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thesis entitled

Interrupted Helical Screw Impeller To Characterize
Fluid Foods With Large Particulates

presented by

Alison Paige Omura

has been accepted towards fulfillment
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M.S. dcgfimin Biosystems Engineering

 

 

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c1/CIRC/DateDuep65-p15

 

INTERRUPI'ED HELICAL SCREW IMPELLER TO CHARACTERIZE FLUID
FOODS WITH LARGE PARTICULATES

By

Alison Paige Omura

A THESIS

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

MASTER OF SCIENCE
Department of Agricultural Engineering

2002

ABSTRACT

INTERRUPTED HELICAL SCREW IMPELLER TO CHARACTERIZE FLUID
FOODS WITH LARGE PARTICULATES

By

Alison Paige Omura

Mixer viscometry is an effective means of characterizing fluids containing
particulates. An interrupted helical screw impeller used to determine the flow behavior
of fresh concrete was scaled-down to analyze fluid foods with large particulates. The
mixer viscometer constant was determined to be 1.6 rad‘l by the matching viscosity
method. Large particulate food materials successfully investigated in this study were
cream corn, salsa, a smooth pasta sauce and a chunkier pasta sauce.

Apparent viscosity curves were constructed for products with moderately sized
particulates, or those not exhibiting significant particle-to-particle interaction based on
the raw data: torque and angular velocity. Testing materials exhibited shear-thinning
behavior and temperature dependence. Regression analysis revealed K and n values
ranging from 10.1 Pa 3'1 to 40.3 Pa sn and 0.17 to 0.36, respectively. Regression control
charts of In apparent viscosity versus ln average shear rate were constructed for each food
product. A protocol was suggested for producing and utilizing these charts as a statistical

quality control tool for industry.

ACKNOWLEDGEMENTS

With my deepest sincerity, I thank Dr. James Steffe for the opportunities he has
opened to me. I greatly appreciate his invaluable guidance and support throughout the
years. I thank my parents for their encouragement and unwavering faith in me. The
friendships I have formed and kept during my years at Michigan State University I will
treasure always for keeping my life balanced. I would also like to thank the Department
of Agricultural Engineering and Food Science for acting as an extended family to me. A
special thanks is given to Richard Wolthuis for his services in manufacturing the

interrupted helical screw impeller.

iii

TABLE OF CONTENTS

List of Tables
List of Figures

Nomenclature

1. Introduction
1.1. Overall Description
1.2. Objectives

2. Literature Review

2.1. Fluid Food Rheology

2.2. Mixer Viscometry
2.2.1. Mixer Viscometer Constant (k ')
2.2.2. Fluid Food Applications

2.3. Rheology of Suspensions

2.4. Rheology of Particulate Fluid Foods

2.5. Concrete Rheology

2.6. Statistical Quality Control

3. Theoretical Development
3.1. Mixer Viscometry
3.2. Evaluation of Mixer Viscometry Constant (k ')
3.2.1. Slope Method
3.2.2. Matching Viscosity Method
3.2.3. Torque Curve Method
3.3. Determination of Fluid Properties

4. Materials and Methods
4.1. Equipment
4.2. Experimental Materials
4.3. Data Collection
4.3.1. Phase Characterization
4.3.2. Determination of Mixer Viscometry Constants (k " and k ')
4.3.3. Particulate Food Flow Behavior
' 4.3.3.1. Room Temperature
4.3.3.2. Hot Testing
4.3.3.3. Cold Testing
4.4. Data Analysis
4.4.1. Phase Characterization
4.4.2. Determination of Mixer Viscometry Constants (k " and k ')

iv

Page
vi

viii

Table of Contents (cont’d)

4.4.3. Particulate Food Flow Behavior
4.4.4. Regression Control Charts

5. Results and Discussion
5.1. Phase Characterization
5.2. Mixer Viscometry Constants (k " and k ')
5.3. Particulate Food Flow Behavior
5.4. Regression Control Charts
5.5. Statistical Quality Control Protocol

6. Summary and Conclusions
7. Future Research
Appendix

References

30
30

31
31
34
36
48
51
53
55

69

LIST OF TABLES

Table

2.1.

4.1.

4.2.

