
15
15

15

l/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

1/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

l/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

67

WU'IU'ILDU'ILDU'IUIU'IO mmwmmmmmmo 0000000000 0000000000 0000000000

U'lU'lU'IU'IUIanLflUID

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

srate

119.

.46801
.93602
.87204
.74407
.48814
.9763
.9526
.9052

81

in

srate

-0

bfikJNNO-‘O

In

.7593
-0.
.62703
.32017
.01332
.70647
.39962
.09276
.78591

0661

srate

-O.
.0661

.62703
.32017
.01332
.70647
.39962
.09276
.78591

-0

hflUNNl—‘O

1n

7593

srate

-0

thNNHO

in

.7593
-0.
.62703
.32017
.01332
.70647
.39962
.09276
.78591

0661

srate

—0
-0

#bUNNl-‘O

1n

.7593

.0661

.62703
.32017
.01332
.70647
.39962
.09276
.78591

srate

-0

##UNNHO

1n

.7593
-0.
.62703
.32017
.01332
.70647
.39962
.09276
.78591

0661

srate

-0
-0

bhuNNl—‘O

.7593

.0661

.62703
.32017
.01332
.70647
.39962
.09276
.78591

sstress
1.13168
1.96472
3.55222
6.61718
12.8257
25.337
49.7939
96.8843
49.8411

sstress
1.25742
2.01187
3.42647
6.1928
11.6154
22.3821
43.7268
85.7247
43.7268

sstress
2.35767
3.89801
6.85295
12.3856
23.2623
44.4656
84.6245

sstress
1.83898
3.56793
6.85295
13.2186
25.9972
50.2654
95.5641

sstress
2.26336
4.00803
7.29305
13.6273
25.95
51.8529
95.9884

SSCIBSS
2.24764
3.9766
7.26161

13.5802
25.9972
50.2969
95.4855

sstress
2.3891
4.08662
7.32448
13.4701
25.5099
48.7722
92.3733

sstress
2.35767
3.89801
6.85295
12.3856
23.2623
44.4656
84.6245

1n
sstress
0.1237
0.67535
.2675?
.88967
.55145
.23227
.90789
.57352
.90884

“#WUNHH

1n

sstress
0.22906
0.69907
.23153
.82339
.45233
.10826
.77796
.45114
.77796

WDUUNHH

1n

sstress
0.85767
1.36047
.92468
.51653
.14683
.79472
.43822

hUUNH

1n
sstress
0.60921
1.27199
.92468
.58163
.25799
.91732
.5598

hwuNt—e

1n
sstress
0.81685
1.3883
.98692
.61208
.25617
.94841
.56423

fiWWNH

1n
sstress
0.80988
1.38043
.9826
.60861
.25799
.91794
.55897

hUUNH

1n

sstress
.87092
.40772
.99122
.60047
.23907
.88716
.52584

#UUNHHO

1n

sstress
0.85767
1.36047
1.92468
2.51653
3.14683
3.79472
4.43822

5-15-1

.31452
.31452
.31452
.31452
.31452
.31452
.31452
.31452
.31452

U"
I
H
UI
I
N

.3482
.3482
.3482
.3482
.3482
.3482
.3482
.3482
.3482

w
I
H
m
I
U

.06651
.06651
.06651
.06651
.06651
.06651
.06651

5-25-1

.78933
.78933
.78933
.78933
.78933
.78933
.78933

5-25-2

.27999
.27999
.27999
.27999
.27999
.27999
.27999

5-25-1

.25536
.25536
.25536
.25536
.25536
.25536
.25536

5-25-2

.38426
.38426
.38426
.38426
.38426
.38426
.38426

5-25-3

.18732
.18732
.18732
.18732
.18732
.18732
.18732

hbbbbfihxw ##DbhhfiXN bébbbbéflk’ bbfififibfixw UUUUUNUXN MNNNNNNNN NNNNNNNNNNN NNNNNNNNNXN

.8392
.8392
.8392
.8392
.8392
.8392
.8392
.8392
.8392

000000000

1nK

.85365
.85365
.85365
.85365
.85365
.85365
.85365
.85365
.85365

000000000

1nK

0.72586
0.72586
0.72586
0.72586
0.72586
0.72586
0.72586

1nK

1.33219
1.33219
1.33219
1.33219
1.33219
1.33219
1.33219

1nK

1.45395
1.45395
1.45395
1.45395
1.45395
1.45395
1.45395

1nK

1.44818
1.44818
1.44818
1.44818
1.44818
1.44818
1.44818

1nK

1.47802
1.47802
1.47802
1.47802
1.47802
1.47802
1.47802

1nK

1.43206
1.43206
1.43206
1.43206
1.43206
1.43206
1.43206

T

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.
298.
298.

68

15

15
15

15
15
15
15

15
15
15
15
15
15
15
15
15

15
15
15
15
15
15
15

15
15
15
15
15
15
15

15
15
15
15
15
15
15

15
15
15
15
15
15
15

15
15
15
15
15
15
15

15
15
15
15

15
15

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

1/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335
.00335

000000000

0.00335
0.00335
0.00335
0.00335
0.00335
0.00335
0.00335

0.00335
0.00335
0.00335
0.00335
0.00335
0.00335
0.00335

1/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335

0000000

1/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335

0000000

1/T

.00335
.00335
.00335
.00335
.00335
.00335
.00335

0000000

.00335
.00335
.00335
.00335
.00335
.00335
.00335

0000000

C
15

15
15

15
15
15
15

15
15
15
15
15

15
15
15

15
15
15
15
15
15
15

25
25
25
25
25
25
25

25
25

25
25
25
25

25
25
25
25
25
25
25

25
25
25
25

25
25

25
25
25
25

25

srate
0.46801
0.93602
1.87204
3.74407
7.48814
14.9763
29.9526
59.9052
119.81

srate
0.46801
0.93602
1.87204
3.74407
7.48814
14.9763
29.9526
59.9052
119.81

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

thwI-‘OO

NH

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

094091600

NH

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

0%QWH00

KJH

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

\DfidUI—‘OO

NH

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

WhQWI-‘OO

NH

srate
.46801
.93602
.87204
.74407
.48814
.9763
.9526

\DDQUHOO

NH

1n

srate
-0.7593
-0.0661
.62703
.32017
.01332
.70647
.39962
.09276
.78591

DéUMNI-‘O

srate
-0.7593
-0.0661
0.62703
1.32017
2.01332
2.70647
3.39962
4.09276
4.78591

srate
-0.7593
-0.0661
0.62703
1.32017
2.01332
2.70647
3.39962

srate
-0.7593
-0.0661
.62703
.32017
.01332
.70647
.39962

UNNHO

srate
—0.7593
-0.0661
0.62703
1.32017
2.01332
2.70647
3.39962

srate
-0.7593
-0.0661
.62703
.32017
.01332
.70647
.39962

wNNr—‘0

srate

-0.7593

~0.0661
0.62703
1.32017
2.01332
2.70647
3.39962

srate
.7593
.0661
.62703
.32017
.01332
.70647
.39962

I I
WNNHOOO

sstress
5.0454
8.84911
15.6077
28.1505
51.68
95.1868

sstress
1.82339
2.35431
2.90751
3.48234
4.08478

sstress
5.86273
10.1851
17.7296
31.4355
56.9926

sstress
2.26336
4.00803
7.29305
13.6273
25.95

sstress
2.24764
3.9766
7.26161
13.5802
25.9972

1n

sstress
1.61848
.18032
.74777
.33757
.94507
.55584

hUWNN

1n
sstress
0.6007
0.85625
1.0673
1.2477
1.40727

1n

sstress
1.76862
2.32093
2.87524
3.44794
4.04292

1n
sstress
0.81685
1.3883
1.98692
2.61208
3.25617

1n

sstress
0.80988
1.38043
1.9826
2.60861
3.25799

11.2379
11.2379
11.2379
11.2379
11.2379

25—35-3
K

10.7634
10.7634
10.7634
10.7634
10.7634

25-25-7

.29066
.29066
.29066
.29066
.29066

5-25-8

.25536
.25536
.25536
.25536
.25536

pohaoxw bébbbx

1nK

2.23863
2.23863
2.23863
2.23863
2.23863
2.23863

1nK

2.41929
2.41929
2.41929
2.41929
2.41929

1nK

2.37615
2.37615
2.37615
2.37615
2.37615

1nK

1.45644
1.45644
1.45644
1.45644
1.45644

1nK

1.44818
1.44818
1.44818
1.44818
1.44818

T

298.
298.
298.
298.
298.
298.

298.
298.
298.
298.
298.

298.
298.
298.
298.
298.

298.
298.
298.
298.
298.

298.
298.
298.
298.
298.

69

15
15
15
15

15

15
15
15

15

15

15
15
15

15
15
15

15

15
15
15
15
15

1/T

.00335
.00335
.00335
.00335
.00335
.00335

000000

1/T

0.00335
0.00335
0.00335
0.00335
0.00335

1/T

0.00335
0.00335
0.00335
0.00335
0.00335

1/T

0.00335
0.00335
0.00335
0.00335
0.00335

1/T

0.00335
0.00335
0.00335
0.00335
0.00335

C

35
35
35

35
35

35
35

35
35

35

35
35
35

25
25
25

25

25
25
25
25
25

srate
0.46801
0.93602
1.87204
3.74407
7.48814
4.

1 9763

srate

.46801
.93602
.87204
.74407
.48814

QUE-‘00

srate
0.46801
0.93602
1.87204
3.74407
7.48814

srate
0.46801
0.93602
1.87204
3.74407
7.48814

srate

.46801
.93602
.87204
.74407
.48814

QUE-'00

1n

srate

-0.7593

-0.0661
0.62703
1.32017
2.01332
2.70647

1n
srate
-0.7593
-0.0661
0.62703
1.32017
2.01332

1n
srate
-0.7593
-0.0661
0.62703
1.32017
2.01332

1n

srate

—0.7593

-0.0661
0.62703
1.32017
2.01332

1n

srate

-0.7593

-0.0661
0.62703
1.32017
2.01332

X. APPENDIX 4. MEASUREMENTS PERFORMED AT 40°C.

1.- Mixer Viscometry, 0%, 0 9 corn syrup

rpm readings Average
1 0 2 0.2 0.1 0.2 0.1 0.2 0.2 0.2 0.175
2 0 2 0.2 0.2 0.3 0.2 0.3 0.2 0.2 0.225
4 0 4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
8 0.6 0.7 0.7 0.6 0.7 0.7 0.7 0.7 0.675
16 1.3 1.3 1.3 1.4 1.3 1.4 1.3 1.3 1.325
32 2 6 2.7 2.6 2.7 2.6 2.6 2.7 2.6 2.6375
64 5 3 5.4 5.3 5.4 5.2 5.4 5.3 5.3 5.325
128 10 8 10.8 10.9 10.9 10.9 10.9 10 9 10.9 10.875
256 23 4 23.4 23.4 23.4 23.5 23.5 23.5 23.5 23.45
512 53 5 53.6 53.6 53.6 53.6 53.6 53.6 53.6 53.588
256 23 2 23.2 23.2 23.2 23.2 23.2 23.2 23.2 23.2
128 10 9 10.9 10.9 10.8 10.8 10.8 10.9 10.9 10.863
64 5 3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3
32 2 7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7
16 1 4 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.375
8 0 7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
4 0 4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
2 0 3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2375
1 0 1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0025 3E-05 -0.98 -4.602
2 0.2094 0.0032 38-05 -0.679 -4.493
4 0.4188 0.0057 63-05 -0.378 -4.243
8 0.8376 0.0096 IE—O4 -0.077 -4.016
16 1.6752 0.0189 0.0002 0.2241 -3.723
32 3.3504 0.0377 0.0004 0.5251 -3.424
64 6.7009 0.0761 0.0008 0.8261 -3.119
128 13.402 0.1554 0.0016 1.1272 -2.809
256 26.803 0.335 0.0034 1.4282 -2.475
512 53.607 0.7656 0.0077 1.7292 -2.116
256 26.803 0.3315 0.0033 1.4282 -2.48
128 13.402 0.1552 0.0016 1.1272 -2.809
64 6.7009 0.0757 0.0008 0.8261 -3.121
32 3.3504 0.0386 0.0004 0.5251 ~3.414
16 1.6752 0.0196 0.0002 0.2241 -3.707
8 0.8376 0.01 0.0001 -0.077 -4
4 0.4188 0.0057 GE-OS —0.378 -4.243
2 0.2094 0.0034 38—05 —0.679 ‘4.469
1 0.1047 0.0014 IE-OS -0.98 —4.845
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
K = consistency coefficient, Pa.s‘n
k' = 4.47
average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2
Maximum torque: 1.428716915 Nm (MM)
Sigma/ Ln
KG“(n-1) Gamma 1/3 1/3
angular average average average average average average
velocit viscosi shear shear Lnshear Lnshear viscosi shear shear
rpm rad/s Pa.s rate stress stress rate Pa.s stress stress
1 0.1047 0.3248 0.468 0.2277 -1.48 -0.759 0.4865 0.2238 -1.497
2 0.2094 0.3134 0.936 0.2927 -1.229 -0.066 0.3127 0.2878 -1.246
4 0.4188 0.3023 1.8721 0.5204 -0.653 0.627 0.278 0.5116 -0.67
8 0.8376 0.2917 3.7441 0.8782 -0.13 1.3202 0.2346 0.8633 —0.147
16 1.6752 0.2814 7.4882 1.7238 0.5446 2.0133 0.2302 1.6947 0.5275
32 3.3504 0.2715 14.976 3.4314 1.233 2.7065 0.2291 3.3734 1.2159
64 6.7009 0.262 29.953 6.9279 1.9356 3.3996 0.2313 6.8108 1.9185
128 13.402 0.2527 59.906 14.149 2.6496 4.0928 0.2362 13.909 2.6326
256 26.803 0.2438 119.81 30.509 3.418 4.7859 0.2546 29.993 3.401
512 53.607 0.2353 239.62 69.718 4.2445 5.4791 0.2909 68.54 4.2274
x y
Regression Statistics
R Square 0.9902
Observations 10

Coeffici Standar t Statis P-value Lower 95% Upper 95%
K = 0.3071 Interce -1.181 0.1021 -11.56 18-06 -1.416 -0.945
x1 0.9394 0.0331 28.412 4E-10 0.8632 1.0157

70

71

Mixer Viscometry, 0%, 0 g corn syrup

rpm readings Average
1 0 0.1 0 0 0 0 0.1 0 0.025
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
4 0.3 0.3 0.2 0.2 0.3 0.2 0.3 0.3 0.2625
8 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
16 1.3 1.2 1.3 1.2 1.2 1.3 1.3 1.3 1.2625
32 2.6 2.6 2.5 2.5 2.6 2.5 2.7 2.5 2.5625
64 5.2 5.3 5.3 5.3 5.3 5.2 5.2 5.3 5.2625
128 10.9 10.7 10.8 10.9 10.8 10.9 10.9 10.9 10.85
256 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5
512 53.9 53.8 53.9 54 53.9 53.7 53.8 53.9 53.863
256 23.5 23.5 23.4 23.6 23.5 23.6 23.5 23.6 23.525
128 10.7 10.8 10.8 10.7 10.8 10.7 10.8 10.9 10.775
64 5.1 5.3 5.1 5.2 5.2 5.3 5.1 5.1 5.175
32 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.5 2.55
16 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.2 1.2375
8 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1 0 0 0.1 0.1 0 0 0 0.1 0.0375
rad/s (N cm) (N m)
rpm omega M M log om log M
1 0.1047 0.0004 4B-06 -0.98 -5.447
2 0.2094 0.0014 lE-OS -0.679 -4.845
4 0.4188 0.0038 4E-05 -0.378 -4.426
8 0.8376 0.0086 98-05 -0.077 -4.067
16 1.6752 0.018 0.0002 0.2241 -3.744
32 3.3504 0.0366 0.0004 0.5251 -3.436
64 6.7009 0.0752 0.0008 0.8261 -3.124
128 13.402 0.155 0.0016 1.1272 -2.81
256 26.803 0.3357 0.0034 1.4282 —2.474
512 53.607 0.7695 0.0077 1.7292 -2.114
256 26.803 0.3361 0.0034 1.4282 —2.474
128 13.402 0.1539 0.0015 1.1272 -2.813
64 6.7009 0.0739 0.0007 0.8261 -3.131
32 3.3504 0.0364 0.0004 0.5251 -3.439
16 1.6752 0.0177 0.0002 0.2241 -3.753
8 0.8376 0.0086 9E-05 —0.077 «4.067
4 0.4188 0.0043 4E-05 -0.378 -4.368
2 0.2094 0.0014 18-05 -0.679 -4.845
1 0.1047 0.0005 58—06 -0.98 -5.271
Determination of average shear rate
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

K = consistency coefficient, Pa.s“n

k' : 4.47
average shear stress = 2 M / (pi d‘3 ' (b/d + 1/3) )
( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)
Maximum torque= 1.428716915 Nm (MM)

Sigma/
Gamma
angular average average average
rpm velocit shear shear Lnshear Lnshear viscosi
1 rad/s rate stress stress rate Pa.s
1 0.1047 0.468 0.0325 -3.426 -0.759 0.0695
2 0.2094 0.936 0.1301 -2.039 -0.066 0.139
4 0.4188 1.8721 0.3415 -1.074 0.627 0.1824
8 0.8376 3.7441 0.7806 -0.248 1.3202 0.2085
16 1.6752 7.4882 1.6425 0.4962 2.0133 0.2193
32 3.3504 14.976 3.3338 1.2041 2.7065 0.2226
64 6.7009 29.953 6.8466 1.9238 3.3996 0.2286
128 13.402 59.906 14.116 2.6473 4.0928 0.2356
256 26.803 119.81 30.574 3.4201 4.7859 0.2552
512 53.607 239.62 70.076 4.2496 5.4791 0.2924
y x
Regression Statistics
R Square 0.9917
Observations 10

Coeffici Standar t Stati P-value Lower 95% Upper 95%
K = 0.1311 Interce -2.032 0.1163 -17.47 3E—08 -2.3 -1.763
x1 1.164 0.0377 30.897 28-10 1.0771 1.2509

72

Mixer viscometry, 0%, 65.4 9 corn syrup, T = 40.8°C, 22.1 g CaCO3

rpm readings Average
1 0.1 0.1 0.1 0.1 0.2 0.1 0.2 0.1 0.125
2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
8 0.8 0.7 0.8 0.7 0.8 0.7 0.7 0.7 0.7375
16 1.3 1.4 1.4 1.3 1.4 1.4 1.4 1.4 1.375
32 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
64 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3
128 11 11 11 11 11 11 11 11 11
256 24 24 24 24 24 24 24 24 24
512 54.6 54.7 54.7 54.7 54.7 54.7 54.7 54.7 54.688
256 24 24 24 24 24 24 24 24 24
128 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1 11.1
64 5.4 5.4 5.4 5.3 5.3 5.3 5.3 5.3 5.3375
32 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
16 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2875
8 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
l 0 0 0 0 0 0 0 0 0
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0018 2E-05 -0.98 -4.748
2 0.2094 0.0029 3E—05 ~0.679 -4.544
4 0.4188 0.0057 6E-05 —0.378 -4.243
8 0.8376 0.0105 0.0001 -0.077 —3.977
16 1.6752 0.0196 0.0002 0.2241 -3.707
32 3.3504 0.0371 0.0004 0.5251 -3.43
64 6.7009 0.0757 0.0008 0.8261 -3.121
128 13.402 0.1572 0.0016 1.1272 -2.804
256 26.803 0.3429 0.0034 1.4282 -2.465
512 53.607 0.7813 0.0078 1.7292 -2.107
256 26.803 0.3429 0.0034 1.4282 -2.465
128 13.402 0.1586 0.0016 1.1272 -2.8
64 6.7009 0.0763 0.0008 0.8261 -3.118
32 3.3504 0.0371 0.0004 0.5251 —3.43
16 1.6752 0.0184 0.0002 0.2241 -3.735
8 0.8376 0.0086 9E—05 -0.077 —4.067
4 0.4188 0.0043 4E-05 -0.378 -4.368
2 0.2094 0.0014 18—05 -0.679 -4.845
1 0.1047 0 0 -0.98 ERR

Determination of average shear rate.

average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

R = consistency coefficient, Pa.s“n

k' = 4.47

average shear stress = 2 M / (pi d‘3 * (b/d + 1/3) )

( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque: 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1626 —0.759 -1.816 0.3475
2 0.2094 0.936 0.2602 —0.066 -1.346 0.278
4 0.4188 1.8721 0.5204 0.627 -0.653 0.278
8 0.8376 3.7441 0.9595 1.3202 -0.041 0.2563
16 1.6752 7.4882 1.7889 2.0133 0.5816 0.2389
32 3.3504 14.976 3.3826 2.7065 1.2187 0.2259
64 6.7009 29.953 6.8954 3.3996 1.9309 0.2302

128 13.402 59.906 14.311 4.0928 2.661 0.2389

256 26.803 119.81 31.224 4.7859 3.4412 0.2606

512 53.607 239.62 71.149 5.4791 4.2648 0.2969

X Y

Regression Statistics

R Square 0.9965

Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 0.2798 Interce -1.274 0.0628 -20.28 88-09 -1.419 -1.129
x1 0.9737 0.0203 47.857 4E-12 0.9268 1.0207

'a;

73

Mixer Viscometry. 5%, 61.7 9 corn syrup, T = 40°C. 3.1 g CaCO3

rpm readings Average
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
16 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
32 3.2 3.4 3.2 3.3 3.3 3.4 3.2 3.3 3.2875
64 6.7 6.7 6.7 6.7 6.6 6.7 6.6 6.7 6.675
128 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.3 13.475
256 28.4 28.4 28.4 28.4 28.4 28.4 28.4 28.4 28.4
512 58.5 58.6 58 6 58.6 58.6 58 6 58.6 58.6 58.588
256 27.8 27.7 27.7 27.7 27.7 27 7 27.7 27.7 27.712
128 13.5 13.4 13.4 13.4 13.4 13.4 13.4 13.4 13.413
64 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6
32 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3 3.3
16 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0014 lE-OS -0.98 -4.845
2 0.2094 0.0029 3E-05 -0.679 -4.544
4 0.4188 0.0057 68-05 -0.378 -4.243
8 0.8376 0.0114 0.0001 -0.077 -3.942
16 1.6752 0.0229 0.0002 0.2241 -3.641
32 3.3504 0.047 0.0005 0.5251 -3.328
64 6.7009 0.0954 0.001 0.8261 -3.021
128 13.402 0.1925 0.0019 1.1272 —2.716
256 26.803 0.4058 0.0041 1.4282 -2.392
512 53.607 0.837 0.0084 1.7292 -2.077
256 26.803 0.3959 0.004 1.4282 -2.402
128 13.402 0.1916 0.0019 1.1272 -2.718
64 6.7009 0.0943 0.0009 0.8261 -3.026
32 3.3504 0.0471 0.0005 0.5251 -3.327
16 1.6752 0.0229 0.0002 0.2241 -3.641
8 0.8376 0.0114 0.0001 —0.077 -3.942
4 0.4188 0.0057 6E-05 -0.378 -4.243
2 0.2094 0.0029 3E-05 -0.679 -4.544
1 0.1047 0.0014 18-05 -0.98 —4.845

Determination of average shear rate.

average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress I shear rate

K = consistency coefficient, Pa.s“n

k' = 4.47

average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )

( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque: 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 -2.039 0.278
2 0.2094 0.936 0.2602 -0.066 -1.346 0.278
4 0.4188 1.8721 0.5204 0.627 -0.653 0.278
8 0.8376 3.7441 1.0408 1.3202 0.04 0.278
16 1.6752 7.4882 2.0816 2.0133 0.7331 0.278
32 3.3504 14.976 4.2771 2.7065 1.4533 0.2856
64 6.7009 29.953 8.6843 3.3996 2.1615 0.2899

128 13.402 59.906 17.531 4.0928 2.864 0.2926

256 26.803 119.81 36.949 4.7859 3.6095 0.3084

512 53.607 239.62 76.223 5.4791 4.3337 0.3181

X Y

Regression Statistics

R Square 0.9999

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.2745 Interce -1.293 0.0116 -111.7 28—15 -1.319 -1.266
x1 1.0205 0.0037 272.19 68-19 1.0119 1.0292

74

Mixer Viscometry, 5%, 64.3 9 corn syrup, T = 40°C, 3.2 g CaCO3

rpm readings Average
1 0 0.1 0 0.1 0 0 0 0 0.025
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
4 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3125
8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
16 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4
32 3 3 3 3 3 3 3 3 3
64 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3
128 13.2 13.2 13.2 13.2 13.2 13.2 13.2 13.2 13.2
256 27.8 27.9 27.9 27.9 27.9 27.9 27.9 27.9 27 887
512 58.9 58.9 58.9 58.9 59 59 59 58.9 58.938
256 28.2 28.2 28.2 28.2 28.2 28.2 28.2 28.2 28.2
128 13.2 13.2 13.2 13.2 13.2 13.2 13.2 13.2 13.2
64 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3
32 3 3 3 3 3 3 3 3 3
16 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3125
8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
4 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1125
2 0.1 0.1 0 0.1 0 0.1 0 0.1 0.0625
1 0 0 0 0 0 0 0 0 0
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0004 48-06 -0.98 -5.447
2 0.2094 0.0014 18-05 -0.679 -4.845
4 0.4188 0.0045 4E-05 -0.378 -4.35
8 0.8376 0.01 0.0001 -0.077 -4
16 1.6752 0.02 0.0002 0.2241 -3.699
32 3.3504 0.0429 0.0004 0.5251 -3.368
64 6.7009 0.09 0.0009 0.8261 -3.046
128 13.402 0.1886 0.0019 1.1272 -2.724
256 26.803 0.3984 0.004 1.4282 —2.4
512 53.607 0.8421 0.0084 1.7292 -2.075
256 26.803 0.4029 0.004 1.4282 -2.395
128 13.402 0.1886 0.0019 1.1272 —2.724
64 6.7009 0.09 0.0009 0.8261 -3.046
32 3.3504 0.0429 0.0004 0.5251 -3.368
16 1.6752 0.0188 0.0002 0.2241 —3.727
8 0.8376 0.0071 7E—05 -0.077 -4.146
4 0.4188 0.0016 28-05 -0.378 -4.794
2 0.2094 0.0009 9E—06 —0.679 -5.049
1 0.1047 0 0 -0.98 ERR
Determination of average shear rate.
average shear stress = 2 M / pi b d‘2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
R = consistency coefficient, Pa.s‘n
k' = 4.47
average shear stress = 2 M / (pi d‘3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque: 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 -2.039 0.278
2 0.2094 0.936 0.4066 -0.066 ~0.9 0.4344
4 0.4188 1.8721 0.9107 0.627 -0.094 0.4865
8 0.8376 3.7441 1.8214 1.3202 0.5996 0.4865
16 1.6752 7.4882 3.903 2.0133 1.3618 0.5212
32 3.3504 14.976 8.1964 2.7065 2.1037 0.5473
64 6.7009 29.953 17.173 3.3996 2.8434 0.5733
128 13.402 59.906 36.282 4.0928 3.5913 0.6057
256 26.803 119.81 76.679 4.7859 4.3396 0.64
512 53.607 239.62 36.689 5.4791 3.6025 0.1531
X Y
Regression Statistics
R Square 0.9574
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.4502 Interce -0.798 0.2281 -3.498 0.0067 -1.324 -0.272
x1 0.9911 0.0739 13.413 3E—07 0.8207 1.1615

75

Mixer Viscometry, 5%, 63.6 9 corn syrup, T = 40°C, 3.1 g CaCO3

rpm readings Average
1 0 0 0 0 0 0 0 0 0
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
4 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.1875
8 0.6 0.6 0.6 0.6 0.6 0.5 0.6 0.5 0.575
16 1.3 1.2 1.3 1.3 1.2 1.3 1.3 1.3 1.275
32 2.8 2.9 2.8 2.9 2.8 2.9 2.8 2.9 2.85
64 6.2 6 6.1 6 6 6.1 6 6.1 6.0625
128 12.9 12.8 12.9 12.7 12.8 12.8 12.7 12.8 12.8
256 27.3 27.2 27.3 27.2 27.2 27.2 27.2 27.3 27.238
512 58.2 58.1 58.2 58.1 58.1 58.2 58.2 58.1 58.15
256 27.3 27.2 27.3 27.2 27.2 27.2 27.2 27.3 27.238
128 12.8 12.7 12.8 12.8 12.7 12.8 12.7 12.8 12.763
64 6 6.1 6.2 6 6.1 6.1 6 6.1 6.075
32 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8
16 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
8 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1 0 0 0 0.1 0 0.1 0 0 0.025
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0 0 —0.98 ERR
2 0.2094 0.0014 lE-OS -0.679 -4.845
4 0.4188 0.0027 3E—05 -0.378 -4.572
8 0.8376 0.0082 88-05 —0.077 -4.085
16 1.6752 0.0182 0.0002 0.2241 -3.74
32 3.3504 0.0407 0.0004 0.5251 -3.39
64 6.7009 0.0866 0.0009 0.8261 -3.062
128 13.402 0.1829 0.0018 1.1272 -2.738
256 26.803 0.3891 0.0039 1.4282 -2.41
512 53.607 0.8308 0.0083 1.7292 -2.081
256 26.803 0.3891 0.0039 1.4282 -2.41
128 13.402 0.1823 0.0018 1.1272 -2.739
64 6.7009 0.0868 0.0009 0.8261 -3.062
32 3.3504 0.04 0.0004 0.5251 -3.398
16 1.6752 0.0171 0.0002 0.2241 -3.766
8 0.8376 0.0057 6E-05 -0.077 -4.243
4 0.4188 0.0029 3E-05 -0.378 -4.544
2 0.2094 0.0014 1E-05 -0.679 -4.845
1 0.1047 0.0004 4E-06 -0.98 -5.447

Determination of average shear rate.

average shear stress = 2 M / pi b d‘2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress I shear rate

R = consistency coefficient, Pa.s‘n

k' = 4.47

average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )

( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque: 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0 -0.759 ERR 0

2 0.2094 0.936 0.1301 -0.066 -2.039 0.139

4 0.4188 1.8721 0.2439 0.627 -1.411 0.1303
8 0.8376 3.7441 0.7481 1.3202 -0.29 0.1998
16 1.6752 7.4882 1.6588 2.0133 0.5061 0.2215
32 3.3504 14.976 3.7079 2.7065 1.3105 0.2476
64 6.7009 29.953 7.8874 3.3996 2.0653 0.2633
128 13.402 59.906 16.653 4.0928 2.8126 0.278
256 26.803 119.81 35.436 4.7859 3.5677 0.2958
512 53.607 239.62 75.654 5.4791 4.3262 0.3157
X Y
Regression Statistics
R Square 0.9976
Observations 9

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.1453 Interce —1.929 0.0692 -27.88 3E-09 -2.093 -1.765
x1 1.1581 0.0213 54.318 1E—11 1.1077 1.2085

76

Mixer Viscometry, 15%, 58.7 9 corn syrup. T = 40.8°C, 8.8 g CaCO3

rpm readings Average
1 0 1 0.1 0.1 0.1 0.2 0.1 0.1 0.2 0.125
2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
4 0.6 0.7 0.6 0.7 0.7 0.6 0.6 0.6 0.6375
8 1 3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
16 2 6 2.6 2.6 2.6 2.6 2.5 2.5 2.5 2.5625
32 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1
64 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
128 20.3 20.3 20.3 20.3 20.2 20.2 20.2 20.2 20.25
256 39.8 39 9 39.9 39.9 39.8 39.5 39.4 39.4 39.7
512 75 75 74.9 74.9 74.9 74.9 74.9 74.9 74.925
256 36.3 36.3 36.3 36.4 36.4 36.4 36.4 36.4 36.362
128 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.3 19.388
64 9.9 9.9 9.9 9.9 9.9 9.9 9.9 9.9 9.9
32 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1
16 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
8 1.3 1.4 1.3 1.3 1.4 1.3 1.3 1.3 1.325
4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0018 ZE-OS -0.98 -4.748
2 0.2094 0.0043 4E-05 -0.679 -4.368
4 0.4188 0.0091 9E—05 -0.378 -4.041
8 0.8376 0.0186 0.0002 -0.077 -3.731
16 1.6752 0.0366 0.0004 0.2241 -3.436
32 3.3504 0.0729 0.0007 0.5251 -3.137
64 6.7009 0.1457 0.0015 0.8261 -2.836
128 13.402 0.2893 0.0029 1.1272 -2.539
256 26.803 0.5672 0.0057 1.4282 —2.246
512 53.607 1.0705 0.0107 1.7292 -1.97
256 26.803 0.5195 0.0052 1.4282 -2.284
128 13.402 0.277 0.0028 1.1272 -2.558
64 6.7009 0.1414 0.0014 0.8261 -2.849
32 3.3504 0.0729 0.0007 0.5251 -3.137
16 1.6752 0.0371 0.0004 0.2241 -3.43
8 0.8376 0.0189 0.0002 —0.077 -3.723
4 0.4188 0.01 0.0001 -0.378 -4
2 0.2094 0.0057 6E-05 -0.679 -4.243
1 0.1047 0.0029 3E-05 -0.98 -4.544
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
R = consistency coefficient, Pa.s“n
k' = 4.47
average shear stress = 2 M / (pi d*3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque: 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1626 -0.759 -1.816 0.3475
2 0.2094 0.936 0.3903 —0.066 -0.941 0.417
4 0.4188 1.8721 0.8294 0.627 -0.187 0.443
8 0.8376 3.7441 1.6913 1.3202 0.5255 0.4517
16 1.6752 7.4882 3.3338 2.0133 1.2041 0.4452
32 3.3504 14.976 6.6352 2.7065 1.8924 0.443
64 6.7009 29.953 13.27 3.3996 2.5855 0.443
128 13.402 59.906 26.346 4.0928 3.2713 0.4398
256 26.803 119.81 51.65 4.7859 3.9445 0.4311
512 53.607 239.62 97.478 5.4791 4.5796 0.4068
X Y
Regression Statistics
R Square 0.9988
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.4123 Interce -0.886 0.038 -23.34 2E-09 -0.974 - 0.798
x1 1.0136 0.0123 82.429 3E-14 0.9852 1.0419

77

Mixer Viscometry, 15%, 15.02%, 61.9 9 corn syrup, T = 40°C, 9.3 g CaCO3
rpm readings Average
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2 0.2 0.3 0.2 0.3 0.3 0.2 0.2 0.2 0.2375
4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
8 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
16 2.4 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.4875
32 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1
64 10.2 10.3 10.2 10.3 10.3 10.3 10.3 10.3 10.275
128 20.5 20.5 20.5 20.5 20.5 20.5 20.5 20.5 20.5
256 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3 41.3
512 78.1 78 77.9 77.9 77.9 77.9 77.9 77.8 77.925
256 37.5 37.4 37.4 37.4 37.4 37.5 37.4 37.5 37.438
128 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5 19.5
64 10 10 10 10 10 10 10 10 10
32 5.1 5.1 5.1 5 5.1 5 5.1 5 5.0625
16 2.5 2.5 2.5 2.5 2.5 2.5 2.6 2.6 2.525
8 1.3 1.3 1.2 1.3 1.2 1.3 1.2 1.3 1.2625
4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
1 0.1 0.1 0.1 0.1 0.2 0.1 0.2 0.1 0.125
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0014 lE-OS -0.98 —4.845
2 0.2094 0.0034 3E-05 -0.679 -4.469
4 0.4188 0.0086 9E-05 -0.378 -4.067
8 0.8376 0.0171 0.0002 -0.077 —3.766
16 1.6752 0.0355 0.0004 0.2241 -3.449
32 3.3504 0.0729 0.0007 0.5251 -3.137
64 6.7009 0.1468 0.0015 0.8261 -2.833
128 13.402 0.2929 0.0029 1.1272 -2.533
256 26.803 0.5901 0.0059 1.4282 -2.229
512 53.607 1.1133 0.0111 1.7292 -1.953
256 26.803 0.5349 0.0053 1.4282 -2.272
128 13.402 0.2786 0.0028 1.1272 -2.555
64 6.7009 0.1429 0.0014 0.8261 -2.845
32 3.3504 0.0723 0.0007 0.5251 -3.141
16 1.6752 0.0361 0.0004 0.2241 -3.443
8 0.8376 0.018 0.0002 -0.077 -3.744
4 0.4188 0.0086 9E-05 -0.378 -4.067
2 0.2094 0.0043 4E-05 -0.679 —4.368
1 0.1047 0.0018 2E-05 -0.98 -4.748
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
K = consistency coefficient, Pa.s“n
k' = 4.47
average shear stress = 2 M / (pi d‘3 ' (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque: 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 —2.039 0.278
2 0.2094 0.936 0.309 -0.066 -1.174 0.3301
4 0.4188 1.8721 0.7806 0.627 -0.248 0.417
8 0.8376 3.7441 1.5612 1.3202 0.4455 0.417
16 1.6752 7.4882 3.2363 2.0133 1.1744 0.4322
32 3.3504 14.976 6.6352 2.7065 1.8924 0.443
64 6.7009 29.953 13.368 3.3996 2.5929 0.4463
128 13.402 59.906 26.671 4.0928 3.2836 0.4452
256 26.803 119.81 53.732 4.7859 3.984 0.4485
512 53.607 239.62 101.38 5.4791 4.6189 0.4231
x y
Regression Statistics
R Square 0.9977
Observations 10
Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.3532 Interce -1.041 0.055 -18.91 lE-08 -1.168 -0.914
x1 1.0567 0.0178 59.294 68-13 1.0156 1.0978

78

Mixer Viscometry, 15%, 60.7 9 corn syrup, T = 40.2°C, 9.1 g CaC03

rpm readings Average
1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
2 0.7 0.6 0.7 0.6 0.7 0.6 0.7 0.6 0.65
4 1 1 1 1 1 1 1 1 1
8 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
16 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9
32 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3 5.3
64 10.6 10.5 10.5 10.6 10.5 10.6 10.5 10.5 10.538
128 21.1 21.2 21.2 21.2 21.2 21.2 21.2 21.1 21.175
256 42.4 42.4 42.4 42.4 42.4 42.4 42.5 42.4 42.413
512 78.5 78.4 78.4 78.4 78.3 78.3 78.3 78.2 78.35
256 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7 37.7
128 20 20 20 20 20 20 19.9 19.9 19.975
64 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2
32 5.3 5.2 5.3 5.2 5.3 5.2 5.3 5.2 5.25
16 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.8 2.7125
8 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4
4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7125
2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

rad/s (N cm) (N m)
rpm omega M M log Om log M

1 0.1047 0.0071 7E-05 -0.98 -4.146

2 0.2094 0.0093 9E~05 -0.679 -4.032

4 0.4188 0.0143 0.0001 -0.378 -3.845

8 0.8376 0.0229 0.0002 -0.077 -3.641
16 1.6752 0.0414 0.0004 0.2241 -3.383
32 3.3504 0.0757 0.0008 0.5251 -3.121
64 6.7009 0.1506 0.0015 0.8261 -2.822
128 13.402 0.3025 0.003 1.1272 -2.519
256 26.803 0.606 0.0061 1.4282 -2.218
512 53.607 1.1194 0.0112 1.7292 -1.951
256 26.803 0.5386 0.0054 1.4282 -2.269
128 13.402 0.2854 0.0029 1.1272 -2.545
64 6.7009 0.1457 0.0015 0.8261 -2.836
32 3.3504 0.075 0.0008 0.5251 -3.125
16 1.6752 0.0388 0.0004 0.2241 -3.412
8 0.8376 0.02 0.0002 -0.077 -3.699

4 0.4188 0.0102 0.0001 -0.378 -3.992

2 0.2094 0.0057 6E-05 -0.679 -4.243

1 0.1047 0.0029 3E-05 -0.98 —4.544

Determination of average shear rate.

average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

K = consistency coefficient, Pa.s“n

k' = 4.47

average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )

( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque: 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.6505 -0.759 -0.43 1.3899
2 0.2094 0.936 0.8457 -0.066 —0.168 0.9035
4 0.4188 1.8721 1.301 0.627 0.2631 0.695
8 0.8376 3.7441 2.0816 1.3202 0.7331 0.556
16 1.6752 7.4882 3.7729 2.0133 1.3279 0.5039
32 3.3504 14.976 6.8954 2.7065 1.9309 0.4604
64 6.7009 29.953 13.709 3.3996 2.6181 0.4577

128 13.402 59.906 27.549 4.0928 3.316 0.4599

256 26.803 119.81 55.179 4.7859 4.0106 0.4606

512 53.607 239.62 101.93 5.4791 4.6243 0.4254

X Y

Regression Statistics

R Square 0.9883

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.8491 Interce -0.164 0.1 —1.636 0.1363 —0.394 0.067
x1 0.8416 0.0324 25.987 9E-10 0.767 0.9163

79

10.- Mixer viscometry, 25%, 24.96%, 65.3 g corn syrup, T = 40.8°C, 16.3 g CaCO3
rpm readings Average
1 1 1 1 1 1 1 1 1 1
2 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
8 4.1 4 4 4.1 4 4.1 4 4 4.0375
16 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4
32 14.1 14.1 14.1 14.1 14.1 14.1 14.1 14.1 14.1
64 26.5 26.7 26.7 26.7 26.7 26.7 26.6 26.6 26 65
128 50.7 50.9 50.9 50.8 50.8 50.9 51 51 50 875
256 96.8 97 97 97 97 96.9 96.9 96.8 96 925
128 50.8 50.8 50.7 50.7 50.7 50.8 50.8 50.8 50.762
64 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5 26.5
32 14.1 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.925
16 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4
8 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1 4.1
4 2.3 2.3 2.3 2.4 2.3 2.4 2.4 2.3 2.3375
2 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.425
1 1 1 1 1 1 1 1 1 1
rad/s (N cm) (N m)
rpm omega M M log Om 10g M
1 0.1047 0.0143 0.0001 -0.98 -3.845
2 0.2094 0.0214 0.0002 -0.679 -3.669
4 0.4188 0.0343 0.0003 -0.378 —3.465
8 0.8376 0.0577 0.0006 -0.077 -3.239
16 1.6752 0.1057 0.0011 0.2241 -2.976
32 3.3504 0.2014 0.002 0.5251 -2.696
64 6.7009 0.3808 0.0038 0.8261 -2.419
128 13.402 0.7269 0.0073 1.1272 —2.139
256 26.803 1.3848 0.0138 1.4282 —1.859
128 13.402 0.7253 0.0073 1.1272 -2.14
64 6.7009 0.3786 0.0038 0.8261 -2.422
32 3.3504 0.1989 0.002 0.5251 -2.701
16 1.6752 0.1057 0.0011 0.2241 -2.976
8 0.8376 0.0586 0.0006 -0.077 -3.232
4 0.4188 0.0334 0.0003 -0.378 -3.476
2 0.2094 0.0204 0.0002 -0.679 -3.691
1 0.1047 0.0143 0.0001 -0.98 -3.845
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
R = consistency coefficient, Pa.s“n
k' = 4.47
average shear stress = 2 M I (pi d‘3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque: 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 1.301 -0.759 0.2631 2.7799
2 0.2094 0.936 1.9515 -0.066 0.6686 2.0849
4 0.4188 1.8721 3.1224 0.627 1.1386 1.6679
8 0.8376 3.7441 5.2528 1.3202 1.6588 1.403
16 1.6752 7.4882 9.6275 2.0133 2.2646 1.2857
32 3.3504 14.976 18.344 2.7065 2.9093 1.2249
64 6.7009 29.953 34.672 3.3996 3.5459 1.1576
128 13.402 59.906 66.189 4.0928 4.1925 1.1049
256 26.803 119.81 126.1 4.7859 4.8371 1.0525
512 53.607 239.62 66.043 5.4791 4.1903 0.2756
X Y
Regression Statistics
R Square 0.961
Observations 10
Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 2.2041 Interce 0.7903 0.1654 4.777 0.001 0.4088 1.1718
x1 0.7528 0.0536 14.05 ZE—O7 0.6293 0.8764