5.1.

5.2.

5.3.

5.4.

5.5.

5.6.

5.7.

5.8.

A.l.

A2.

A3.

Mixer viscometer constants.
Ingredient list of the fluid foods with large particulates selected for testing.

Fluid food products with particulates that did and did not require a pre-shear
phase.

Measurements a, b, and c and the ranges of each dimension of foodstuffs in
the fluid food products.

Power law, rheological parameters of the fluid phase of foods with
particulates at 23 °C determined by the helical ribbon system.

Rheological parameters of the standard fluids at 23 °C used to evaluate
k" and k '.

Comparison of the interrupted helical screw impeller and concentric
cylinder using ketchup at 23 °C.

Rheological parameters for foods with particulates at cold, room, and hot
temperatures using the interrupted helical screw impeller.

Activation energy and A values for each fluid food with particulates using
the interrupted helical screw impeller.

Comparison of the rheological parameters of whole fluid food products with
large particulates at room temperature (23 °C) using the interrupted helical
screw impeller to the fluid phase at room temperature (23 °C) using a
helical ribbon.

Comparison of standard errors for each fluid food with large particulates at
each temperature.

Interrupted helical screw impeller data to determine k " using Newtonian
fluids at 23 °C.

Interrupted helical screw impeller data to determine k' using non-
Newtonian fluids at 23 °C.

Interrupted helical screw impeller data for cream corn.

vi

Page

24

27

33

33

34

36

41

42

45

48

56

58

61

List of Tables (cont’d)
A.4. Interrupted helical screw impeller data for Prego.
A.5. Interrupted helical screw impeller data for Ragu.

A.6. Interrupted helical screw impeller data for salsa.

vii

63

65

67

LIST OF FIGURES

Figure
4.1. Interrupted helical screw impeller.

4.2. Interrupted helical screw impeller and container.

5.1. Percentage by weight of solid and fluid phases in foods with particulates.

5.2. Viscosity times angular velocity versus torque for the interrupted helical
screw impeller with Newtonian standard fluids for the determination of the

mixer coefficient constant, k " at 23 °C.

5.3. Mixer viscometer constant, k ' , versus angular velocity for the interrupted
helical screw impeller using non-Newtonian standard fluids at 23 °C.

5.4. A typical raw data set from one trial using the interrupted helical screw
impeller with Prego sauce at 8 °C.

5.5. 1n 11 versus ln 7“ for cream corn at cold (5 °C), room (23 °C) and hot (80
°C) temperatures using the interrupted helical screw impeller.

5.6. In 1] versus 1n 7,, for Prego at cold (8 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

5.7. In T] versus In 7'“ for Ragu at cold (7 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

5.8. 1n 1] versus In 7,, for salsa at cold (7 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

5.9. 1n 11 versus l/T at 18.88 Us for each fluid food with particulates using the
interrupted helical screw impeller.

5.10. 1n 1] versus In 70 of fluid food products with large particulates at cold
temperature (58 °C) using the interrupted helical screw impeller.

5.11. 1n 1] versus ln 7, of fluid food products with large particulates at room
temperature (23 °C) using the interrupted helical screw impeller.

5.12. 1n 1] versus ln 7“ of fluid food products with large particulates at hot
temperature (80 °C) using the interrupted helical screw impeller.

viii

Page
21

22
32

35

36

37

38

39

39

40

42

43

44

List of Figures (cont’d)

5.13. 1n 11 versus In 70 for Prego sauce at cold temperature (5 °C) using the
interrupted helical screw impeller.

ix

47

NONIENCLATURE

A = constant (dimensionless)
d = spindle diameter (m)
D = container diamter (m)
E, = energy of activation for flow (cal g'l mole")
h = impeller height (m)
k' = mixer viscometer constant (rad")
k "= mixer coefficient constant (rad m")
K = consistency coefficient (Pa 8")
M = torque (N m)
N = rotational speed (rev 3")
n = flow behavior index (dimensionless)
n = number of data points
NPO= Power number (dimensionless)
NR“ = impeller Reynolds number (dimensionless)
P = power (N m s“)
R = universal gas constant (1.987 cal/(g - mole K))
se = standard error of predicted y
T = temperature (°C)
T,= reference temperature (°C)
x = independent variable
y = dependent variable
7 = shear rate (5")
Ya = average shear rate (5")
77 = apparent viscosity (Pa 3)
77, = reference apparent viscosity (Pa 8)
y = Newtonian viscosity (Pa 3)
pm: plastic viscosity of a Bingharn fluid (Pa 3)
p = density (kg m3)
0' = shear stress (Pa)
0'II = average shear stress (Pa)
0'o = yield stress (Pa)
9 = rotational speed (rad s")