80

11.- Mixer Viscometry, 25%, 25.04%, 57.1 9 corn syrup, T = 40°C, 14.3 g CaC03

rpm readings Average
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
4 1.2 1.1 1.1 1.1 1.1 1.2 1.2 1.1 1.1375
8 2.3 2.3 2.4 2.3 2.4 2.4 2.4 2.4 2.3625
16 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7
32 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3
64 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18.2 18 2
128 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35.3 35 3
256 66.9 66.9 66.9 66 9 66.9 66.9 66.9 66.9 66.9
128 34.5 34.5 34.5 34.5 34.5 34.5 34.6 34.6 34 525
64 18 17.9 17.9 17.9 17.9 17.9 17.9 17.9 17.913
32 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3 9.3
16 4.8 4.7 4.8 4.7 4.8 4.7 4.7 4.7 4.7375
8 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
2 0.5 0.6 0.5 0.5 0.6 0.5 0.5 6 1.2125
1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

rad/s (N cm) (N m)
rpm omega M M log Om log M

1 0.1047 0.0029 3E~05 -0.98 -4.544

2 0.2094 0.0071 7E-05 -0.679 -4.146

4 0.4188 0.0163 0.0002 -0.378 -3.789

8 0.8376 0.0338 0.0003 -0.077 -3.472

16 1.6752 0.0671 0.0007 0.2241 -3.173

32 3.3504 0.1329 0.0013 0.5251 -2.877

64 6.7009 0.26 0.0026 0.8261 -2.585

128 13.402 0.5043 0.005 1.1272 -2.297
256 26.803 0.9558 0.0096 1.4282 -2.02

128 13.402 0.4933 0.0049 1.1272 -2.307

64 6.7009 0.2559 0.0026 0.8261 -2.592

32 3.3504 0.1329 0.0013 0.5251 -2.877
16 1.6752 0.0677 0.0007 0.2241 -3.17

8 0.8376 0.0343 0.0003 ~-0.077 -3.465

4 0.4188 0.0171 0.0002 -0.378 -3.766

2 0.2094 0.0173 0.0002 -0.679 -3.761

1 0.1047 0.0029 3E-05 -0.98 -4.544

Determination of average shear rate.

average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

R = consistency coefficient, Pa.s‘n

k' = 4.47

average shear stress = 2 M / (pi d‘3 ' (b/d + 1/3) )

( b/d 4 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque: 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.2602 -0.759 -1.346 0.556
2 0.2094 0.936 0.6505 -0.066 -0.43 0.695
4 0.4188 1.8721 1.4799 0.627 0.392 0.7905
8 0.8376 3.7441 3.0736 1.3202 1.1229 0.8209
16 1.6752 7.4882 6.1148 2.0133 1.8107 0.8166
32 3.3504 14.976 12.099 2.7065 2.4932 0.8079
64 6.7009 29.953 23.678 3.3996 3.1646 0.7905

128 13.402 59.906 45.926 4.0928 3.827 0.7666

256 26.803 119.81 87.038 4.7859 4.4663 0.7265

512 53.607 239.62 44.918 5.4791 3.8048 0.1875

X Y

Regression Statistics

R Square 0.9552

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.796 Interce -0.228 0.2163 -l.055 0.3191 —0.727 0.2707
x1 0.9147 0.0701 13.054 4E-07 0.7531 1.0763

81

12.- Mixer Viscometry, 25%, T=40.6°C, 59.2 9 corn syrup, 14.8 22.1 g CaCO3

rpm readings Average
1 0.5 0.5 0.5 0.5 0.4 0.4 0 4 0.5 0.4625
2 0.8 0.8 0.8 0.8 0.8 0.8 0 8 0.8 0.8
4 1.5 1.5 1.5 1.5 1.5 1.5 1 5 1.5 1.5
8 2.8 2.8 2.8 2.8 2.8 2.8 2 8 2.8 2.8
16 5.2 5.2 5.3 5.2 5.3 5.3 5 3 5.3 5.2625
32 10.3 10.3 10.3 10.3 10.2 10.2 10 2 10.1 10.238
64 19.7 19.7 19.7 19.7 19.7 19.7 19 7 19.7 19.7
128 37.9 37.9 37.8 37.8 37.8 37.8 37.8 37.8 37.825
256 70.6 71.1 70 70.9 70.8 70.7 70.7 70.7 70.688
128 36.7 36.7 36.7 36.7 36.7 36.7 36 7 36.7 36.7
64 19.2 19.2 19.2 19.2 19.2 19.2 19 2 19.4 19.225
32 10.1 10.1 10.1 10.1 10.1 10.1 10 1 10.1 10.1
16 5.3 5.3 5.3 5.3 5.3 5.3 5 3 5.3 5.3
8 2.8 2.8 2.8 2.8 2.8 2.8 2 8 2.8 2.8
4 1.5 1.5 1.5 1.5 1.5 1.5 1 5 1.5 1.5
2 0.8 0.9 0.9 0.8 0.9 0.8 0 9 0.8 0.85
1 0.5 0.5 0.5 0.5 0.5 0.5 0 5 0.5 0.5
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0066 7E-05 -0.98 -4.18
2 0.2094 0.0114 0.0001 -0.679 -3.942
4 0.4188 0.0214 0.0002 -0.378 ~3.669
8 0.8376 0.04 0.0004 -0.077 -3.398
16 1.6752 0.0752 0.0008 0.2241 -3.124
32 3.3504 0.1463 0.0015 0.5251 -2.835
64 6.7009 0.2815 0.0028 0.8261 -2.551
128 13.402 0.5404 0.0054 1.1272 -2.267
256 26.803 1.0099 0.0101 1.4282 -1.996
128 13.402 0.5243 0.0052 1.1272 -2.28
64 6.7009 0.2747 0.0027 0.8261 -2.561
32 3.3504 0.1443 0.0014 0.5251 -2.841
16 1.6752 0.0757 0.0008 0.2241 —3.121
8 0.8376 0.04 0.0004 —0.077 -3.398
4 0.4188 0.0214 0.0002 -0.378 -3.669
2 0.2094 0.0121 0.0001 -0.679 -3.916
1 0.1047 0.0071 7E-05 -0.98 -4.146
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0 02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
R = consistency coefficient, Pa.s‘n
k' = 4.47
average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque: 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.6017 -0.759 -0.508 1.2857
2 0.2094 0.936 1.0408 -0.066 0.04 1.1119
4 0.4188 1.8721 1.9515 0.627 0.6686 1.0424
8 0.8376 3.7441 3.6428 1.3202 1.2928 0.973
16 1.6752 7.4882 6.8466 2.0133 1.9238 0.9143
32 3.3504 14.976 13.319 2.7065 2.5892 0.8893
64 6.7009 29.953 25.63 3.3996 3.2438 0.8557
128 13.402 59.906 49.211 4.0928 3.8961 0.8215
256 26.803 119.81 91.965 4.7859 4.5214 0.7676
512 53.607 239.62 47.747 5.4791 3.8659 0.1993
X Y

Regression Statistics
R Square 0.961
Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 1.254 Interce 0.2263 0.1797 1.2598 0.2394 -0.188 0.6406
x1 0.8166 0.0582 14.034 ZE-O7 0.6824 0.9508

82
12 a.- Mixer Viscometry, 25%, T: 40.2°C, 58.4 9 corn syrup, 14.6 22.1 g CaCO3
rpm readings Average
1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 .3
2 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
8 2.5 2.6 2.5 2.6 2.6 2.6 2.5 2.5 2.55
16 4.9 4.9 4.9 5 4.9 5 4.9 5 4.9375
32 9.7 9.7 9.7 9.7 9.7 9.7 9.7 9.6 9.6875
64 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.7 18.788
128 36.2 36.2 36.2 36.3 36.3 36.3 36.3 36.3 36.263
256 65.1 65 65 65 65 65 65 65 65.012
128 33.2 33.2 33.2 33.2 33.2 33.2 33.3 33.3 33.225
64 17.7 17.7 17.7 17.7 17.7 17.7 17.7 17.7 17.7
32 9.4 9.4 9.5 9.4 9.4 9.5 9.5 9.5 9.45
16 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9
8 2.6 2.6 2.6 2.5 2.6 2.5 2.6 2.6 2.575
4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3125
2 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
1 0.3 0.4 0.3 0.4 0.3 0.4 0.3 0.3 0.3375
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0043 4E-05 -0.98 -4.368
2 0.2094 0.01 0.0001 -0.679 -4
4 0.4188 0.0186 0.0002 -0.378 —3.731
8 0.8376 0.0364 0.0004 -0.077 -3.439
16 1.6752 0.0705 0.0007 0.2241 -3.152
32 3.3504 0.1384 0.0014 0.5251 -2.859
64 6.7009 0.2684 0.0027 0.8261 —2.571
128 13.402 0.5181 0.0052 1.1272 -2.286
256 26.803 0.9288 0.0093 1.4282 —2.032
128 13.402 0.4747 0.0047 1.1272 -2.324
64 6.7009 0.2529 0.0025 0.8261 -2.597
32 3.3504 0.135 0.0014 0.5251 —2.87
16 1.6752 0.07 0.0007 0.2241 -3.155
8 0.8376 0.0368 0.0004 -0.077 —3.434
4 0.4188 0.0188 0.0002 -0.378 -3.727
2 0.2094 0.01 0.0001 -0.679 -4
1 0.1047 0.0048 SE-OS -0.98 —4.317

Determination of average shear rate.

average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

R = consistency coefficient, Pa.s“n

k' = 4.47

average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )

( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)

Maximum torque= 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.3903 -0.759 -0.941 0.834
2 0.2094 0.936 0.9107 -0.066 -0.094 0.973
4 0.4188 1.8721 1.6913 0.627 0.5255 0.9035
8 0.8376 3.7441 3.3176 1.3202 1.1992 0.8861
16 1.6752 7.4882 6.4238 2.0133 1.86 0.8578
32 3.3504 14.976 12.604 2.7065 2.534 0.8416
64 6.7009 29.953 24.443 3.3996 3.1963 0.816

128 13.402 59.906 47.178 4.0928 3.8539 0.7875

256 26.803 119.81 84.582 4.7859 4.4377 0.706

512 53.607 239.62 43.226 5.4791 3.7664 0.1804

X Y

Regression Statistics

R Square 0.9558

Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 1.0246 Interce 0.0243 0.1998 0.1216 0.9059 —0.437 0.4851
x1 0.8516 0.0647 13.157 4E—07 0.7023 1.0008

83

    

 

13.- Mixer Viscometry, 35%, 33.945%, 65.4 9 corn syrup, T = 40°C, 22.2 g CaCO3 ?
rpm readings Average ;E
1 2.2 2.2 2.2 2.2 2.2 2.3 2.3 2.3 2.2375 ?§
2 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3:
4 5.5 5.6 5.5 5.6 5.6 5.5 5.6 5.5 5.55 é?
8 9.3 9.2 9.2 9.3 9.2 9.2 9.2 9.2 9.225 2—
16 16.3 16.2 16.3 16.3 16.3 16.3 16.4 16.3 16.3 2:7
32 29.2 29.2 29.2 29.2 29.2 29.1 29.2 29.1 29.175 5%,
64 52.7 52.7 52.8 52.8 52.7 52.7 52.8 52.8 52.75 ?Q
128 95.9 95.9 95.8 95.9 95.8 95.9 95.9 95.9 95.875
64 52.7 52.7 52.8 52.8 52.7 52.7 52.8 52.8 52.75
32 28.7 28.7 28.6 28.6 28.7 28.7 28.7 28.7 28.675
16 15.9 15.9 15.9 15.8 15.9 15.8 15.9 15.8 15.863
8 9.1 9 9 8.9 8.9 8.9 8.9 8.9 8.95
4 5.2 5.1 5.1 5.1 5.2 5.2 5.2 5.2 5.1625
2 3.1 3.1 3.1 3.1 3 3.1 3.1 3 3.075
1 2 2 1.9 1.9 1.9 1.9 1.9 1.9 1.925
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.032 0.0003 -0.98 -3.495
2 0.2094 0.05 0.0005 -0.679 -3.301
4 0.4188 0.0793 0.0008 -0.378 -3.101
8 0.8376 0.1318 0.0013 -0.077 -2.88
16 1.6752 0.2329 0.0023 0.2241 -2.633
32 3.3504 0.4168 0.0042 0.5251 -2.38
64 6.7009 0.7536 0.0075 0.8261 -2.123
128 13.402 1.3698 0.0137 1.1272 -1.863
64 6.7009 0.7536 0.0075 0.8261 -2.123
32 3.3504 0.4097 0.0041 0.5251 -2.388
16 1.6752 0.2266 0.0023 0.2241 -2.645
8 0.8376 0.1279 0.0013 -0.077 -2.893
4 0.4188 0.0738 0.0007 -0.378 -3.132
2 0.2094 0.0439 0.0004 —0.679 -3.357
1 0.1047 0.0275 0.0003 -0.98 -3.561
Determination of average shear rate.
average shear stress = 2 M / pi b d‘2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate
R = consistency coefficient, Pa.s‘n
k' = 4.47
average shear stress = 2 M / (pi d“3 * (b/d + 1/3) )
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque= 1.428716915 Nm (MM)
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 2.911 -0.759 1.0685 6.2199
2 0.2094 0.936 4.5535 -0.066 1.5159 4.8648
4 0.4188 1.8721 7.2206 0.627 1.9769 3.8571
8 0.8376 3.7441 12.002 1.3202 2.4851 3.2055
16 1.6752 7.4882 21.207 2.0133 3.0543 2.832
32 3.3504 14.976 37.957 2.7065 3.6365 2.5345
64 6.7009 29.953 68.628 3.3996 4.2287 2.2912
128 13.402 59.906 124.73 4.0928 4.8262 2.0822
256 26.803 119.81 68.628 4.7859 4.2287 0.5728
512 53.607 239.62 37.307 5.4791 3.6192 0.1557
X Y

Regression Statistics
R Square 0.8119
Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 5.9571 Interce 1.7846 0.2849 6.2644 0.0001 1.1276 2.4415
x1 0.5421 0.0923 5.8758 0.0002 0.3294 0.7549

l4.- Mixer Viscometry, 35%,

rpm

a)
H
QWQWQO‘QHQWQQUIQG

rad/s

omega

.1047
.2094
.4188
.8376
.6752
.3504
.7009
.402

.7009
.3504
.6752
.8376
.4188
.2094
.1047

H
0000Hh’0iUO‘UP—‘0000

readings
1.6
2.7 2
4.5 4
7.7 7
13.7 13
26 26
46.9 46
81.2 81
44.7 44
24.6 24
13.8 13
7.9 7
4.7 4
2.9 2
1.8 1
(N cm)
M
0.0229
0.038
0.0643
0.11
0.1963
0.3724
0.6674
1.1612
0.6376
0.3515
0.1972
0.1129
0.0671
0.0414
0.0259

1.

84

35%, 62.2 9 corn syrup,

QOQWOO‘GNQ QQMQO‘

h
at
00400010914 \IQLDQO‘

(N m)
M
.0002
.0004
.0006
.0011
.002
.0037
.0067
.0116
.0064
.0035
.002
.0011
.0007
.0004
.0003

000000000000000

log
-0.
-0
-0.
-0

0

0
0
1.
0
0
0.
-0.
-0.

-0
-0

a)
H
GOQOGQOUQHQQU‘QO‘

Om
98

.679

378

.077

.2241
.5251
.8261

1272

.8261
.5251

2241
077
378

.679
.98

Determination of average shear rate.
average shear stress =
average shear rate = 4.47 angular velocity

average app. viscosity

K = consistency coefficient, Pa.s“n
k‘ = 4.47
average shear stress = 2 M / (pi d‘3 (b/d
( b/d + 1/3) = 0.9831
s.stress = M 9106.2 ($d$108)
Maximum torque= 1.428716915 Nm (MM)
angular average average
velocit shear shear Lnshear Lnshear
rpm rad/s rate stress rate stress
1 0.1047 0.468 2.0816 -0.759 0.7331
2 0.2094 0.936 3.464 -0.066 1.2424
4 0.4188 1.8721 5.8546 0.627 1.7672
8 0.8376 3.7441 10.018 1.3202 2.3044
16 1.6752 7.4882 17.873 2.0133 2.8833
32 3.3504 14.976 33.908 2.7065 3.5236
64 6.7009 29.953 60.774 3.3996 4.1072
128 13.402 59.906 105.74 4.0928 4.661
256 26.803 119.81 58.058 4.7859 4.0614
512 53.607 239.62 32.005 5.4791 3.4659
X Y
Regression Statistics
R Square 0.8121
Observations 10
Coeffic Standar
K = 4.6503 Interce 1.5369 0.2978 5.1618
x1 0.567 0.0964 5.8794

2 M / pi b d‘2

shear stress / shear ra

lo
-3

-3.
-3.

-2
-2
-2
-2
-1
-2
-2
-2

-2.
-3.

—3
-3

H
00Q0000UOH0flm00

g M
.641

192
.959
.707
.429
.176
.935
.195
.454
.705
947
173
.383
.587

b
d

T:

te

+

0.0006
0.0002 0.3446

40.8°C, 21.
.6 1.6
.6 2.6
.5 4.5
.7 7.7
.8 13.8
.2 26.2
.6 46.6
.4 81.4
.6 44.6
.6 24.6
.8 13.8
.9 7.9
.7 4.7
.9 2.9
.9 1.8
0.02692 m
0.04143 m

1/3)

Sigma/
Gamma
viscos
Pa.s
.4478
.7007
.1273
.6756
.3868
.2641
.029
.7651
.4846
.1336

00HNNNNUU§

)

7 g CaCO3

Average

1.6

2.6625

4.5

7.7
13.738
26.063
46.713
81.275
44.625

6
8
.9
7
9
8

125

t Stati P—value Lower 95% Upper 95%
0.8503

2.2235
0.7894

 

85

15.- Mixer Viscometry, 35%, 34.96%, 65.5 9 corn syrup, T = 40.8°C, 22.9 g CaCO3

rpm readings Average
1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
2 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8
4 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8
8 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3
16 14.7 14.7 14.7 14.8 14.8 14.7 14.7 14.7 14.725
32 25.9 26 26 26 26.1 26 1 26.2 26.2 26.063
64 46.8 46.9 46.8 46.7 46.7 46 6 46.6 46.6 46.713
128 84.9 85 85 85 85 84 9 84.9 84.8 84.938
64 46.8 46.7 46.7 46.6 46.6 46 6 46.5 46.5 46.625
32 25.6 25.6 25.6 25.6 25.6 25 6 25.6 25.8 25.625
16 14.4 14.4 14.4 14.4 14.4 14.4 14.4 14.4 14.4
8 8.2 8.2 8.2 8.2 8.3 8.2 8.3 8.3 8.2375
4 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9
2 3 3 3 3 3 3 3 3 3
1 2 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9125
rad/s (N cm) (N m)
rpm omega M M log Om log M
1 0.1047 0.0243 0.0002 -0.98 —3.615
2 0.2094 0.04 0.0004 -0.679 —3.398
4 0.4188 0.0686 0.0007 —0.378 -3.164
8 0.8376 0.1186 0.0012 -0.077 -2.926
16 1.6752 0.2104 0.0021 0.2241 -2.677
32 3.3504 0.3724 0.0037 0.5251 -2.429
64 6.7009 0.6674 0.0067 0.8261 -2.176
128 13.402 1.2135 0.0121 1.1272 -1.916
64 6.7009 0.6661 0.0067 0.8261 -2.176
32 3.3504 0.3661 0.0037 0.5251 —2.436
16 1.6752 0.2057 0.0021 0.2241 -2.687
8 0.8376 0.1177 0.0012 -0.077 -2.929
4 0.4188 0.07 0.0007 -0.378 -3.155
2 0.2094 0.0429 0.0004 -0.679 -3.368
1 0.1047 0.0273 0.0003 -0.98 -3.563
Determination of average shear rate.
average shear stress = 2 M / pi b d“2 b = 0.02692 m
average shear rate = 4.47 angular velocity d = 0.04143 m
average app. viscosity = shear stress / shear rate

R = consistency coefficient, Pa.s“n

k' = 4.47
average shear stress = 2 M / (pi 6‘3 ‘ (b/d + 1/3) )
( b/d + 1/3) = 0.9831

s.stress = M 9106.2 ($d$108)
Maximum torque= 1.428716915 Nm (MM)

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 2.2117 -0.759 0.7938 4.7258
2 0.2094 0.936 3.6428 -0.066 1.2928 3.8918
4 0.4188 1.8721 6.2449 0.627 1.8318 3.3358
8 0.8376 3.7441 10.798 1.3202 2.3794 2.8841
16 1.6752 7.4882 19.157 2.0133 2.9527 2.5583
32 3.3504 14.976 33.908 2.7065 3.5236 2.2641
64 6.7009 29.953 60.774 3.3996 4.1072 2.029
128 13.402 59.906 110.5 4.0928 4.7051 1.8446
256 26.803 119.81 60.66 4.7859 4.1053 0.5063
512 53.607 239.62 33.338 5.4791 3.5067 0.1391
X Y

Regression Statistics
R Square 0.814
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 4.9264 Interce 1.5946 0.293 5.4419 0.0004 0.9189 2.2703
x1 0.5616 0.0949 5.917 0 0002 0.3427 0.7804

 

XI. APPENDIX 5. CALCULATIONS TO FIT THE GLOBAL MODEL.

These calculations were used to fit a model using the values coming from the three different
temperatures.