CHAPTER 1
1. Introduction
1.1. Overall Description

Rheology, or the study of the manner'in which materials respond to an applied
stress or strain, is widely used for process engineering, product development, and quality
control applications within the food industry. Flow behavior information is critical to
efficiently design processing operations such as mixing, pumping and heating.
Characterizing fluid foods is also needed to standardize and quantitatively evaluate
product quality.

Product quality is very important in most industries. Quality is a measure of a
product’s acceptability to consumers. The food industry successfully utilizes statistical
methods such as control charts and regression analysis to monitor and control quality
variables. Fill-level, microbiological safety, and shelf life are examples of variables that
can be monitored and controlled. Rheological information provides a quantitative
measure of the physical material quality for food products.

The utilization of mixer Viscometry to evaluate the rheological properties of fluids
has been extensive. Mixer Viscometry involves the rotation of an impeller immersed in a
sample material. Rheological properties are determined from information concerning the
system geometry, rotational speed, and resulting torque. An advantage to using mixer
Viscometry over traditional rotational Viscometry, such as concentric cylinders and cone
and plate systems, is its ability to assess difficult fluids. Examples of difficult foods are
those exhibiting slip, time-dependent behavior, particle settling problems, and those with

large particles.

Many prepared foods are essentially coarse solid-liquid mixtures. Examples
include salsas, pasta sauces, cream corn and baked beans. Foods that contain large
particulates pose problems with effective analysis and therefore, control. Presently, the
individual solid and liquid phases that comprise the final product are tested separately,
and/or an empirical quality control test is performed. However, the behavior of the
separate phases will be different from the final product mixture. Also, empirical test
results are very difficult to relate to fundamental rheological properties. No agreed upon
means to test for objective, standard characteristics of a final fluid food product with
large particulates exists. This research proposes a method to objectively test the
rheological properties of these products.

The success of using an interrupted helical screw impeller to determine
rheological properties of fresh concrete inspired the experimental technology transfer
described in this work. The name of the impeller describes the discontinuous helical
pattern of the screw. A scaled down interrupted helical screw impeller has been
designed to overcome some of the difficulties presented by complex foods.

1.2. Objectives

The ultimate goal for this research was to develop an impeller for mixer
Viscometry applications that is appropriate for fluid foods with large particulates, with the
potential for use in statistical quality control programs. Specifically, the objectives were:

1) To design, construct and characterize an interrupted helical screw impeller;
2) To evaluate the potential of the interrupted helical screw impeller to characterize

the flow behavior of fluid foods with large particulates;

3) To develop regression control charts for typical fluid foOds containing large

particulates;

4) To develop a statistical quality control protocol for fluid foods with large

particulates.

CHAPTER 2
2. Literature Review
2.1. Fluid Food Rheology

Mathematical models aid in the description of the flow behavior of fluid foods. A

Newtonian model for fluids,

0' = M" [11}
illustrates a simple, linear relationship between shear stress and shear rate. Typical food
products that exhibit this behavior are water, corn oil, and corn syrup. The power law

model,
0' = K 7" [2.2]
represents fluids that are shear-thinning (n < l) or shear-thickening (n > 1). Common

examples of power law fluids are applesauce, orange juice concentrate, and tomato

ketchup. Another standard fluid model is the Bingham plastic,
0=#,.,(7)+0. [2.31
which incorporates a yield stress component, a finite stress required to initiate flow.
Peanut butter, cream cheese, and toothpaste are often considered Bingham plastic fluids.
Apparent viscosity is an important quantitative parameter for fluid foods. It is
calculated by dividing the shear stress by the shear rate. For Newtonian fluids, the
apparent viscosity is a constant value, independent of the shear rate. However, in the

case of power law fluids, apparent viscosity changes with shear rate (Steffe, 1996):