MIX40-1.WK1

1n 40-0-1 ln
sstres sstress k lnk T 1/T C srate srate
0.2277 ~1.48 0.3071 -l.181 313.15 0.0032 0 0.468 —0.759
0.2927 -1.229 0.3071 -1.181 313.15 0.0032 0 0.936 -0.066
0.5204 -0.653 0.3071 -1.181 313.15 0.0032 0 1.8721 0.627
0.8782 -0.13 0.3071 -1.181 313.15 0.0032 0 3.7441 1.3202
1.7238 0.5446 0.3071 -1.181 313.15 0.0032 0 7.4882 2.0133
3.4314 1.233 0.3071 -1.181 313.15 0.0032 0 14.976 2.7065
6.9279 1.9356 0.3071 -1.181 313.15 0.0032 0 29.953 3.3996
14.149 2.6496 0.3071 -1.181 313.15 0.0032 0 59.906 4.0928
30.509 3.418 0.3071 -1.181 313.15 0.0032 0 119.81 4.7859
69.718 4.2445 0.3071 -1.181 313.15 0.0032 0 239.62 5.4791
In 40—0-2 1n
sstres sstress k lnk T l/T C srate srate
0.0325 -3.426 0.1311 -2.032 313.15 0.0032 0 0.468 -0.759
0.1301 -2.039 0.1311 -2.032 313.15 0.0032 0 0.936 -0.066
0.3415 -1.074 0.1311 -2.032 313.15 0.0032 0 1.8721 0.627
0.7806 -0.248 0.1311 -2.032 313.15 0.0032 0 3.7441 1.3202
1.6425 0.4962 0.1311 -2.032 313.15 0.0032 0 7.4882 2.0133
3.3338 1.2041 0.1311 —2.032 313.15 0.0032 0 14.976 2.7065
6.8466 1.9238 0.1311 -2.032 313.15 0.0032 0 29.953 3.3996
14.116 2.6473 0.1311 -2.032 313.15 0.0032 0 59.906 4.0928
30.574 3.4201 0.1311 —2.032 313.15 0.0032 0 119.81 4.7859
70.076 4.2496 0.1311 -2.032 313.15 0.0032 0 239.62 5.4791
In 40—0-3 ln
sstres sstress k lnk T 1/T C srate srate
0.1626 -1.816 0.2798 -1.274 313.15 0.0032 0 0.468 ~0.759
0.2602 ~1.346 0.2798 -1.274 313.15 0.0032 0 0.936 -0.066
0.5204 -0.653 0.2798 —1.274 313.15 0.0032 0 1.8721 0.627
0.9595 -0.041 0.2798 -1.274 313.15 0.0032 0 3.7441 1.3202
1.7889 0.5816 0.2798 -1.274 313.15 0.0032 0 7.4882 2.0133
3.3826 1.2187 0.2798 -1.274 313.15 0.0032 0 14.976 2.7065
6.8954 1.9309 0.2798 -1.274 313.15 0.0032 0 29.953 3.3996
14.311 2.661 0.2798 -1.274 313.15 0.0032 0 59.906 4.0928
31.224 3.4412 0.2798 -1.274 313.15 0.0032 0 119.81 4.7859
71.149 4.2648 0.2798 —1.274 313.15 0.0032 0 239.62 5.4791
In 40-5-1 1n
sstres sstress k lnk T 1/T C srate srate
0.1301 -2.039 0.2745 -1.293 313.15 0.0032 5 0.468 -0.759
0.2602 -1.346 0.2745 -1.293 313.15 0.0032 5 0.936 -0.066
0.5204 -0.653 0.2745 -1.293 313.15 0.0032 5 1.8721 0.627
1.0408 0.04 0.2745 -1.293 313.15 0.0032 5 3.7441 1.3202
2.0816 0.7331 0.2745 -1.293 313.15 0.0032 5 7.4882 2.0133
4.2771 1.4533 0.2745 -1.293 313.15 0.0032 5 14.976 2.7065
8.6843 2.1615 0.2745 -1.293 313.15 0.0032 5 29.953 3.3996
17.531 2.864 0.2745 -1.293 313.15 0.0032 5 59.906 4.0928
36.949 3.6095 0.2745 -1.293 313.15 0.0032 5 119.81 4.7859
76.223 4.3337 0.2745 -1.293 313.15 0.0032 5 239.62 5.4791
ln 40-5-2 ln
sstres sstress k lnk T 1/T C srate srate
0.1301 -2.039 0.4502 -0.798 313.15 0.0032 5 0.468 -0.759
0.4066 -0.9 0.4502 —0.798 313.15 0.0032 5 0.936 -0.066
0.9107 -0.094 0.4502 -0.798 313.15 0.0032 5 1.8721 0.627
1.8214 0.5996 0.4502 -0.798 313.15 0.0032 5 3.7441 1.3202
3.903 1.3618 0.4502 —0.798 313.15 0.0032 5 7.4882 2.0133
8.1964 2.1037 0.4502 -0.798 313.15 0.0032 5 14.976 2.7065
17.173 2.8434 0.4502 —0.798 313.15 0.0032 5 29.953 3.3996
36.282 3.5913 0.4502 -0.798 313.15 0.0032 5 59.906 4.0928
76.679 4.3396 0.4502 -0.798 313.15 0.0032 5 119.81 4.7859
36.689 3.6025 0.4502 -0.798 313.15 0.0032 5 239.62 5.4791
In 40-5-3 1n
sstres sstress k lnk T l/T C srate srate
0 ERR 0.1453 ~1.929 313.15 0.0032 5 0.468 -0.759
0.1301 -2.039 0.1453 —1.929 313.15 0.0032 5 0.936 —0.066
0.2439 —1.411 0.1453 -1.929 313.15 0.0032 5 1.8721 0.627
0.7481 -0.29 0.1453 -1.929 313.15 0.0032 5 3.7441 1.3202
1.6588 0.5061 0.1453 -1.929 313.15 0.0032 5 7.4882 2.0133
3.7079 1.3105 0.1453 -1.929 313.15 0.0032 5 14.976 2.7065
7.8874 2.0653 0.1453 -1.929 313.15 0.0032 5 29.953 3.3996
16.653 2.8126 0.1453 -1.929 313.15 0.0032 5 59.906 4.0928
35.436 3.5677 0.1453 -1.929 313.15 0.0032 5 119.81 4.7859
75.654 4.3262 0.1453 -1.929 313.15 0.0032 5 239.62 5.4791

sstres

deP‘OCDC)

13
26
51.
97.

.1626
.3903
.8294
.6913
.3338
.6352
.27
.346

65
478

sstres

.1301
.309
.7806
.5612
.2363
.6352
.368
.671
.732
.38

sstres

QLJL)HC30

13
27.
55.
101.

.6505
.8457
.301

.0816
.7729
.8954
.709

549
179
93

sstres

.301
.9515
.1224
.2528
.6275
.344
.672
.189
.1
.043

sstres

0

3
6.
12
23.
45.
87

.2602
.6505
.4799
.0736

1148

.099

678
926

.038
44.

918

sstres

.6017
.0408
.9515
.6428
.8466
.319
.63
.211
.965
.747

In
sstress
-1.816
-0.941
-0.187
0.5255
1.2041
.8924
.5855
.2713
.9445
.5796

#LJUJNF‘

sstress
-2.039
-1.174
-0.248
0.4455
.1744
.8924
.5929
.2836
.984
.6189

DLUUJNF‘F‘

1n
sstress
-0.43
—0.168
0.2631
0.7331
.3279
.9309
.6181
.316
.0106
.6243

pauwpp

1n
sstress
.2631
.6686
.1386
.6588
.2646
.9093
.5459
.1925
.8371
.1903

#lbédd83Ntdh‘OCD

1n
sstress
-1.346
-0.43
0.392
1.1229
.8107
.4932
.1646
.827
.4663
.8048

OJDJALMKJH

1n
sstress
-0.508
0.04
0.6686
.2928
.9238
.5892
.2438
.8961
.5214
.8659

UJOIHUJNF‘H

0-15-1

.4123
.4123
.4123
.4123
.4123
.4123
.4123
.4123
.4123
.4123

0-15-2

Xib C30<30C30C30C307Vh

.3532
.3532
.3532
.3532
.3532
.3532
.3532
.3532
.3532
.3532

0-15-3

.8491
.8491
.8491
.8491
.8491
.8491
.8491
.8491
.8491
.8491

0-25-1

.2041
.2041
.2041
.2041
.2041
.2041
.2041
.2041
.2041
.2041

0-25-2

.796
.796
.796
.796
.796
.796
.796
.796
.796
.796

0-25-3

.254
.254
.254
.254
.254
.254
.254
.254
.254
.254

HHHHHHHHHHxa ooooooooooxa NNMNNNNNNNXA ooooooooooxn 0000000000

.886
.886
.886
.886
.886
.886
.886
.886
.886
.886

lnk

-1
-1
-1

-1.

-1
-1
-1
-1
-1
-1

1n

-0.
-0.
-0.
-0.
-0.
-0.
-0.
-O.
-0.
-0.

0¢DC>0<DC30¢DC>0

-0.

-0

-0.
-0.

-0
-0
-0
-0
-0
-0

0(3C>0<DC)0<DC>0

.041
.041
.041
041
.041
.041
.041
.041
.041
.041

k

164
164
164
164
164
164
164
164
164
164

.7903
.7903
.7903
.7903
.7903
.7903
.7903
.7903
.7903
.7903

228
.228
228
228
.228
.228
.228
.228
.228
.228

.2263
.2263
.2263
.2263
.2263
.2263
.2263
.2263
.2263
.2263

T
313.
313.
313.
313.
313.
313.
313.
313.
313.
313.

313.
313.
313.
313.
313.
313.
313.
313.
313.
313.

313.
313.
313.
313.
313.
313.
313.
313.
313.
313.

313.
313.
313.
313.
313.
313.
313.
313.
313.
313.

313

313.
313.
313.
313.
313.
313.
313.
313.
313.

313.
313.
313.
313.
313.
313.
313.
313.
313.
313.

15
15
15
15
15
15
15
15
15
15

.15

15
15
15
15
15
15
15
15
15

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0¢3C>043C>0<3C>0

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0<3C>0<3C>0<3C>0

1/T

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0<3C>0C3C>0<DC>0

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0<DC>0<3C>0<3C>0

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0<3C>0<DC>0<3C>0

.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032
.0032

0CDC>0<DC>0CDC>0

srate

.468
.936
.8721
.7441
.4882
.976
.953
.906
.81
.62

srate

.468
.936
.8721
.7441
.4882
.976
.953
.906

.62

srate

119

239.

.468
.936
.8721
.7441
.4882
.976
.953
.906
.81

62

srate

.468
.936
.8721
.7441
.4882
.976
.953
.906
119.
239.

81
62

srate

119
239

.468
.936
.8721
.7441
.4882
.976
.953
.906
.81
.62

srate

.468
.936
.8721
.7441
.4882
.976
.953
.906
.81
.62

srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

(”@bbtdk>NP*C>

srate
-0.759
-0.066
0.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

Lflfibhtflkle‘

1n
srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

LflfiHhUJNIOF‘O

1n
srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

Ifl‘bbcthNhi0

1n
srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

Ln#uthN!0F‘0

srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

WlbhlthNFJC

 

88
In 40-25-4 1n
sstres sstress k lnk T 1/T C srate srate
0.3903 -0.941 1.0245 0.0242 313.15 0.0032 25 0.468 -0.759
0.9107 -0.094 1.0245 0.0242 313.15 0.0032 25 0.936 -0.066
1.6913 0.5255 1.0245 0.0242 313.15 0.0032 25 1.8721 0 627
3.3176 1.1992 1.0245 0.0242 313.15 0.0032 25 3.7441 1.3202
6.4238 1.86 1.0245 0.0242 313.15 0.0032 25 7.4882 2.0133
12.604 2.534 1.0245 0.0242 313.15 0.0032 25 14.976 2.7065
24.443 3.1963 1.0245 0.0242 313.15 0.0032 25 29.953 3.3996
47.178 3.8539 1.0245 0.0242 313.15 0.0032 25 59.906 4.0928
84.582 4.4377 1.0245 0.0242 313.15 0.0032 25 119.81 4.7859
43.226 3.7664 1.0245 0.0242 313.15 0.0032 25 239.62 5.4791
In 40-35-1 1n
sstres sstress k lnk T 1/T C srate srate
2.911 1.0685 5.9571 1.7846 313.15 0.0032 35 0.468 -0.759
4.5535 1.5159 5.9571 1.7846 313.15 0.0032 35 0.936 -0.066
7.2206 1.9769 5.9571 1.7846 313.15 0.0032 35 1.8721 0.627
12.002 2.4851 5.9571 1.7846 313.15 0.0032 35 3.7441 1.3202
21.207 3.0543 5.9571 1.7846 313.15 0.0032 35 7.4882 2.0133
37.957 3.6365 5.9571 1.7846 313.15 0.0032 35 14.976 2.7065
68.628 4.2287 5.9571 1.7846 313.15 0.0032 35 29.953 3.3996
124.73 4.8262 5.9571 1.7846 313.15 0.0032 35 59.906 4.0928
68.628 4.2287 5.9571 1.7846 313.15 0.0032 35 119.81 4.7859
37.307 3.6192 5.9571 1.7846 313.15 0.0032 35 239.62 5.4791 ;
ln 40-35-2 1n
sstres stress k lnk T 1/T C srate srate } J
2.0816 0.7331 4.6503 1.5369 313.15 0.0032 35 0.468 -0.759
3.464 1.2424 4.6503 1.5369 313.15 0.0032 35 0.936 -0.066
5.8546 1.7672 4.6503 1.5369 313.15 0.0032 35 1.8721 0.627
10 018 2.3044 4.6503 1.5369 313.15 0.0032 35 3.7441 1.3202
17.873 2.8833 4.6503 1.5369 313.15 0.0032 35 7.4882 2.0133
33.908 3.5236 4.6503 1.5369 313.15 0.0032 35 14.976 2.7065
60.774 4.1072 4.6503 1.5369 313.15 0.0032 35 29.953 3.3996
105.74 4.661 4.6503 1.5369 313.15 0.0032 35 59.906 4.0928
58.058 4.0614 4.6503 1.5369 313.15 0.0032 35 119.81 4.7859
32.005 3.4659 4.6503 1.5369 313.15 0.0032 35 239.62 5.4791
in 40-35-3 ln
sstres sstress k lnk T 1/T C srate srate
2.2117 0.7938 4.9264 1.5946 313.15 0.0032 35 0.468 -0.759
3.6428 1.2928 4.9264 1.5946 313.15 0.0032 35 0.936 —0.066
6.2449 1.8318 4.9264 1.5946 313.15 0.0032 35 1.8721 0.627
10.798 2.3794 4.9264 1.5946 313.15 0.0032 35 3.7441 1.3202
19.157 2.9527 4.9264 1.5946 313.15 0.0032 35 7.4882 2.0133
33.908 3.5236 4.9264 1.5946 313.15 0.0032 35 14.976 2.7065
60.774 4.1072 4.9264 1.5946 313.15 0.0032 35 29.953 3.3996
110.5 4.7051 4.9264 1.5946 313.15 0.0032 35 59.906 4.0928
60.66 4.1053 4.9264 1.5946 313.15 0.0032 35 119.81 4.7859
33.338 3.5067 4.9264 1.5946 313.15 0.0032 35 239.62 5.4791

 

XII. APPENDIX 6. MEASUREMENTS PERFORNIED AT 55°C.

1.- Mixer Viscometry, 0%, 0%, 0 9 corn syrup, T = 55°C.

rpm readings Average
1 0.1 0 0.1 0.1 0.1 0.1 0 0.1 0.075
2 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1125
4 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.1875
8 0.3 0.2 3.3 0.3 0.2 0.3 0.3 0.3 0.2375
16 0.5 0.6 0.5 0.6 0.5 0.5 0.6 0.5 0.5375
32 1 1 1 1 1 1 1 1 1
64 2.2 2.1 2.2 2.1 2.1 2.1 2.1 2.1 2.125
128 4.7 4.8 4.7 4.7 4.7 4.7 4.7 4.7 4.7125
256 11.7 11.7 11.6 11.7 11.7 11.7 11.7 11.7 11.687
512 33.1 33.1 33.1 33.1 33.1 33.1 33 33 33.075
256 11.6 11.6 11.6 11.6 11.6 11.7 11.6 11.6 11.612
128 4.7 4.7 4.7 4.7 4.7 4.7 4.6 4.7 4.6875
64 2.1 2.1 2.1 2.1 2.1 2.1 2 2.1 2.0875
32 1 1 1 1 1 1 1 1 1
16 0.6 0.5 0.6 0.5 0.5 0.6 0.5 0.6 0.55
8 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.1 0.2 0.1 0.1 0.1 0.1 0.2 0.1 0.125
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0011 lE-OS -0.98 —4.97
2 0.2094 0.0016 zE-OS —0.679 -4.794
4 0.4188 0.0027 3E—05 -0.378 -4.572
8 0.8376 0.0034 3E-05 —0.077 -4.469
16 1.6752 0.0077 8E-05 0.2241 -4.115
32 3.3504 0.0143 0.0001 0.5251 -3.845
64 6.7008 0.0304 0.0003 0.8261 -3.518
128 13.402 0.0673 0.0007 1.1272 -3.172
256 26.803 0.167 0.0017 1.4282 -2.777
512 53.606 0.4725 0.0047 1.7292 -2.326
256 26.803 0.1659 0.0017 1.4282 -2.78
128 13.402 0.067 0.0007 1.1272 -3.174
64 6.7008 0.0298 0.0003 0.8261 -3.525
32 3.3504 0.0143 0.0001 0.5251 -3.845
16 1.6752 0.0079 8E—05 0.2241 —4.105
8 0.8376 0.0043 48-05 -0.077 -4.368
4 0.4188 0.0029 3E-05 -0.378 -4.544
2 0.2094 0.0018 ZE-OS -0.679 -4.748
1 0.1047 0.0014 1E-05 -0.98 —4.845
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k’ 4.47
K = consistency coefficient, Pa.s“n
average shear stress = 2 M l ( ( pi d‘3*
b/d + 1/3 = 0.9831
shear stress: M 9106.2 Se$103
angular average average
velocit shear shear Lnshear
rpm rad/s rate stress rate
1 0.1047 0.468 0.0976 —0.759
2 0.2094 0.936 0.1464 -0.066
4 0.4188 1.872 0.2439 0.627
8 0.8376 3.7441 0.309 1.3202
16 1.6752 7.4881 0.6993 2.0133
32 3.3504 14.976 1.301 2.7065
64 6.7008 29.953 2.7647 3.3996
128 13.402 59.905 6.131 4.0928
256 26.803 119.81 15.206 4.7859
512 53.606 239.62 43.031 5.4791
X

Regression Statistics
R Square 0.9761
Observations 10

Coeffic St
0.1295 Interce -2.044 0.
0.9672 x1 0.9672 0.

x
u u

andar t Stati P-value Lower 95% Upper 95%
1651 -12.38
0535 18.089

(b/d + 1/3) ) )

Lnshear
stress
-2.327
-1.922
-1.411
«1.174
-0.358
.2631
.0169
.8134
.7217
.7619

UNHHO

89

63-07
2E-08

Sigma/
Gamma
viscos

.2085
.1564
.1303
.0825
.0934
.0869
.0923
.1023
.1269
.1796

0000000000

-2.425
0.8439

-l.663
1.0905

. h— a..—

 

Mixer Viscometry,

rpm

HUH
oo OOHNbHUHhNHOOOOO
ww quwmm HabNHH

Hid

rad/s
omega
0.1047
0.2094
0.4188
0.8376
1.6752
3.3504
6.7008
13.402
26.803
53.606
26.803
13.402
6.7008
3.3504
1.6752
0.8376
0.4188
0.2094
0.1047

\IGHO‘O‘H QbNNH

HHNUU‘

(N cm)
M

.0014
.002

.0029
.0129
.0091
.0146
.0291
.0659
.1666
.4722
.1666
.0668
.0295
.0141
.0075
.0043
.0029
.0016
.0014

0000000000000000000

O‘DNHH

thh‘
00000HNDHWH§NH00000

HNNWQ HO‘N‘ ~10.

ONO-#00000

quwuawwuawww

HHNUU‘I

0%, 9 corn syrup, T =

bNt-‘00000
HHNDJU'IVDHQOH‘JO‘H O‘DNNH

wt»
hiH

H
OOOOOONbH

Log Om
-0.98
.679
.378
.077
.2241
.5251
.8261
.1272
.4282
.7292
.4282
.1272
.8261
.5251
.2241
—0.077
-0.378
—O.679
-0.98

I I I
000HHHHH000000

Determination of average shear rate
average shear rate = 4.47 angular velocity
average apparent viscosity = shear stress/ shear

k' 4.47
K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( Di d‘3*
b/d + 1/3 = 0.9831
shear stress: M 9106.2 $e$103
angular average average
velocit shear shear Lnshear

rpm rad/s rate stress rate

1 0.1047 0.468 0.1301 -0.759

2 0.2094 0.936 0.1789 ~0.066

4 0.4188 1.872 0.2602 0.627

8 0.8376 3.7441 1.1709 1.3202

16 1.6752 7.4881 0.8294 2.0133

32 3.3504 14.976 1.3335 2.7065

64 6.7008 29.953 2.6508 3.3996
128 13.402 59.905 6.0009 4.0928
256 26.803 119.81 15.173 4.7859
512 53.606 239.62 42.999 5.4791

x
Regression Statistics
R Square 0.9581
Observations 10
Coeffic

K = 0.1896 Interce -1.663 0.2033 -8.
n = 0.891 x1 0.891 0.0659 13.

9O

55°C

thh‘
HCJF‘DOOF‘OCDCJOCD
Htaaawtn H-J~J 4hd\ ~Jb!0k*H

00000HNfi

Log M
-4.845
-4.707
-4.544
-3.891
-4.041
-3.834
—3.536
~3.181
-2.778
-2.326
-2.778
-3.175
-3.531
-3.851
-4.125
-4.368
-4.544
-4.794
-4.845

P‘w
Ht»

H
HbNI—‘OOOOO

00000HNA
HHNUO‘

O‘hNNH

‘10

thb*
Htura

d:

(b/d + 1/3) ) )

Lnshear
stress
-2.039
-1.721
-1.346
0.1578
—0.187
.2878
.9749
.7919
.7195
.7612

WNHOO

Sigma/
Gamma
viscos
Pa.s
0.278
0.1911
0.139
0.3127
0.1108
0.089
0.0885
0.1002
0.1266
0.1794

00000HN|§

DNH00000

HHNUU’I Hum ~14

O‘fiNHH

-2.132
0.7392

Average

.1375

.6375
.025
.0375
.6125
.662
33.05
11.662
.675
.0625
.9875
.525

H
HhND—‘00000

.1125

000000N0

0.02692 m
0.04143 m

Standar t Stati P-value Lower 95% Upper 95%
178 28-05
531 3E-07

-1.194
1.0429

 

91

Mixer Viscometry, 0%, 65.4 9 corn syrup, T = 55°C
rpm readings

1 0.1 0.1 0.1 0.1 0.1 0.1

2 0.2 0.1 0.2 0.2 0.1 0.1

4 0.2 0.2 0.2 0.2 0.2 0.2

8 0.3 0.4 0.3 0.4 0.3 0.4

16 0.7 0.6 0.6 0.6 0.6 0.6

32 1 1 1 1 1 1

64 2.1 2.1 2 2 2.1 2
128 4.6 4.6 4.7 4.6 4.5 4.6
256 11.5 11.5 11.6 11.5 11.5 11.5 1
512 32.8 32.8 32.7 32.8 32.8 32.8 3
256 11.5 11.5 11.6 11.5 11.5 11.5 1
128 4.6 4.6 4.7 4.6 4.6 4.7

64 2 2.1 2 2.1 2 2.1

32 1 1 1 1 1 1

16 0.6 0.5 0.5 0.5 0.5 0.5

8 0.3 0.4 0.3 0.3 0.3 0.3

4 0.2 0.1 0.2 0.2 0.1 0.2

2 0.1 0.1 0.1 0.1 0.1 0.1

1 0.1 0.1 0.1 0.1 0.1 0.1

rad/s (N cm) (N m)
rpm omega M M Log Om Log M

1 0.1047 0.0014 lE-OS -0.98 -4.845

2 0.2094 0.0021 ZE-OS -0.679 -4.669

4 0.4188 0.0029 38-05 -0.378 -4.544

8 0.8376 0.005 58-05 -0.077 -4.301

16 1.6752 0.0088 9E-05 0.2241 -4.058

32 3.3504 0.0143 0.0001 0.5251 —3.845

64 6.7008 0.0293 0.0003 0.8261 -3.533

128 13.402 0.0657 0.0007 1.1272 -3.182

256 26.803 0.1645 0.0016 1.4282 -2.784
512 53.606 0.4683 0.0047 1.7292 -2.33

256 26.803 0.1647 0.0016 1.4282 ~2.783
128 13.402 0.0661 0.0007 1.1272 -3.18

64 6.7008 0.0291 0.0003 0.8261 -3.536

32 3.3504 0.0143 0.0001 0.5251 -3.845

16 1.6752 0.0073 7E-05 0.2241 -4.135
8 0.8376 0.0045 4E-05 -0.077 -4.35

4 0.4188 0.0023 23—05 -0.378 -4.634

2 0.2094 0.0014 lE-OS -0.679 -4.845

1 0.1047 0.0014 13-05 -0.98 -4.845

Determination of average shear rate

average shear rate = 4.47 angular velocity
average apparent viscosity = shear stress/ shear
k’ = 4.47

K = consistency coefficient, Pa.s“n

H

NHIbND-‘00000

00000HND

.1 0.
.2 0.
2 0.
3 0.
6 0.

1
1 2
6 4.
.5 11.
.7 32
.5 11
6 4.

2

1
5 0.
3 0.
1 0.
1 0.
1 0.

b:
d:

average shear stress = 2 M I ( ( pi d‘3* (b/d + 1/3) ) )

b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
angular average average
velocit shear shear Lnshear Lnshear
rpm rad/s rate stress rate stress
1 0.1047 0.468 0.1301 -0.759 —2.039
2 0.2094 0.936 0.1952 -0.066 -1.634
4 0.4188 1.872 0.2602 0.627 -1.346
8 0.8376 3.7441 0.4554 1.3202 -0.787
16 1.6752 7.4881 0.7969 2.0133 -0.227
32 3.3504 14.976 1.301 2.7065 0.2631
64 6.7008 29.953 2.6671 3.3996 0.981
128 13.402 59.905 5.9847 4.0928 1.7892
256 26.803 119.81 14.978 4.7859 2.7066
512 53.606 239.62 42.641 5.4791 3.7528
X Y
Regression Statistics
R Square 0.9706

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.1653 Interce —1.8 0.1726 —10.43 3E—06
= 0.9092 x1 0.9092 0.0559 16.262 68-08

Sigma/
Gamma
viscos
Pa.s
.278
.2085
.139
.1216
.1064
.0869
.089
.0999
.125
.178

0000000000

mmmmm

O‘hND—‘H

HHNwU‘

~2.l98
0.7803

Average
.1

.15

.2

.35
.6125

.05
.6
.513
.775
.525
.625
.0375

.5125
.3125
.1625
.1
.1

F‘U3H
OOOOOHNhHNHhNHOOOOO

0.02692 m
0.04143 m

-1.402
1.0381

 

92

Mixer Viscometry, 5%, 4.9685%, 74.67 9 corn syrup, Tue, fe, T = 40°C, 3.71 g CaCO3

rpm readings Average

1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

2 0.6 0.6 0.5 0.6 0.6 0.6 0.6 0.5 0.575

4 0.6 0.7 0.7 0.6 0.6 0.6 0.6 0.7 0.6375

8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

16 1 1 1 1 1 1 1 1 1

32 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

64 2.9 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.725
128 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7 5.7
256 13.8 13.8 13.7 13.7 13.7 13.7 13.7 13.7 13.725
512 38 38 38 38 38 38 38.1 38.1 38.025
256 13.7 13.7 13.7 13.7 13.7 13.7 13.7 13.7 13.7
128 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8

64 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.7

32 1.4 1.5 1.4 1.5 1.4 1.5 1.5 1.4 1.45

16 0.9 0.9 0.8 0.9 0.8 0.9 0.8 0.9 0.8625

8 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6

4 0.5 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.425

2 0.4 0.4 0.4 0.3 0.4 0.3 0.4 0.3 0.3625

1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

rad/s (N cm) (N m)
rpm omega M M Log Om Log M

1 0.1047 0.0071 7E-05 -0.98 -4.146

2 0.2094 0.0082 8E-05 -0.679 -4.085

4 0.4188 0.0091 9E-05 -0.378 -4.041

8 0.8376 0.0114 0.0001 -0.077 —3.942

16 1.6752 0.0143 0.0001 0.2241 -3.845

32 3.3504 0.0214 0.0002 0.5251 -3.669
64 6.7008 0.0389 0.0004 0.8261 -3.41

128 13.402 0.0814 0.0008 1.1272 -3.089

256 26.803 0.1961 0.002 1.4282 -2.708

512 53.606 0.5433 0.0054 1.7292 —2.265

256 26.803 0.1957 0.002 1.4282 -2.708

128 13.402 0.0829 0.0008 1.1272 -3.082

64 6.7008 0.0386 0.0004 0.8261 -3.414

32 3.3504 0.0207 0.0002 0.5251 -3.684

16 1.6752 0.0123 0.0001 0.2241 -3.909

8 0.8376 0.0086 9E—05 -0.077 —4.067

4 0.4188 0.0061 6E-05 -0.378 -4.217

2 0.2094 0.0052 SE-OS -0.679 -4.286

1 0.1047 0.0043 4E-05 -0.98 -4.368

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d‘3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.6505 -0.759 -0.43 1.3899
2 0.2094 0.936 0.7481 ~0.066 —0.29 0.7992
4 0.4188 1.872 0.8294 0.627 -0.187 0.443
8 0.8376 3.7441 1.0408 1.3202 0.04 0.278
16 1.6752 7.4881 1.301 2.0133 0.2631 0.1737
32 3.3504 14.976 1.9515 2.7065 0.6686 0.1303
64 6.7008 29.953 3.5453 3.3996 1.2656 0.1184
128 13.402 59.905 7.4158 4.0928 2.0036 0.1238
256 26.803 119.81 17.856 4.7859 2.8824 0.149
512 53.606 239.62 49.471 5.4791 3.9014 0.2065
X Y
Regression Statistics
R Square 0.8924

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.5706 Interce -0.561 0.2527 -2.221 0.0535 -1.144 0.0215
0.6665 x1 0.6665 0.0818 8.1447 28—05 0.4778 0.8552

:3
II II

93

Mixer Viscometry, 5%, 5.0342%, 71.71 g corn syrup, T = 40°C, 3.61 g CaCO3

rpm readings Average
1 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
4 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667
8 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
16 0.6 0.6 0.6 0.6 0.5 0.5 0.6 0.6 0.575
32 1.2 1.1 1 2 1.1 1.2 1.1 1.2 1.1 1.15
64 2.4 2.4 2 4 2.4 2.4 2.4 2.4 2.4 2.4
128 5.4 5.3 5.4 5.3 5.4 5.3 5.3 5.3 5.3375
256 13.1 13.2 13.1 13.2 13.1 13.21 13.2 13.1 13.151
512 37.1 37.1 37.2 37.1 37.1 37.2 37.1 37.1 37.125
256 13.1 13.2 13.1 13.2 13.1 13.2 13.1 13.2 13.15
128 5.4 5.4 5.3 5.4 5.4 5.4 5.3 5.4 5.375
64 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
32 1.1 1.1 1.2 1.1 1.2 1.2 1.1 1.2 1.15
16 0.6 0.6 0.5 0.6 0.5 0.6 0.6 0.6 0.575
8 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.2875
4 0.1 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.15
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667
omega (N cm) (N m)
rpm rad/s M M Log Om Log M
1 0.1047 0.001 lE-OS -0.98 —5.021
2 0.2094 0.0014 lE-OS —0.679 —4.845
4 0.4188 0.0024 2E-05 -0.378 -4.623
8 0.8376 0.0043 4E-05 -0.077 -4.368
16 1.6752 0.0082 8E—05 0.2241 -4.085
32 3.3504 0.0164 0.0002 0.5251 -3.784
64 6.7008 0.0343 0.0003 0.8261 —3.465
128 13.402 0.0763 0.0008 1.1272 -3.118
256 26.803 0.1879 0.0019 1.4282 -2.726
512 53.606 0.5304 0.0053 1.7292 -2.275
256 26.803 0.1879 0.0019 1.4282 -2.726
128 13.402 0.0768 0.0008 1.1272 -3.115
64 6.7008 0.0343 0.0003 0.8261 -3.465
32 3.3504 0.0164 0.0002 0.5251 -3.784
16 1.6752 0.0082 8E-05 0.2241 -4.085
8 0.8376 0.0041 4E—05 —0.077 -4.386
4 0.4188 0.0021 28-05 -0.378 -4.669
2 0.2094 0.0014 lE-OS -0.679 -4.845
1 0.1047 0.001 lE-OS -0.98 -5.021
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47

K = consistency coefficient, Pa.s‘n

average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.0867 -0.759 -2.445 0.1853
2 0.2094 0.936 0.1301 -0.066 -2.039 0.139
4 0.4188 1.872 0.2168 0.627 -1.529 0.1158
8 0.8376 3.7441 0.3903 1.3202 -0.941 0.1042
16 1.6752 7.4881 0.7481 2.0133 -0.29 0.0999
32 3.3504 14.976 1.4962 2.7065 0.4029 0.0999
64 6.7008 29.953 3.1224 3.3996 1.1386 0.1042
128 13.402 59.905 6.9442 4.0928 1.9379 0.1159
256 26.803 119.81 17.11 4.7859 2.8397 0.1428
512 53.606 239.62 48.3 5.4791 3.8774 0.2016
X Y
Regression Statistics
R Square 0.9857

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.1244 Interce -2.084 0.1327 -15.71 88-08 -2.39 -1.778
1.0083 x1 1.0083 0.043 23.468 ZE-O9 0.9092 1.1074

74
II II

94

Mixer Viscometry, 5%, 4.9701%, 61.77 9 corn syrup, T = 40°C, 3.07 g CaCO3
rpm readings Average
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
4 0.2 0.3 0.3 0.2 0.3 0.3 0.2 0.3 0.2625
8 0.4 0.4 0.4 0.5 0.4 0.4 0.4 0.4 0.4125
16 0.7 0.7 0.8 0.7 0.8 0.8 0.7 0.8 0.75
32 1.3 1.3 1.2 1.3 1.2 1.3 1.2 1.3 1.2625
64 2.6 22.6 2.6 2.5 2.6 2.5 2.6 2.6 5.075
128 5.7 5.6 5.7 5.6 5.7 5.7 5.6 5.6 5.65
256 13.5 13.5 13.5 13.4 13.5 13.5 13.5 13.5 13.488
512 37.8 37.9 37.8 37.9 38 37.9 37.9 38 37.9
256 13.5 13.6 13.5 13.5 13.5 13.6 13.6 13.6 13.55
128 5.6 5.7 5.7 5.6 5.7 5.6 5.7 5.6 5.65
64 2.6 2.5 2.5 2.5 2.6 2.5 2.5 2.6 2.5375
32 1.3 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.225
16 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
8 0.3 0.3 0.3 0.3 0.2 0.3 0.2 0.3 0.275
4 0.1 0.1 0.1333 0.1333 0.1333 0.1333 0.1667 0.1333 0.1292
2 0.0333 0.0667 0.0333 0.0667 0.0667 0.0667 0.0667 0.0667 0.0583
1 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0014 lE-OS -0.98 -4.845
2 0.2094 0.0029 3E-05 -0.679 -4.544
4 0.4188 0.0038 4E-05 -0.378 -4.426
8 0.8376 0.0059 6E-05 -0.077 -4.23
16 1.6752 0.0107 0.0001 0.2241 -3 97
32 3.3504 0.018 0.0002 0.5251 —3 744
64 6.7008 0.0725 0.0007 0.8261 -3 14
128 13.402 0.0807 0.0008 1.1272 -3 093
256 26.803 0.1927 0.0019 1.4282 -2 715
512 53.606 0.5415 0.0054 1.7292 -2 266
256 26.803 0.1936 0.0019 1.4282 —2 713
128 13.402 0.0807 0.0008 1.1272 -3 093
64 6.7008 0.0363 0.0004 0.8261 -3 441
32 3.3504 0.0175 0.0002 0.5251 -3 757
16 1.6752 0.0086 9E-05 0.2241 -4 067
8 0.8376 0.0039 4E-05 -0.077 -4.406
4 0.4188 0.0018 28-05 -0.378 -4.734
2 0.2094 0.0008 88-06 -0.679 —5.079
1 0.1047 0.0005 5E-06 -0.98 -5.322

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k’ = 4.47

K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 -2.039 0.278
2 0.2094 0.936 0.2602 -0.066 -1.346 0.278
4 0.4188 1.872 0.3415 0.627 -1.074 0.1824
8 0.8376 3.7441 0.5367 1.3202 -0.622 0.1433
16 1.6752 7.4881 0.9758 2.0133 -0.025 0.1303
32 3.3504 14.976 1.6425 2.7065 0.4962 0.1097
64 6.7008 29.953 6.6026 3.3996 1.8875 0.2204
128 13.402 59.905 7.3507 4.0928 1.9948 0.1227
256 26.803 119.81 17.547 4.7859 2.8649 0.1465
512 53.606 239.62 49.308 5.4791 3.8981 0.2058
X Y
Regression Statistics
R Square 0.9768

Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
= 0.2039 Interce -1.59 0.1564 —10.17 3E—06 -1.951 -1.229
n = 0.9296 x1 0.9296 0.0507 18.348 28-08 0.8127 1.0464

95

Checking the values of 5%..
rpm readings Average
1 0.1667 0.1667 0.1667 0.2 0.2 0.1667 0.1667 0.1667 0.175
2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
4 0.3 0.2 0.3 0.2 0.3 0.2 0.3 0.2 0.25
8 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
16 0.6 0.7 0.6 0.7 0.6 0.7 0.6 0.6 0.6375
32 1.1 1.2 1.1 1.2 1.1 1.2 1.1 1.2 1.15
64 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
128 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5
256 13.4 13.4 13.5 13.3 13.4 13.4 13.4 13.4 13.4
512 38 38 38 38 38 38 38 38 38
256 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5 13.5
128 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5
64 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4
32 1.2 1.1 1.2 1.1 1.1 1.1 1.2 1.1 1.1375
16 0.5 0.5 0.5 0.5 0.5 0.6 0.5 0.6 0.525
8 0.3 0.2 0.3 0.2 0.2 0.3 0.2 0.3 0.25
4 0.1333 0.1333 0.1333 0.1333 0.1333 0.1467 0.1333 0.1333 0.135
2 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667
1 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0025 3E-05 -0.98 —4.602
2 0.2094 0.0029 3E-05 -0.679 -4.544
4 0.4188 0.0036 4E-05 -0.378 -4.447
8 0.8376 0.0057 6E-05 -0.077 —4.243
16 1.6752 0.0091 9E-05 0.2241 -4.041
32 3.3504 0.0164 0.0002 0.5251 -3.784
64 6.7008 0.0343 0.0003 0.8261 -3.465
128 13.402 0.0786 0.0008 1.1272 -3.105
256 26.803 0.1914 0.0019 1.4282 —2.718
512 53.606 0.5429 0.0054 1.7292 —2.265
256 26.803 0.1929 0.0019 1.4282 -2.715
128 13.402 0.0786 0.0008 1.1272 —3.105
64 6.7008 0.0343 0.0003 0.8261 -3.465
32 3.3504 0.0163 0.0002 0.5251 -3.789
16 1.6752 0.0075 BE-OS 0.2241 -4.125
8 0.8376 0.0036 4E-05 —0.077 -4.447
4 0.4188 0.0019 2E—05 —0.378 -4.715
2 0.2094 0.001 1E-05 -0.679 -5.021
1 0.1047 0.0005 58—06 -0.98 —5.322
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47
K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831
shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.2277 -0.759 -1.48 0.4865
2 0.2094 0.936 0.2602 —0.066 -1.346 0.278
4 0.4188 1.872 0.3253 0.627 -1.123 0.1737
8 0.8376 3.7441 0.5204 1.3202 -0.653 0.139
16 1.6752 7.4881 0.8294 2.0133 -0.187 0.1108
32 3.3504 14.976 1.4962 2.7065 0.4029 0.0999
64 6.7008 29.953 3.1224 3.3996 1.1386 0.1042
128 13.402 59.905 7.1556 4.0928 1.9679 0.1194
256 26.803 119.81 17.434 4.7859 2.8584 0.1455
512 53.606 239.62 49.439 5.4791 3.9007 0.2063
X Y
Regression Statistics
R Square 0.9499
Observations 10
Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.223 Interce -1.501 0.2175 —6.899 7E-05 -2.002 -0.999
n = 0.8681 x1 0.8681 0.0704 12.322 6E-07 0.7056 1.0305