77 = K ()"Y’"1 [2.4]
The above models describe fluids that are considered time-independent. Other

fluids will increase or decrease in shear stress over time at a constant shear rate: they are

known as rheopectic and thixotropic materials, respectively. Viscosity can also be

modeled as a function of temperature:

 

Ed
# - f (T) — ACXP[RT] [25]

Using the above equation, apparent viscosities considered at a constant shear rate can be

found at any temperature using reference values:

melee—a '

This equation assumes that temperature has a negligible effect on the flow behavior
index. Larger E, values indicate a faster change in viscosity with temperature.

2.2. Mixer Viscometry

2.2.1. Mixer Viscometer Constant (k ')

The original investigators of non-Newtonian fluids using mixer Viscometry are
Metzner and Otto (1957). They proposed a method based on a matching viscosity
assumption (also known as the matching viscosity method), which asserts that the
average shear rate for a non-Newtonian fluid is equal to shear rate for a Newtonian fluid
when the Newtonian viscosity equals the apparent viscosity of the non-Newtonian fluid.
They also assumed that the average shear rate is linearly related to the rotational speed of

the impeller by a constant k ':
7.. = k'N [2.7]
A constant value for k' was assumed, although the possibility of variation with the flow

behavior index, n, was not dismissed. Table 2.1 contains a listing of k' values and

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Rieger and Novak (1973) developed a test that served as an indicator of the
suitability of the Metzner-Otto assumption (Eq. [2.7]). The Rieger-Novak method, also
known as the slope method, provided an alternative means to determine k ' . The authors
used several types of agitators to analyze the power consumption in mixing highly
viscous, time-independent, inelastic non-Newtonian fluids with pseudoplastic behavior.
The accuracy of the k' values for the anchor and pitched blade anchor agitators were best
fit as functions of n, rather than constants. The authors compiled a table of k' values for
comparison.

Ducla et al (1983) showed that k' for varying turbine impellers was constant
when mixing true pseudoplastic fluids over the entire shear rate range tested by using the
Metzner-Otto method. The aim of this project was industrial mixing operations.
Edwards et al (1976) established k' values of an anchor, helical ribbon, and two helical
screw impellers using the matching viscosity method. This was one step in a process to
calculate the power consumption with time when agitating a thixotropic liquid. Fluid
properties were observed to influence k '; however, the authors chose not to elaborate on
these relationships and instead accepted constant values as reasonable.

Sestak et al (1986) developed k' as a function of n for anchor agitators. The
function deduced was recommended as a first step of an iterative series to find a
converging value for k'. This procedure was considered successful for both
pseudoplastic and thixotropic fluids.

The matching viscosity method and slope method were compared for the
determination of an average shear rate by Rao and Cooley (1984). The flag impeller in

the study done by Rao (1975) was used in this work along with a star impeller that has 8

vanes. k' values for both methods were in good agreement using each impeller. When
k' is around 20 llrev or greater, the slope method must be used with caution because of a
greater sensitivity to error. Overall, small errors are magnified because of the log-log
relationship required in the slope method. The decided advantage of the slope method
was its simplicity.

Briggs and Steffe (1996) found k' for a Brookfield small sample adapter with a
flag impeller using the slope and matching viscosity methods. While the slope method
resulted in a constant value, the influence of the angular velocity was apparent when
using the matching viscosity method. In this investigation, the flow behavior index
produced inconsistent, but small, effects on k '. Nonetheless, both methods gave similar
results and the use of a constant value was recommended.

Castell-Perez and Steffe (1990) concluded that k' is dependent on n, as well as
other variables for paddle impellers. Two versions of the matching viscosity method
(power curve and torque curve) and the slope method were evaluated to determine the
influence of fluid properties, system geometries and impeller rotational speeds on k'.
The authors found that k' is directly related to n and inversely related to K. Above
rotational speeds of 20 rpm, k.' can be assumed constant. Small gaps between the
impeller and the cup were recommended to reduce the influence of fluid properties.