96

7.— Mixer Viscometry, 15%, 15.005%, 70.31 g corn syrup, T = 40.8°C, 10.55 g CaCO3
rpm readings Average
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
2 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.2 0.15
4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
8 0.5 0.5 0.6 0.6 0.5 0.5 0.5 0.6 0.5375
16 1 1 1 0.9 0.9 1 1 1 0.975
32 1.9 1.8 1.8 1.9 1.8 1.8 1.8 1.8 1.825
64 3.8 3.7 3.7 3.7 3.7 3.7 3.8 3.7 3.725
128 7.9 8 7.8 7.8 7.9 7.8 7.9 7.8 7.8625
256 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1 18.1
512 49 48.9 49 48.9 49 48.9 49 48.9 48.95
256 18.1 18.2 18.2 18.1 18.2 18.1 18.1 18.1 18.138
128 7.9 7.8 7.9 7.9 7.9 7.9 7.9 7.9 7.8875
64 3.7 3.7 3.6 3.7 3.7 3.7 3.7 3.7 3.6875
32 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
16 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
8 0.5 0.4 0.5 0.4 0.5 0.4 0.5 0.4 0.45
4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
1 0.0667 0.0667 0.0667 0.1 0.1 0.1 0.0667 0.1 0.0833
rad/s (N cm) (N m)
rpm omega M M Log 0m Log M
1 0.1047 0.0014 lE-OS —0.98 -4.845
2 0.2094 0.0021 28-05 -0.679 -4.669
4 0.4188 0.0043 4E-05 -0.378 —4.368
8 0.8376 0.0077 8E-05 -0.077 -4.115
16 1.6752 0.0139 0.0001 0.2241 -3.856
32 3.3504 0.0261 0.0003 0.5251 -3.584
64 6.7008 0.0532 0.0005 0.8261 -3.274
128 13.402 0.1123 0.0011 1.1272 -2.949
256 26.803 0.2586 0.0026 1.4282 -2.587
512 53.606 0.6994 0.007 1.7292 -2.155
256 26.803 0.2591 0.0026 1.4282 -2.586
128 13.402 0.1127 0.0011 1.1272 -2.948
64 6.7008 0.0527 0.0005 0.8261 -3.278
32 3.3504 0.0257 0.0003 0.5251 —3.59
16 1.6752 0.0129 0.0001 0.2241 -3.891
8 0.8376 0.0064 6E-05 -0.077 -4.192
4 0.4188 0.0029 3E-05 -0.378 -4.544
2 0.2094 0.0014 1E-05 -0.679 -4.845
1 0.1047 0.0012 1E-05 -0.98 -4.924
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.026 92 m
average apparent viscosity = shear stress/ shear d = 0.041 43 m

k' = 4.47

K = consistency coefficient, Pa.s“n

average shear stress = 2 M / ( ( pi d‘3' (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 -2.039 0.278
2 0.2094 0.936 0.1952 -0.066 -1.634 0.2085
4 0.4188 1.872 0.3903 0.627 -0.941 0.2085
8 0.8376 3.7441 0.6993 1.3202 —0.358 0.1868
16 1.6752 7.4881 1.2685 2.0133 0.2378 0.1694
32 3.3504 14.976 2.3744 2.7065 0.8647 0.1585
64 6.7008 29.953 4.8463 3.3996 1.5782 0.1618
128 13.402 59.905 10.229 4.0928 2.3252 0.1708
256 26.803 119.81 23.548 4.7859 3.1591 0.1965
512 53.606 239.62 63.685 5.4791 4.1539 0.2658
X Y
Regression Statistics
R Square 0.9914
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.2065 Interce —1.577 0.0997 —15.83 7E-08 -1.807 -1.348
0.9798 x1 0.9798 0.0323 30.35 28—10 0.9053 1.0542

’4
II II

Mixer Viscometry, 15%, 15.02%, 71.53 9 corn syrup, T= 40°C, 10.75 g CaCO3

rpm readings Average
1 0.1 0.2 0.1 0.2 0.2 0.2 0.1 0.2 0.1625
2 0.2667 0.2667 0.2667 0.2333 0.2667 0.2667 0.2667 0.3 0.2667
4 0.3667 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3958
8 0.6333 0.6333 0.6333 0.6333 0.6333 0.6333 0.6333 0.6333 0.6333
16 0.9667 0.9333 0.9667 0 9667 0.9667 0 9667 0.9667 0.9667 0.9625
32 1.8333 1.8333 1.8333 1 8333 1.8333 1 8333 1.8333 1.8333 1.8333
64 3.7333 3.7667 3.7333 3 7333 3.7 3.7333 3.7 3.7 3.725
128 7.9333 7.9667 7.9333 7.9333 7.9333 7.9333 7.9333 7.9333 7.9375
256 18.4 18.433 18.433 18.433 18.467 18.467 18.5 18.5 18.454
512 49.9 50.1 50.2 50.1 50.1 50.1 50.2 50.1 50.1
256 18.7 18.6 18.6 18.6 18.6 18.7 18.6 18.7 18.638
128 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1 8.1
64 3.7 3.7 3.7 3.7 3.7 3.8 3.7 3.8 3.725
32 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
16 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
8 0.4667 0.4333 0.4333 0.4333 0.4333 0.4333 0.4333 0.4333 0.4375
4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.1 0.0667 0.1 0.0667 0.0667 0.0667 0.0667 0.1 0.0792
1 0.033 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0023 28-05 -0.98 -4.634
2 0.2094 0.0038 4E-05 -0.679 -4.419
4 0.4188 0.0057 6E-05 -0.378 -4.248
8 0.8376 0.009 9E-05 -0.077 -4.043
16 1.6752 0.0138 0.0001 0.2241 —3.862
32 3.3504 0.0262 0.0003 0.5251 -3.582
64 6.7008 0.0532 0.0005 0.8261 -3.274
128 13.402 0.1134 0.0011 1.1272 -2.945
256 26.803 0.2637 0.0026 1.4282 -2.579
512 53.606 0.7158 0.0072 1.7292 -2.145
256 26.803 0.2663 0.0027 1.4282 -2.575
128 13.402 0.1157 0.0012 1.1272 -2.937
64 6.7008 0.0532 0.0005 0.8261 -3.274
32 3.3504 0.0257 0.0003 0.5251 -3.59
16 1.6752 0.0129 0.0001 0.2241 -3.891
8 0.8376 0.0063 6E-05 -0.077 -4.204
4 0.4188 0.0029 3E—05 -0.378 -4.544
2 0.2094 0.0011 1E-05 -0.679 -4.947
1 0.1047 0.0005 5E-06 —0.98 -5.322
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.2114 -0.759 -1.554 0.4517
2 0.2094 0.936 0.3469 -0.066 -1.059 0.3707
4 0.4188 1.872 0.515 0.627 -0.664 0.2751
8 0.8376 3.7441 0.824 1.3202 -0.194 0.2201
16 1.6752 7.4881 1.2522 2.0133 0.2249 0.1672
32 3.3504 14.976 2.3852 2.7065 0.8693 0.1593
64 6.7008 29.953 4.8463 3.3996 1.5782 0.1618
128 13.402 59.905 10.327 4.0928 2.3347 0.1724
256 26.803 119.81 24.009 4.7859 3.1784 0.2004
512 53.606 239.62 65.181 5.4791 4.1772 0.272
X Y
Regression Statistics
R Square 0.9766
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.2954 Interce -1.219 0.151 -8.074 2E—05 -1.S68 -0.871
0.8935 x1 0.8935 0.0489 18.269 2E-08 0.7807 1.0063

:3
II II

98

Mixer Viscometry, 15%, 14.99%, 60.7 9 corn syrup, T = 40.2°C, 9.1 g CaCO3
rpm readings Average
1 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
4 0.2667 0.2667 0.2667 0.2667 0.2333 0.2667 0.2667 0.2667 0.2625
8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
16 1 1 1 1 1 1 1 1 1
32 2 2 2 2 1.9 1.9 2 1.9 1.9625
64 4 4 4 4 4 4 4 4 4
128 8.4 8.4 8.4 8.4 8.4 8.5 8.4 8.4 8.4125
256 19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2
512 50.8 50.8 50.8 50.8 50.8 50.8 50.8 50.8 50.8
256 19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2 19.2
128 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4
64 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9
32 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
16 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
8 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
2 0.0667 0.0667 0.0667 0.0667 0.0667 0.0667 0.1 0.1 0.075
1 0.0333 0.0333 0 0.0333 0.0333 0.0333 0.0333 0 0.025
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0005 SE—06 -0.98 -5.322
2 0.2094 0.0014 lE-OS -0 679 -4.845
4 0.4188 0.0038 4E-05 -0.378 -4.426
8 0.8376 0.0071 7E-05 -0.077 -4.146
16 1.6752 0.0143 0.0001 0.2241 -3.845
32 3.3504 0.028 0.0003 0.5251 —3.552
64 6.7008 0.0571 0.0006 0.8261 —3.243
128 13.402 0.1202 0.0012 1.1272 -2.92
256 26.803 0.2743 0.0027 1.4282 -2.562
512 53.606 0.7258 0.0073 1.7292 -2.139
256 26.803 0.2743 0.0027 1.4282 -2.562
128 13.402 0.12 0.0012 1.1272 -2.921
64 6.7008 0.0557 0.0006 0.8261 -3.254
32 3.3504 0.0271 0.0003 0.5251 -3.566
16 1.6752 0.0129 0.0001 0.2241 -3.891
8 0.8376 0.0057 68—05 -0.077 -4.243
4 0.4188 0.0029 3E-05 -0.378 -4.544
2 0.2094 0.0011 1E-05 -0.679 -4.97
1 0.1047 0.0004 4E-06 -0.98 -5.447
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47
K = consistency coefficient, Pa.s“n
average shear stress = 2 M l ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831
shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.0434 —0.759 -3.138 0.0927
2 0.2094 0.936 0.1301 -0.066 -2.039 0.139
4 0.4188 1.872 0.3415 0.627 -1.074 0.1824
8 0.8376 3.7441 0.6505 1.3202 -0.43 0.1737
16 1.6752 7.4881 1.301 2.0133 0.2631 0.1737
32 3.3504 14.976 2.5532 2.7065 0.9374 0.1705
64 6.7008 29.953 5.2041 3.3996 1.6494 0.1737
128 13.402 59.905 10.945 4.0928 2.3929 0.1827
256 26.803 119.81 24.979 4.7859 3.2181 0.2085
512 53.606 239.62 66.092 5.4791 4.191 0.2758
X Y
Regression Statistics
R Square 0.9957
Observations 10
Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.1322 Interce -2.024 0.0796 -25.41 lE—09 —2.207 -1.84
n = 1.1106 x1 1.1106 0.0258 43.053 lE-ll 1.0511 1.17

10.- Mixer Viscometry, 25%, 24.94%, 70.29 9 corn syrup, T: 40.8°C, 17.53 g CaCO3

 

rpm readings Average
1 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667 0.1667
2 0.3 0.3333 0.3 0.3 0.3 0.3 0.3 0.3333 0.3083
4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
8 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
16 2.1 2.1 2.1 2.1 2.1 2.1 2 2.1 2.0875
32 4 4 4 4 4 4 4 4 4
64 7.9 7.9 7.9 7.9 7.8 7.9 7.9 7.9 7.8875
128 16 16 16 16 16.1 16 16 16 16.013
256 32.8 32.8 32.8 32.7 32.6 32.6 32.6 32.6 32.688
512 70.7 70.7 70.7 70.6 70.6 70.5 70.5 70.5 70.6
256 31.1 31.1 31.2 31.2 31.2 31.2 31.2 31.2 31.175
128 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.3 15.213
64 7.7 7.7 7.7 7.6 7.6 7.7 7.7 7.7 7.675
32 4 3.9 3.9 3.994 3.9 4 3.9 4 3.9493
16 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
2 0.1 0.1 0.2 0.1 0.2 0.1 0.2 0.1 0.1375
1 0.0333 0.0667 0.0333 0.0667 0.0333 0.0333 0.0333 0.0667 0.0458
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0024 2E—05 -0.98 -4.623
2 0.2094 0.0044 4E-05 -0.679 -4.356
4 0.4188 0.0086 9E-05 ~0.378 -4.067
8 0.8376 0.0157 0.0002 —0.077 -3.804
16 1.6752 0.0298 0.0003 0.2241 -3.525
32 3.3504 0.0571 0.0006 0.5251 -3.243
64 6.7008 0.1127 0.0011 0.8261 -2.948
128 13.402 0.2288 0.0023 1.1272 -2.641
256 26.803 0.467 0.0047 1.4282 —2.331
512 53.606 1.0087 0.0101 1.7292 -1.996
256 26.803 0.4454 0.0045 1.4282 -2.351
128 13.402 0.2173 0.0022 1.1272 -2.663
64 6.7008 0.1097 0.0011 0.8261 -2.96
32 3.3504 0.0564 0.0006 0.5251 -3.249
16 1.6752 0.0271 0.0003 0.2241 -3.566
8 0.8376 0.0129 0.0001 -0.077 -3.891
4 0.4188 0.0057 68—05 -0.378 -4.243
2 0.2094 0.002 2E-05 -0.679 -4.707
1 0.1047 0.0007 7E-06 -0.98 -5.184
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
= 0.04143 m

average apparent viscosity = shear stress/ shear d
k' = 4.47

K = consistency coefficient, Pa.s‘n l
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

 

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.2169 -0.759 -1.528 0.4634
2 0.2094 0.936 0.4011 -0.066 -0.913 0.4286
4 0.4188 1.872 0.7806 0.627 -0.248 0.417
8 0.8376 3.7441 1.4311 1.3202 0.3585 0.3822
16 1.6752 7.4881 2.7159 2.0133 0.9991 0.3627
32 3.3504 14.976 5.2041 2.7065 1.6494 0.3475
64 6.7008 29.953 10.262 3.3996 2.3284 0.3426
128 13.402 59.905 20.832 4.0928 3.0365 0.3478
256 26.803 119.81 42.527 4.7859 3.7501 0.355
512 53.606 239.62 91.852 5.4791 4.5202 0.3833
X Y
Regression Statistics
R Square 0.9989
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.4165 Interce —0.876 0.0346 -25.34 lE-09 -0.955 -0.796
0.9624 x1 0.9624 0.0112 85.977 2E-14 0.9365 0.9882

:3
II II

100

11.- Mixer Viscometry, 25%, 25.01%, 71.54, 9 corn syrup, T = 40°C, 17.89 g CaCO3

rpm readings Average
1 0.0667 0.0667 0.1 0.0667 0.0667 0.0667 0.0667 0.0667 0.0708
2 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
4 0.2667 0.2667 0.2667 0.2667 0.2667 0.2667 0.2667 0.2667 0.2667
8 0.7 0.8 0.7 0.7 0.8 0.7 0.7 0.7 0.725
16 1.7 1.6 1.6 1.7 1.6 1.7 1.6 1.7 1.65
32 3.6 3.5 3.6 3.5 3.6 3.5 3.6 3.5 3.55
64 7.1 7.1 7.2 7.1 7.2 7.1 7.2 7.1 7.1375
128 14.7 14.6 14.6 1.5 14.5 14.5 14.6 14.5 12.938
256 30 5 30.5 30.5 30 5 30.5 30.4 30.3 30.4 30.45
512 69 69.1 69 69 69 69 69 69.1 69 025
256 29 6 29.6 29.7 29.6 29.7 29.6 29.6 29.7 29.638
128 14.1 14.2 14.1 14.2 14.2 14.1 14.1 14.2 14.15
64 7 6.9 6.9 7 7.1 7 7 7 6.9875
32 3.5 3.5 3.5 3.6 3.5 3.5 3.6 3.5 3.525
16 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
4 0.3333 0.3333 0.3667 0.3 0.3333 0.3667 0.3667 0.3667 0.3458
2 0.1 0.1 0. 0.1 0.1 0.0667 0.1 0.1 0.0958
1 0.0333 0 0.0333 0 0 0 0 0 0.0083
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.001 1E-05 -0.98 -4.995
2 0.2094 0.0005 5E-06 -0.679 -5.322
4 0.4188 0.0038 4E-05 -0.378 -4.419
8 0.8376 0.0104 0 0001 -0.077 -3.985
16 1.6752 0.0236 0 0002 0.2241 -3.628
32 3.3504 0.0507 0 0005 0.5251 -3.295
64 6.7008 0.102 0 001 0.8261 -2.992
128 13.402 0.1848 0 0018 1.1272 -2.733
256 26.803 0.435 0.0044 1.4282 -2.361
512 53.606 0.9862 0.0099 1.7292 -2.006
256 26.803 0.4234 0 0042 1.4282 -2.373
128 13.402 0.2022 0 002 1.1272 -2.694
64 6.7008 0.0998 0 001 0.8261 -3.001
32 3.3504 0.0504 0 0005 0.5251 -3.298
16 1.6752 0.0243 0 0002 0.2241 —3.615
8 0.8376 0.0114 0.0001 -0.077 -3.942
4 0.4188 0.0049 SE-OS -0.378 -4.306
2 0.2094 0.0014 lE-OS —0.679 -4.864
1 0.1047 0.0001 1E-06 -0.98 -5.924
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47

K = consistency coefficient, Pa.s“n

average shear stress = 2 M / ( ( pi d‘3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.0922 -0.759 -2.384 0.1969
2 0.2094 0.936 0.0434 -0.066 —3.138 0.0463
4 0.4188 1.872 0.3469 0.627 -1.059 0.1853
8 0.8376 3.7441 0.9432 1.3202 -0.058 0.2519
16 1.6752 7.4881 2.1467 2.0133 0.7639 0.2867
32 3.3504 14.976 4.6186 2.7065 1.5301 0.3084
64 6.7008 29.953 9.286 3.3996 2.2285 0.31
128 13.402 59.905 16.832 4.0928 2.8233 0.281
256 26.803 119.81 39.616 4.7859 3.6792 0.3307
512 53.606 239.62 89.803 5.4791 4.4976 0.3748
X Y
Regression Statistics
R Square 0.9697
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.1448 Interce -1.932 0.2307 —8.377 2E—05 —2.464 -1.4
1.1952 x1 1.1952 0.0747 15.998 68—08 1.0229 1.3675

:3
II II

101

12.— Mixer Viscometry, 25%, 0.25%, 70.88 g corn syrup 17.72, 22.1 g CaCO3

rpm readings Average

1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

2 0.2 0.3 0.2 0.3 0.2 0.3 0.2 0.3 0.25

4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

8 1 1 1 1 1 1 1 1 1

16 1.9 1.9 1.9 1.9 1.9 1.8 1.9 1.9 1.8875

32 3.6 3.6 3.5 3.5 3.5 3.5 3.5 3.6 3.5375

64 7 7 7 7 7.1 7 7.1 7 7.025
128 14.3 14.3 14.3 14.3 14.4 14.4 14.3 14.3 14.325
256 29.7 29.7 29.7 29 6 29.7 29.7 29.6 29.5 29.65
512 66.2 66.3 66.3 66 3 66.3 66.3 66.4 66.4 66.313
256 28.5 28.5 28.5 28 6 28.5 28.5 28.5 28.5 28.513
128 13.7 13.6 13.7 13.6 13.7 13.6 13.7 13.6 13.65

64 6.9 6.8 6.8 6.8 6.8 6.8 6.8 6.8 6.8125

32 3.5 3.5 3.5 3.5 3.4 3.5 3.5 3.5 3.4875

16 1.7 1.7 1.7 1.7 1.7 1.8 1.7 1.7 1.7125

8 0.8 0.9 0.9 0.9 0.8 0.9 0.8 0.9 0.8625

4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.1875

1 0.1 0.1 0.1 0.6667 0.1 0.1 0.6667 0.1 0.2417

rad/s (N cm) (N m)
M

rpm omega M Log Om Log M
1 0.1047 0.0014 lE-OS -0.98 -4.845
2 0.2094 0.0036 4E-05 -0.679 -4.447
4 0.4188 0.0071 7E—05 -0.378 -4.146
8 0.8376 0.0143 0.0001 -0.077 -3.845
16 1.6752 0.027 0.0003 0.2241 -3.569
32 3.3504 0.0505 0.0005 0.5251 -3.296
64 6.7008 0.1004 0.001 0.8261 -2.998
128 13.402 0.2047 0.002 1.1272 -2.689
256 26.803 0.4236 0.0042 1.4282 -2.373
512 53.606 0.9474 0.0095 1.7292 -2.023
256 26.803 0.4074 0.0041 1.4282 -2.39
128 13.402 0.195 0.002 1.1272 —2.71
64 6.7008 0.0973 0.001 0.8261 -3.012
32 3.3504 0.0498 0.0005 0.5251 -3.303
16 1.6752 0.0245 0.0002 0.2241 -3.611
8 0.8376 0.0123 0.0001 -0.077 -3.909
4 0.4188 0.0057 6E-05 -0.378 -4.243
2 0.2094 0.0027 3E-05 -0.679 -4.572
1 0.1047 0.0035 38-05 —0.98 —4.462

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s‘n
average shear stress = 2 M / ( ( pi d‘3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 -0.759 -2.039 0.278
2 0.2094 0.936 0.3253 -0.066 -1.123 0.3475
4 0.4188 1.872 0.6505 0.627 —0.43 0.3475
8 0.8376 3.7441 1.301 1.3202 0.2631 0.3475
16 1.6752 7.4881 2.4557 2.0133 0.8984 0.3279
32 3.3504 14.976 4.6023 2.7065 1.5266 0.3073
64 6.7008 29.953 9.1396 3.3996 2.2126 0.3051
128 13.402 59.905 18.637 4.0928 2.9252 0.3111
256 26.803 119.81 38.575 4.7859 3.6526 0.322
512 53.606 239.62 86.274 5.4791 4.4575 0.36
X Y
Regression Statistics
R Square 0.9986
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 0.3193 Interce —1.142 0.0409 -27.92 SE—10 -1.236 —1.047
= 1.0069 x1 1.0069 0.0132 76.03 68—14 0.9763 1.0374

 

 

102

12 a.- Mixer Viscometry, 25%, 0.25%, 70.52 9 corn syrup, 55°C, 17.63, 22.1 g CaCO3

rpm readings Average

1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

2 0.4 0.5 0.4 0.5 0.4 0.5 0.5 0.5 0.4625

4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

8 1.1 1.2 1.2 1.1 1.2 1.1 1.2 1.1 1.15

16 2 2 2 2 2 2 2 2 2

32 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8

64 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4
128 14.8 14.8 14.8 14.8 14.8 14.8 14.8 14.8 14.8
256 30.6 30.6 30.6 30.6 30.7 30.7 30.7 30.7 30.65
512 68 67.8 67.8 67.8 67.8 67.8 67.8 67.8 67.825
256 29.9 29.9 29.9 29.9 29.9 29.8 29.8 29.9 29.875
128 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5

64 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4

32 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9

16 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1

8 1.1 1.1 1.1 1.2 1.1 1.2 1.1 1.2 1.1375

4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7

2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

rad/s (N cm) (N m)
rpm omega M M Log Om Log M

1 0.1047 0.0043 4E-05 -0.98 -4.368
2 0.2094 0.0066 7E—05 -0.679 -4.18
4 0.4188 0.01 0.0001 -0.378 -4
8 0.8376 0.0164 0.0002 -0.077 -3.784
16 1.6752 0.0286 0.0003 0.2241 -3.544
32 3.3504 0.0543 0.0005 0.5251 -3.265
64 6.7008 0.1057 0.0011 0.8261 -2.976
128 13.402 0.2115 0.0021 1.1272 -2.675
256 26.803 0.4379 0.0044 1.4282 -2.359
512 53.606 0.969 0.0097 1.7292 -2.014
256 26.803 0.4268 0.0043 1.4282 -2.37
128 13.402 0.2072 0.0021 1.1272 -2.684
64 6.7008 0.1057 0.0011 0.8261 -2.976
32 3.3504 0.0557 0.0006 0.5251 -3.254
16 1.6752 0.03 0.0003 0.2241 -3.523
8 0.8376 0.0163 0.0002 -0.077 -3.789
4 0.4188 0.01 0.0001 -0.378 ‘4
2 0.2094 0.0057 6E-05 -0.679 -4.243
1 0.1047 0.0043 4E-05 -0.98 -4.368

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.3903 -0.759 -0.941 0.834
2 0.2094 0.936 0.6017 -0.066 -0.508 0.6428
4 0.4188 1.872 0.9107 0.627 -0.094 0.4865
8 0.8376 3.7441 1.4962 1.3202 0.4029 0.3996
16 1.6752 7.4881 2.602 2.0133 0.9563 0.3475
32 3.3504 14.976 4.9439 2.7065 1.5981 0.3301
64 6.7008 29.953 9.6275 3.3996 2.2646 0.3214
128 13.402 59.905 19.255 4.0928 2.9578 0.3214
256 26.803 119.81 39.876 4.7859 3.6858 0.3328
512 53.606 239.62 88.241 5.4791 4.4801 0.3683
X Y
Regression Statistics
R Square 0.9893
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
0.5625 Interce -0.575 0.0987 —5.828 0.0003 -0.803 -0.348
0.8711 x1 0.8711 0.032 27.243 6E-10 0.7974 0.9448

3
II II

 

 

103

12 b.- Mixer Viscometry, 25%, 0.25%, 71.39 9 corn syrup, 55°C, 17.85, 22.1 g CaCO3

rpm readings Average
1 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2875
2 0.4 0.5 0.4 0.5 0.4 0.5 0.5 0.5 0.4625
4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
8 1.1 1.2 1.2 1.1 1.2 1.1 1.2 1.1 1.15
16 2 2 2 2 2 2 2 2 2
32 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.8
64 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4
128 14.8 14.8 14.8 14.8 14.8 14.8 14.8 14.8 14.8
256 30.6 30.6 30.6 30.6 30.7 30.7 30.7 30.7 30.65
512 68 67.8 67.8 67.8 67.8 67.8 67.8 67.8 67.825
256 29.9 29.9 29 9 29.9 29.9 29.8 29.8 29.9 29.875
128 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5 14.5
64 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4 7.4
32 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9
16 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1
8 1.1 1.1 1.1 1.2 1.1 1.2 1.1 1.2 1.1375
4 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
1 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0041 4E-05 -0.98 -4.386
2 0.2094 0.0066 7E—05 —0.679 -4.18
4 0.4188 0.01 0.0001 -0.378 -4
8 0.8376 0.0164 0.0002 -0.077 —3.784
16 1.6752 0.0286 0.0003 0.2241 -3.544
32 3.3504 0.0543 0.0005 0.5251 -3.265
64 6.7008 0.1057 0.0011 0.8261 ~2.976
128 13.402 0.2115 0.0021 1.1272 -2.675
256 26.803 0.4379 0.0044 1.4282 -2.359
512 53.606 0.969 0.0097 1.7292 -2.014
256 26.803 0.4268 0.0043 1.4282 -2.37
128 13.402 0.2072 0.0021 1.1272 -2.684
64 6.7008 0.1057 0.0011 0.8261 —2.976
32 3.3504 0.0557 0.0006 0.5251 -3.254
16 1.6752 0.03 0.0003 0.2241 -3.523
8 0.8376 0.0163 0.0002 -0.077 -3.789
4 0.4188 0.01 0.0001 -0.378 —4
2 0.2094 0.0057 6E-05 -0.679 -4.243
1 0.1047 0.0043 4E-05 -0.98 —4.368
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47

K = consistency coefficient, Pa.s“n

average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.374 -0.759 -0.983 0.7992
2 0.2094 0.936 0.6017 -0.066 -0.508 0.6428
4 0.4188 1.872 0.9107 0.627 -0.094 0.4865
8 0.8376 3.7441 1.4962 1.3202 0.4029 0.3996
16 1.6752 7.4881 2.602 2.0133 0.9563 0.3475
32 3.3504 14.976 4.9439 2.7065 1.5981 0.3301
64 6.7008 29.953 9.6275 3.3996 2.2646 0.3214
128 13.402 59.905 19.255 4.0928 2.9578 0.3214
256 26.803 119.81 39.876 4.7859 3.6858 0.3328
512 53.606 239.62 88.241 5.4791 4.4801 0.3683
X Y
Regression Statistics
R Square 0.9902
Observations 10
Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 0.5557 Interce -0.588 0.095 -6.185 0.0002 -0.807 -0.368
n = 0.8745 x1 0.8745 0.0308 28.42 4E-10 0.8035 0.9454

 

104

13.- Mixer Viscometry, 25%, 0.3501%, 71.13 g corn syrup, 55°C, 24.9, 22.1 g CaCO3

rpm readings Average
1 0 1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 .1
2 0 2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
4 0.5 0.4 0.5 0.4 0.5 0.4 0.5 0.5 0.4625
8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
16 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
32 3 8 3.8 3.9 3.8 3.9 3.8 3.9 3.8 3.8375
64 7.5 7.6 7.6 7.5 7.6 7.6 7.5 7.6 7.5625
128 15.3 15.3 15.3 15.3 15.4 15.4 15 4 15.4 15.35
256 31.3 31.3 31.3 31.3 31.3 31.2 31.3 31.3 31.288
512 65.4 65.4 65.4 65.4 65.4 65.4 65.5 65.4 65.413
256 30.7 30.7 30.8 30.7 30.8 30.8 30.8 30.9 30.775
128 14.9 14.9 14.9 14.9 14.9 14.9 14.9 15 14.913
64 7 5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5
32 3 8 3.8 3.9 3.8 3.9 3.9 3.8 3.9 3.85
16 2 2 2 2 2 2 2 2 2
8 1 1 1.1 1 1.1 1 1 1.1 1.0375
4 0.6 0.5 0.6 0.5 0.6 0.5 0.6 0.5 0.55
2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
1 0.1 0.2 0.1 0.1 0.2 0.1 0.2 0.1 0.1375
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0014 lE-OS -0.98 -4.845
2 0.2094 0.0029 3E—05 -0.679 -4.S44
4 0.4188 0.0066 7E-05 -0.378 -4.18
8 0.8376 0.0129 0.0001 -0.077 —3.891
16 1.6752 0.0271 0.0003 0.2241 -3.566
32 3.3504 0.0548 0.0005 0.5251 -3.261
64 6.7008 0.108 0.0011 0.8261 -2.966
128 13.402 0.2193 0.0022 1.1272 -2.659
256 26.803 0.447 0.0045 1.4282 -2.35
512 53.606 0.9346 0.0093 1.7292 -2.029
256 26.803 0.4397 0.0044 1.4282 -2.357
128 13.402 0.2131 0.0021 1.1272 -2.672
64 6.7008 0.1072 0.0011 0.8261 -2.97
32 3.3504 0.055 0.0006 0.5251 -3.26
16 1.6752 0.0286 0.0003 0.2241 -3.544
8 0.8376 0.0148 0.0001 -0.077 -3.829
4 0.4188 0.0079 8E-05 -0.378 —4.105
2 0.2094 0.0043 4E-05 -0.679 -4.368
1 0.1047 0.002 ZE-OS -0.98 -4.707
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m

k' = 4.47

K = consistency coefficient, Pa.s‘n

average shear stress = 2 M / ( ( pi d03' (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.1301 —0.759 —2.039 0.278
2 0.2094 0.936 0.2602 -0.066 -1.346 0.278
4 0.4188 1.872 0.6017 0.627 -0.508 0.3214
8 0.8376 3.7441 1.1709 1.3202 0.1578 0.3127
16 1.6752 7.4881 2.4719 2.0133 0.905 0.3301
32 3.3504 14.976 4.9926 2.7065 1.608 0.3334
64 6.7008 29.953 9.8389 3.3996 2.2863 0.3285
128 13.402 59.905 19.971 4.0928 2.9943 0.3334
256 26.803 119.81 40.705 4.7859 3.7064 0.3397
512 53.606 239.62 85.103 5.4791 4.4439 0.3552
X Y
Regression Statistics
R Square 0.9997
Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
K = 0.2951 Interce -1.221 0.0193 -63.31 3E-13 -1.265 -1.176
= 1.0345 x1 1.0345 0.0062 165.67 5E—17 1.0201 1.0489

 

105

13 a.- Mixer Viscometry, 25%, 0.3501%, 71.13 9 corn syrup, 55°C, 24.9, 22.1 g CaCO3

rpm readings Average
1 0.2333 0.2333 0.2333 0.2333 0.2333 0.2333 0.2333 0.2333 0.2333
2 0.3333 0.3667 0.3667 0.3667 0.3667 0.3333 0.3667 0.3667 0.3583
4 0.6333 0.6333 0.6 0.6 0.6 0.6 0.6 0.6 0.6083
8 1.1 1.1 1 1.1 1 1.1 1 1.1 1.0625
16 2 1.9 1.9 1.9 1.9 2 1.9 1.9 1.925
32 3.7 3.7 3.7 3.6 3.7 3.7 3.7 3.6 3.675
64 7.1 7.2 7.1 7.2 7.1 7.2 7.1 7.1 7.1375
128 14.3 14.3 14.3 14.3 14.4 14.3 14.4 14.3 14.325
256 29.7 29 6 29.6 29.6 29.6 29.6 29.6 29.6 29.613
512 66.8 66 7 66.8 66.8 66.8 67 67 67.2 66.888
256 28.8 28.9 28.8 28.9 28.8 28.8 28.9 28.9 28.85
128 13.9 13.9 13.9 13.8 13.9 13.9 13.9 13.8 13.875
64 7 7.1 7 7.1 7 7 6.9 7 7.0125
32 3.7 3.6 3.7 3.6 3.7 3.7 3.6 3.6 3.65
16 1.9 1.9 1.8 1.9 1.9 1.8 1.9 1.9 1.875
8 0.9 1 9 1 0.9 1 1 1 1.975
4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
2 0.3 0.2 0.3 0.2 0.3 0.2 0.3 0.3 0.2625
1 0.1667 0.1667 0.1667 0.2 0.1667 0.1667 0.1667 0.1667 0.1708
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0033 3E-05 -0.98 -4.477
2 0.2094 0.0051 SE-OS —0.679 -4.291
4 0.4188 0.0087 9E-05 -0.378 -4.061
8 0.8376 0.0152 0.0002 -0.077 -3.819
16 1.6752 0.0275 0.0003 0.2241 —3.561
32 3.3504 0.0525 0.0005 0.5251 -3.28
64 6.7008 0.102 0.001 0.8261 -2.992
128 13.402 0.2047 0.002 1.1272 -2.689
256 26.803 0.4231 0.0042 1.4282 -2.374
512 53.606 0.9556 0.0096 1.7292 —2.02
256 26.803 0.4122 0.0041 1.4282 -2.385
128 13.402 0.1982 0.002 1.1272 -2.703
64 6.7008 0.1002 0.001 0.8261 -2.999
32 3.3504 0.0521 0.0005 0.5251 -3.283
16 1.6752 0.0268 0.0003 0.2241 -3.572
8 0.8376 0.0282 0.0003 —0.077 -3.549
4 0.4188 0.0071 7E-05 -0.378 -4.146
2 0.2094 0.0038 4E-05 -0.679 -4.426
1 0.1047 0.0024 2E-05 -0.98 -4.612

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s‘n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.3036 -0.759 —1.192 0.6486
2 0.2094 0.936 0.4662 -0.066 -0.763 0 4981
4 0.4188 1.872 0.7915 0.627 -0.234 0 4228
8 0.8376 3.7441 1.3823 1.3202 0.3238 0 3692
16 1.6752 7.4881 2.5045 2.0133 0.9181 0 3345
32 3.3504 14.976 4.7812 2.7065 1.5647 0.3193
64 6.7008 29.953 9.286 3.3996 2.2285 0.31
128 13.402 59.905 18.637 4.0928 2.9252 0.3111
256 26.803 119.81 38.526 4.7859 3.6513 0 3216
512 53.606 239.62 87.022 5.4791 4.4662 0 3632
X Y
Regression Statistics
R Square 0.9939
Observations 10

Coeffic Standar t Stati P—value Lower 95% Upper 95%
= 0.4692 Interce -0.757 0.078 —9.704 SE—O6 —0.937 —0.577
n = 0.9092 x1 0.9092 0.0253 35.998 SE-ll 0.8509 0.9674

106

14.- Mixer Viscometry, 35%, 35%, 62.2 9 corn syrup, 21.7 g CaCO3

rpm readings Average
1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
2 1.4 1.3 1.4 1.3 1.4 1.4 1.3 1.4 1.3625
4 2.3 2.4 2.3 2.4 2.3 2.3 2.3 2.3 2.325
8 4 4 4 4 4 4 4 4 4
16 6.9 6.9 7 6.9 6.9 7 6.9 7 6.9375
32 12.2 12.3 12.3 12.2 12.2 12.2 12.3 12.2 12.238
64 22 21.9 22 21.9 21.9 22 21.9 22 21.95
128 40.3 40.1 40 40.1 40 40 39.9 39 8 40.025
256 72.4 72.3 72.3 72.2 72.1 72 72 72 72.163
128 33.7 33.7 33.7 33.7 33.7 33.7 33.8 33.7 33.713
64 20.3 20.3 20.2 20.1 20 20.1 20 20 20.125
32 11.5 11.4 11.4 11.4 11.4 11.4 11.5 11.4 11.425
16 6.6 6.5 6.6 6.5 6.6 6.5 6.6 6.5 6.55
8 3.7 3.7 3.7 3.8 3.7 3.7 3.6 3.7 3.7
4 2.1 2.1 2.1 2.1 2 2.1 2 2.1 2.075
2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1 0.7 0.6 0.7 0.6 0.7 0.6 0.7 0.6 0.65
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.0114 0.0001 -0.98 -3.942
2 0.2094 0.0195 0.0002 -0.679 -3.711
4 0.4188 0.0332 0.0003 -0.378 —3.479
8 0.8376 0.0571 0.0006 -0.077 -3.243
16 1.6752 0.0991 0.001 0.2241 -3.004
32 3.3504 0.1748 0.0017 0.5251 -2.757
64 6.7008 0.3136 0.0031 0.8261 -2.504
128 13.402 0.5718 0.0057 1.1272 -2.243
256 26.803 1.031 0.0103 1.4282 -1.987
128 13.402 0.4817 0.0048 1.1272 -2.317
64 6.7008 0.2875 0.0029 0.8261 -2.541
32 3.3504 0.1632 0.0016 0.5251 -2.787
16 1.6752 0.0936 0.0009 0.2241 -3.029
8 0.8376 0.0529 0.0005 -0.077 —3.277
4 0.4188 0.0296 0.0003 -0.378 -3.528
2 0.2094 0.0171 0.0002 -0.679 -3.766
1 0.1047 0.0093 9E-05 -0.98 -4.032

Determination of average shear rate

average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient. Pa.s“n
average shear stress = 2 M l ( ( pi d‘3' (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103

Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos

rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 1.0408 -0.759 0.04 2.2239
2 0.2094 0.936 1.7726 -0.066 0.5725 1.8938
4 0.4188 1.872 3.0249 0.627 1.1069 1.6158
8 0.8376 3.7441 5.2041 1.3202 1.6494 1.3899
16 1.6752 7.4881 9.0258 2.0133 2.2001 1.2053
32 3.3504 14.976 15.921 2.7065 2.7676 1.0631
64 6.7008 29.953 28.557 3.3996 3.3519 0.9534
128 13.402 59.905 52.073 4.0928 3.9526 0.8693
256 26.803 119.81 93.884 4.7859 4.5421 0.7836
512 53.606 239.62 43.86 5.4791 3.781 0.183

X Y

Regression Statistics
R Square 0.9492
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
= 2.0496 Interce 0.7176 0.1796 3.9948 0.0031 0.3034 1.1319
n = 0.7114 x1 0.7114 0.0582 12.227 7B—07 0.5772 0.8456

 

107

15.- Mixer Viscometry, 35%, 35%, 65.5 9 corn syrup, T = 40.8°C, 22.9 g CaCO3

rpm readings Average
1 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7
2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
4 2.1 2.2 2.1 2.2 2.1 2.2 2.1 2.2 2.15
8 3.7 3.7 3.8 3.7 3.7 3.8 3.8 3.8 3.75
16 6.7 6.6 6.7 6.6 6.7 6.7 6.7 6.7 6.675
32 11.9 12 12 11.9 11.9 11.9 12 11.9 11.938
64 21.7 21 5 21.7 21.6 21.6 21.5 21.7 21.6 21.613
128 39.2 39 3 39.2 39.1 39.2 39 38.9 39 39.113
256 71.2 71.6 71.4 71.4 71.2 71.2 71.1 71.2 71.288
128 38 38 37.9 38.1 38.1 38.1 38.1 38 38.038
64 20.9 20.9 20.9 20 9 21 21 21 20.9 20.938
32 11.7 11.6 11.6 11.6 11.6 11.7 11.6 11.6 11.625
16 6.5 6.5 6.5 6.5 6.5 6.4 6.4 6.4 6.4625
8 3.7 3.6 3.7 3.6 3.7 3.6 3.7 3.7 3.6625
4 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1
2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1 0.7 0.6 0.7 0.6 0.7 0.6 0.7 0.7 0.6625
rad/s (N cm) (N m)
rpm omega M M Log Om Log M
1 0.1047 0.01 0.0001 -0.98 -4
2 0.2094 0.0171 0.0002 -0.679 -3.766
4 0.4188 0.0307 0.0003 -0.378 -3.513
8 0.8376 0.0536 0.0005 -0.077 -3.271
16 1.6752 0.0954 0.001 0.2241 -3.021
32 3.3504 0.1706 0.0017 0.5251 —2.768
64 6.7008 0.3088 0.0031 0.8261 -2.51
128 13.402 0.5588 0.0056 1.1272 —2.253
256 26.803 1.0185 0.0102 1.4282 -1.992
128 13.402 0.5434 0.0054 1.1272 -2.265
64 6.7008 0.2991 0.003 0.8261 -2.524
32 3.3504 0.1661 0.0017 0.5251 -2.78
16 1.6752 0.0923 0.0009 0.2241 -3.035
8 0.8376 0.0523 0.0005 -0.077 -3.281
4 0.4188 0.03 0.0003 -0.378 -3.523
2 0.2094 0 0171 0.0002 —0.679 -3.766
1 0.1047 0.0095 9E-05 —0.98 —4.024
Determination of average shear rate
average shear rate = 4.47 angular velocity b = 0.02692 m
average apparent viscosity = shear stress/ shear d = 0.04143 m
k' = 4.47

K = consistency coefficient, Pa.s“n
average shear stress = 2 M / ( ( pi d“3* (b/d + 1/3) ) )
b/d + 1/3 = 0.9831

shear stress: M 9106.2 $e$103
Sigma/
angular average average Gamma
velocit shear shear Lnshear Lnshear viscos
rpm rad/s rate stress rate stress Pa.s
1 0.1047 0.468 0.9107 -0.759 -0.094 1.9459
2 0.2094 0.936 1.5612 -0.066 0.4455 1.6679
4 0.4188 1.872 2.7972 0.627 1.0286 1.4942
8 0.8376 3.7441 4.8788 1.3202 1.5849 1.3031
16 1.6752 7.4881 8.6843 2.0133 2.1615 1.1597
32 3.3504 14.976 15.531 2.7065 2.7428 1.037
64 6.7008 29.953 28.118 3.3996 3.3364 0.9388
128 13.402 59.905 50.886 4.0928 3.9296 0.8494
256 26.803 119.81 92.746 4.7859 4.5299 0.7741
512 53.606 239.62 49.487 5.4791 3.9017 0.2065
X Y
Regression Statistics
R square 0.9600
Observations 10

Coeffic Standar t Stati P-value Lower 95% Upper 95%
K = 1.8315 Interce 0.6051 0.1654 3.6587 0.0052 0.2237 0.9866
= 0.7422 x1 0.7422 0.0536 13.855 2E-07 0.6187 0.8658

XIII. APPENDIX 7. CALCULATIONS AT 55°C TO FIT THE GLOBAL MODEL.

These calculations were used to fit a model using the values coming from the three different
temperatures.

MIX55-1.WK1

ln 55-0-1 ln
sstres sstress k lnk T l/T C srate srate
0.0976 -2.327 0.1295 -2.044 328.15 0.003 0 0.468 -0.759
0.1464 -1.922 0.1295 -2.044 328.15 0.003 0 0.936 -0.066
0.2439 -1.411 0.1295 -2.044 328.15 0.003 0 1.872 0.627
0.309 -1.174 0.1295 -2.044 328.15 0.003 0 3.7441 1.3202
0.6993 -0.358 0.1295 -2.044 328.15 0.003 0 7.4881 2.0133
1.301 0.2631 0.1295 —2.044 328.15 0.003 0 14.976 2.7065
2.7647 1.0169 0.1295 -2.044 328.15 0.003 0 29.953 3.3996
6.131 1.8134 0.1295 -2.044 328.15 0.003 0 59.905 4.0928
15.206 2.7217 0.1295 -2.044 328.15 0.003 0 119.81 4.7859
43.031 3.7619 0.1295 -2.044 328.15 0.003 0 239.62 5.4791
In 55—0-2 1n
sstres sstress k lnk T l/T C srate srate
0.1301 -2.039 0.1896 -1.663 328.15 0.003 0 0.468 —0.759
0.1789 —1.721 0.1896 -1.663 328.15 0.003 0 0.936 -0.066
0.2602 -1.346 0.1896 -1.663 328.15 0.003 0 1.872 0 627
1.1709 0.1578 0.1896 -1.663 328.15 0.003 0 3.7441 1 3202
0.8294 —0.187 0.1896 —1.663 328.15 0.003 0 7.4881 2.0133
1.3335 0.2878 0.1896 -1.663 328.15 0.003 0 14.976 2.7065
2.6508 0.9749 0.1896 -1.663 328.15 0.003 0 29.953 3 3996
6.0009 1.7919 0.1896 -1.663 328.15 0.003 0 59.905 4 0928
15.173 2.7195 0.1896 -1.663 328.15 0.003 0 119.81 4 7859
42.999 3.7612 0.1896 -1.663 328.15 0.003 0 239.62 5 4791
In 55-0-3 ln
sstres sstress k lnk T 1/T C srate srate
0.1301 —2.039 0.1653 -1.8 328.15 0.003 0 0.468 -0.759
0.1952 -1.634 0.1653 -1.8 328.15 0.003 0 0.936 -0.066
0.2602 -1.346 0.1653 -1.8 328.15 0.003 0 1.872 0.627
0.4554 -0.787 0.1653 -1.8 328.15 0.003 0 3.7441 1.3202
0.7969 -0.227 0.1653 -1.8 328.15 0.003 0 7.4881 2.0133
1.301 0.2631 0.1653 -1.8 328.15 0.003 0 14.976 2.7065
2.6671 0.981 0.1653 -1.8 328.15 0.003 0 29.953 3.3996
5.9847 1.7892 0.1653 -1.8 328.15 0.003 0 59.905 4.0928
14.978 2.7066 0.1653 -1.8 328.15 0.003 0 119.81 4.7859
42.641 3.7528 0.1653 -1.8 328.15 0.003 0 239.62 5.4791
In 55—5—1 1n
sstres sstress k lnk T l/T C srate srate
0.6505 -0.43 0.5706 -0.561 328.15 0.003 5 0.468 -0.759
0.7481 -0.29 0.5706 -0.561 328.15 0.003 5 0.936 -0.066
0.8294 -0.187 0.5706 -0.561 328.15 0.003 5 1.872 0.627
1.0408 0.04 0.5706 -0.561 328.15 0.003 5 3.7441 1.3202
1.301 0.2631 0.5706 -0.561 328.15 0.003 5 7.4881 2.0133
1.9515 0.6686 0.5706 -0.561 328.15 0.003 5 14.976 2.7065
3.5453 1.2656 0.5706 -0.561 328.15 0.003 5 29.953 3.3996
7.4158 2.0036 0.5706 -0.561 328.15 0.003 5 59.905 4.0928
17.856 2.8824 0.5706 -0.561 328.15 0.003 5 119.81 4.7859
49.471 3.9014 0.5706 -0.561 328.15 0.003 5 239.62 5.4791
In 55—5-2 1n
sstres sstress k lnk T 1/T C srate srate
0.0867 -2.445 0.1244 —2.084 328.15 0.003 5 0.468 -0.759
0.1301 -2.039 0.1244 -2.084 328.15 0.003 5 0.936 -0.066
0.2168 -1.529 0.1244 -2.084 328.15 0.003 5 1.872 0.627
0.3903 —0.941 0.1244 -2.084 328.15 0.003 5 3.7441 1.3202
0.7481 -0.29 0.1244 -2.084 328.15 0.003 5 7.4881 2.0133
1.4962 0.4029 0.1244 -2.084 328.15 0.003 5 14.976 2.7065
3.1224 1.1386 0.1244 -2.084 328.15 0.003 5 29.953 3.3996
6.9442 1.9379 0.1244 -2.084 328.15 0.003 5 59.905 4.0928
17.11 2.8397 0.1244 -2.084 328.15 0.003 5 119.81 4.7859
48.3 3.8774 0.1244 -2.084 328.15 0.003 5 239.62 5.4791
ln 55-5—3 1n
sstres sstress k lnk T 1/T C srate srate
0.1301 -2.039 0.2039 -1.59 328.15 0.003 5 0.468 -0.759
0.2602 -1.346 0.2039 -1.59 328.15 0.003 5 0.936 -0.066
0.3415 -1.074 0.2039 -1.59 328.15 0.003 5 1.872 0.627
0.5367 -0.622 0.2039 -1.59 328.15 0.003 5 3.7441 1.3202
0.9758 —0.025 0.2039 -1.59 328.15 0.003 5 7.4881 2.0133
1.6425 0.4962 0.2039 —1.59 328.15 0.003 5 14.976 2.7065
6.6026 1.8875 0.2039 —1.59 328.15 0.003 5 29.953 3.3996
7.3507 1.9948 0.2039 -1.59 328.15 0.003 5 59.905 4.0928
17.547 2.8649 0.2039 -1.59 328.15 0.003 5 119.81 4.7859
49.308 3.8981 0.2039 -1.59 328.15 0.003 5 239.62 5.4791

108

109

In 55-5-4 1n
sstres sstress k lnk T 1/T C srate srate
0.2277 -1.48 0.223 -1.501 328.15 0.003 5 0.468 -0.759
0.2602 -1.346 0.223 -1.501 328.15 0.003 5 0.936 -0.066
0.3253 -1.123 0.223 -1.501 328.15 0.003 5 1.872 0.627
0.5204 -0.653 0.223 -1.501 328.15 0.003 5 3.7441 1.3202
0.8294 -0.187 0.223 -1.501 328.15 0.003 5 7.4881 2.0133
1.4962 0.4029 0.223 -1.501 328.15 0.003 5 14.976 2.7065
3.1224 1.1386 0.223 -1.501 328.15 0.003 5 29.953 3.3996
7.1556 1.9679 0.223 -1.501 328.15 0.003 5 59.905 4.0928
17.434 2.8584 0.223 -1.501 328.15 0.003 5 119.81 4.7859
49.439 3.9007 0.223 -1.501 328.15 0.003 5 239.62 5.4791
In 55-15-1 ln
sstres sstress k lnk T 1/T C srate srate
0.1301 -2.039 0.2065 -1.577 328.15 0.003 15 0.468 -0.759
0.1952 -1.634 0.2065 -1.577 328.15 0.003 15 0.936 -0.066
0.3903 -0.941 0.2065 -1.577 328.15 0.003 15 1.872 0.627
0.6993 -0.358 0.2065 -1.577 328.15 0.003 15 3.7441 1.3202
1.2685 0.2378 0.2065 -1.577 328.15 0.003 15 7.4881 2.0133
2.3744 0.8647 0.2065 -1.577 328.15 0.003 15 14.976 2.7065
4.8463 1.5782 0.2065 -1.577 328.15 0.003 15 29.953 3.3996
10.229 2.3252 0.2065 -1.577 328.15 0.003 15 59.905 4.0928
23.548 3.1591 0.2065 -1.577 328.15 0.003 15 119.81 4.7859
63.685 4.1539 0.2065 -1.577 328.15 0.003 15 239.62 5.4791
In 55-15-2 1n
sstres sstress k lnk T 1/T C srate srate
0.2114 -1.554 0.2954 -1.219 328.15 0.003 15 0.468 -0.759
0.3469 -1.059 0.2954 -1.219 328.15 0.003 15 0.936 -0.066
0.515 -0.664 0.2954 —1.219 328.15 0.003 15 1.872 0 627
0.824 -0.194 0.2954 -1.219 328.15 0.003 15 3.7441 1 3202
1.2522 0.2249 0.2954 -1.219 328.15 0.003 15 7.4881 2.0133
2.3852 0.8693 0.2954 -1.219 328.15 0.003 15 14.976 2.7065
4.8463 1.5782 0.2954 -1.219 328.15 0.003 15 29.953 3 3996
10.327 2.3347 0.2954 -1.219 328.15 0.003 15 59.905 4 0928
24.009 3.1784 0.2954 -1.219 328.15 0.003 15 119.81 4 7859
65.181 4.1772 0.2954 -1.219 328.15 0.003 15 239.62 5 4791
In 55-15-3 1n
sstres sstress k lnk T 1/T C srate srate
0.0434 —3.138 0.1322 -2.023 328.15 0.003 15 0.468 -0.759
0.1301 -2.039 0.1322 -2.023 328.15 0.003 15 0.936 -0.066
0.3415 -1.074 0.1322 -2.023 328.15 0.003 15 1.872 0.627
0.6505 —0.43 0.1322 -2.023 328.15 0.003 15 3.7441 1.3202
1.301 0.2631 0.1322 -2.023 328.15 0.003 15 7.4881 2.0133
2.5532 0.9374 0.1322 -2.023 328.15 0.003 15 14.976 2.7065
5.2041 1.6494 0.1322 -2.023 328.15 0.003 15 29.953 3.3996
10.945 2.3929 0.1322 -2.023 328.15 0.003 15 59.905 4.0928
24.979 3.2181 0.1322 -2.023 328.15 0.003 15 119.81 4.7859
66.092 4.191 0.1322 -2.023 328.15 0.003 15 239.62 5.4791
ln 55—25-1 1n
sstres sstress k lnk T 1/T C srate srate
0.2169 -1.528 0.4165 -0.876 328.15 0.003 25 0.468 -0.759
0.4011 —0.913 0.4165 -0.876 328.15 0.003 25 0.936 -0.066
0.7806 -0.248 0.4165 -0.876 328.15 0.003 25 1.872 0.627
1.4311 0.3585 0.4165 -0.876 328.15 0.003 25 3.7441 1.3202
2.7159 0.9991 0.4165 -0.876 328.15 0.003 25 7.4881 2.0133
5.2041 1.6494 0.4165 -0.876 328.15 0.003 25 14.976 2.7065
10.262 2.3284 0.4165 -0.876 328.15 0.003 25 29.953 3.3996
20.832 3.0365 0.4165 -0.876 328.15 0.003 25 59.905 4.0928
42.527 3.7501 0.4165 -0.876 328.15 0.003 25 119.81 4.7859
91.852 4.5202 0.4165 -0.876 328.15 0.003 25 239.62 5.4791
In 55-25-2 1n
sstres sstress k lnk T 1/T C srate srate
0.0922 -2.384 0.1448 -1.932 328.15 0.003 25 0.468 -0.759
0.0434 -3.138 0.1448 -1.932 328.15 0.003 25 0.936 -0.066
0.3469 -1.059 0.1448 -1.932 328.15 0.003 25 1.872 0.627
0.9432 -0.058 0.1448 -1.932 328.15 0.003 25 3.7441 1.3202
2.1467 0.7639 0.1448 -1.932 328.15 0.003 25 7.4881 2.0133
4.6186 1.5301 0.1448 -1.932 328.15 0.003 25 14.976 2.7065
9.286 2.2285 0.1448 -1.932 328.15 0.003 25 29.953 3.3996
16.832 2.8233 0.1448 -1.932 328.15 0.003 25 59.905 4.0928
39.616 3.6792 0.1448 -1.932 328.15 0.003 25 119.81 4.7859
89.803 4.4976 0.1448 -1.932 328.15 0.003 25 239.62 5.4791

sstres
0.1301
0.3253
0.6505
1.301
2.4557
4.6023
9.1396
18.637
38.575
86.274

sstres
.3903
.6017
.9107
.4962
.602
.9439
.6275
19.255
39.876
88.241

\Dle-‘000

sstres
.374
.6017
.9107
.4962
.602
.9439
.6275
19.255
39.876
88.241

\Dle-‘000

sstres
.1301
.2602
.6017
.1709
.4719
.9926
.8389
19.971
40.705
85.103

\DbNO-‘000

sstres
.3036
.4662
.7915
.3823
.5045
.7812
.286
18.637
38.526
87.022

\OONHOOO

sstres
1.0408
1.7726
3.0249
5.2041
9.0258
15.921
28.557
52.073
93.884

ln
sstress
-2.039
-1.123
-0.43
.2631
.8984
.5266
.2126
.9252
.6526
.4575

h4d83NtJC>0

1n
sstress
-0.941
-0.508
-0.094
.4029
.9563
.5981
.2646
.9578
.6858
.4801

#UNNHOO

1n
sstress
-0.983
-0.508
—0.094
.4029
.9563
.5981
.2646
.9578
.6858
.4801

htflh’Nr‘CDO

1n
sstress
—2.039
—1.346
-0.508
.1578
.905
.608
.2863
.9943
.7064
.4439

waNt-‘OO

ln
sstress
-1.192
-0.763
-0.234
.3238
.9181
.5647
.2285
.9252
.6513
.4662

DIABJNFJCDO

1n
sstress
.04
.5725
.1069
.6494
.2001
.7676
.3519
.9526
.5421

DNUNNHHOO

5-25-3

.3193
.3193
.3193
.3193
.3193
.3193
.3193
.3193
.3193
.3193

5-25-4

.5625
.5625
.5625
.5625
.5625
.5625
.5625
.5625
.5625
.5625

U"
I
N
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.5557
.5557
.5557
.5557
.5557
.5557
.5557
.5557
.5557
.5557

U1 00000000003‘111 0000000000”!!! 0000000000WUI

U‘
I
N
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I
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.2951
.2951
.2951
.2951
.2951
.2951
.2951
.2951
.2951
.2951

5-25-7

.4692
.4692
.4692
.4692
.4692
.4692
.4692
.4692
.4692
.4692

5-35-1

.0496
.0496
.0496
.0496
.0496
.0496
.0496
.0496
.0496

NNNNNNNNNWU’I 0000000000WU’I 00000000002‘

lnk

-1.142
-1.142
-1.142
-1.142
-1.142
-1.142
-1.142
-1.142
-1.142
—1.142

lnk

-0.575
—0.575
-O.575
—0.575
-0.575
-0.575
—0.575
-0.575
—0.575
—0.575

lnk

-0.588
-0.588
~0.588
-0.588
-0.588
—0.588
-0.588
-0.588
-0.588
-0.588

lnk

-1.22
-1.22
-1.22
-1.22
-1.22
-1.22
-1.22
-1.22
-1.22
-1.22

lnk

-0.757
-0.757
-0.757
-0.757
-0.757
-0.757
-0.757
-0.757
-0.757
-0.757

.7176
.7176
.7176
.7176
.7176
.7176
.7176
.7176
.7176

000000000

328.
328.
328.
328.
328.
328.
328.
328.
328.
328.

328.
328.
328.
328.
328.
328.
328.
328.
328.
328.

328.
328.
328.
328.
328.
328.
328.
328.
328.
328.

328.
328.
328.
328.
328.
328.
328.
328.
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328.

328.
328.
328.
328.
328.
328.
328.
328.
328.
328.

328.
328.
328.
328.
328.
328.
328.
328.
328.

.003
.003
.003
.003
.003
.003
.003
.003
.003
.003

0000000000

.003
.003
.003
.003
.003
.003
.003
.003
.003
.003

0000000000

1/T

.003
.003
.003
.003
.003
.003
.003
.003
.003
.003

0000000000

1/T

.003
.003
.003
.003
.003
.003
.003
.003
.003
.003

0000000000

.003
.003
.003
.003
.003
.003
.003
.003
.003
.003

0000000000

1/T

.003
.003
.003
.003
.003
.003
.003
.003
.003

000000000

srate
0.468
0.936
1.872
3.7441
7.4881
14.976
29.953
59.905
119.81
239.62

srate
0.468
0.936
1.872
3.7441
7.4881
14.976
29.953
59.905
119.81
239.62

srate
0.468
0.936
1.872
3.7441
7.4881
14.976
29.953
59.905
119.81
239.62

srate
0.468
0.936
1.872
3.7441
7.4881

29.953

59.905
119.81
239.62

srate
0.468
0.936
1.872
3.7441
7.4881
14.976
29.953
59.905
119.81
239.62

srate
0.468
0.936
1.872
3.7441
7.4881
14.976
29.953
59.905
119.81

ln
srate
-0.759
—0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859
.4791

U'lfiubUNND-‘O

1n
srate

-0.066

.627

.3202
.0133
.7065
.3996
.0928
.7859
.4791

U'llthNND-‘O

ln
srate

-0.066

.627

.3202
.0133
.7065
.3996
.0928
.7859
.4791

Uihfib-INNHO

1n
srate

~0.066

.627

.3202
.0133
.7065
.3996
.0928
.7859
.4791

mbbUNNi-‘O

srate
-0.759
-0.066
0.627
1.3202
2.0133
2.7065
3.3996
4.0928
4.7859
5.4791

srate
-0.759
-0.066
.627
.3202
.0133
.7065
.3996
.0928
.7859

thNND—‘O

1n 55-35-2 1n
sstres sstress k lnk T l/T C srate srate
0.9107 -0.094 1.8315 0.6051 328.15 0.003 35 0.468 -0.759
1.5612 0.4455 1.8315 0.6051 328.15 0.003 35 0.936 -0.066
2.7972 1.0286 1.8315 0.6051 328.15 0.003 35 1.872 0.627
4.8788 1.5849 1.8315 0.6051 328.15 0.003 35 3.7441 1.3202
8.6843 2.1615 1.8315 0.6051 328.15 0.003 35 7.4881 2.0133
15.531 2.7428 1.8315 0.6051 328.15 0.003 35 14.976 2.7065
28.118 3.3364 1.8315 0.6051 328.15 0.003 35 29.953 3.3996
50.886 3.9296 1.8315 0.6051 328.15 0.003 35 59.905 4.0928
92.746 4.5299 1.8315 0.6051 328.15 0.003 35 119.81 4.7859
In 55-35-3 1n
sstres sstress k lnk T 1/T C srate srate
0.9107 -0.094 1.8315 0.6051 328.15 0.003 35 0.468 -0.759
1.5612 0.4455 1.8315 0.6051 328.15 0.003 35 0.936 -0.066
2.7972 1.0286 1.8315 0.6051 328.15 0.003 35 1.872 0.627
4.8788 1.5849 1.8315 0.6051 328.15 0.003 35 3.7441 1.3202
8.6843 2.1615 1.8315 0.6051 328.15 0.003 35 7.4881 2.0133
15.531 2.7428 1.8315 0.6051 328.15 0.003 35 14.976 2.7065
28.118 3.3364 1.8315 0.6051 328.15 0.003 35 29.953 3.3996
50.886 3.9296 1.8315 0.6051 328.15 0.003 35 59.905 4.0928
92.746 4.5299 1.8315 0.6051 328.15 0.003 35 119.81 4.7859
In 55-35-4 1n
sstres sstress k lnk T l/T C srate srate
0.9107 -0.094 1.8097 0.5932 328.15 0.003 35 0.468 -0.759
1.5775 0.4558 1.8097 0.5932 328.15 0.003 35 0.936 -0.066
2.7321 1.0051 1.8097 0.5932 328.15 0.003 35 1.872 0.627
4.6837 1.5441 1.8097 0.5932 328.15 0.003 35 3.7441 1.3202
8.359 2.1233 1.8097 0.5932 328.15 0.003 35 7.4881 2.0133
15.173 2.7195 1.8097 0.5932 328.15 0.003 35 14.976 2.7065
27.338 3.3083 1.8097 0.5932 328.15 0.003 35 29.953 3.3996
49.097 3.8938 1.8097 0.5932 328.15 0.003 35 59.905 4.0928
90.42 4.5045 1.8097 0.5932 328.15 0.003 35 119.81 4.7859

"11m1111111“