Nagata (1975) produced an exhaustive investigation of mixing principles and
applications. Nagata covered power consumption equations for different impellers and
fluids and flow regimes, as well as flow models. A straightforward approach was
outlined to develop a Power number/Reynolds number curve for pseudoplastic fluids

based on work by Metzner and Otto (1957).

2.2.2. Fluid Food Applications

Extensive work has been done with mixer Viscometry and fluid food materials.
Castell-Perez and Steffe (1992) prepared a complete review of the development of mixer
Viscometry as related to food applications.

Rao (1975) measured the flow properties of food suspensions using a flag
impeller as an alternative to narrow gap and tube viscometers. k' was found using the
slope method. Tomato puree, applesauce, and apple pulp were determined to be
pseudoplastic in nature. The flow properties for this investigation were valid over only
limited ranges of shear rates however. k' was also determined via the slope method by
Cantu-Lozano et a1 (2000) to study the rheological properties of apple suspensions using
a helical ribbon screw agitator.

Rao and Cooley’s (1984) star impeller along with a 6-vaned impeller was used in
another study done by Qiu and Rao (1988). The goal was to evaluate the effectiveness of
mixer Viscometry when analyzing applesauce for its yield stress and power law
parameters. A constant k' was determined for the 6-vaned impeller using the matching
viscosity method. The obtainable shear rate testing range was narrower than if using a
concentric cylinder.

The k' value of a Haake MV paddle impeller used for the analysis of strained
apricots thickened with modified tapioca starch was investigated by Steffe and Ford
(1985) using the slope method. Mixer Viscometry in this study was applied to thixotropic
materials as well as time-independent (after mechanical degradation) materials.

Castell-Perez et al (1987) used a flag impeller with a Brookfield small sample

adaptor. k' was found using the slope method. In this study, as well as the work by

10

Briggs and Steffe (1996) on a flag impeller, the mixing systems were designed for the
analysis of power law fluid foods. A flag impeller was also used by Mackey et a1 (1987)
to analyze shear-thinning behavior of food with mixer Viscometry techniques. A
matching viscosity method was used to define k' because the slope method indicated a
dependency on rotational velocity and therefore an increased chance of error in
calculations. It was also found that the influence of n on k' decreases with increasing
angular velocity. This particular matching viscosity method, later coined the torque
curve method by Castell-Perez and Steffe (1990), was also used in Lai et a1 (2000) to find
the k’ value of a Rapid Visco Analyser (RVA) system impeller. At speeds of 60 rpm
and greater the k' value was considered constant. Applications of the RVA system are
primarily for analyzing the rheological behavior of starch slurries during heating and
cooling.
2.3. Rheology of Suspensions

The rheological properties of particulate suspensions have been investigated for
many purposes such as particle removal from surfaces, fines mobilization in porous
media, transport of proppants in fractured reservoirs, and cleaning of drill holes (Patankar
and Hu, 2000). Wildemuth and Williams (1984) focused on packing fraction when
evaluating the apparent viscosity of concentrated suspensions. These concepts were
intended for examining the rheology of dense coal suspensions.

Using a helical ribbon stirrer, the rheological changes of mixing an emulsion with
a suspension were studied by Hugelshofer et al (2000). These mixtures are relevant for

calorie-reduced food products. Using a model suspension, the slope method and

11

matching viscosity method were both employed to calculate apparent viscosities and
shear rates. These results were similar to concentric cylinder data.
2.4. Rheology of Particulate Fluid Foods

There has been much research on the rheological behavior of fine food particles.
Schubert (1987) discusses the branch of process engineering associated with particles
known as particle technology. Specifically, Schubert’s article addresses fine solid
particles on the order of micrometers (the largest sector of particle technology) and
reviews the properties and characterization of these systems. Examples from food
technology were used to illustrate key aspects. Rao (1987) clarified the relationship
between composition and rheological behavior of food suspensions of plant origin, such
as applesauce and concentrated orange juice. The flow properties of plant food
suspensions were put in terms of temperature, concentration, suspending medium and
suspended solids. Flow behavior studies pertaining to fluids with larger particulates are
less abundant. Currently, there is no agreement on a methodology or instrumentation to
investigate these solid-liquid food mixtures.

Particulate food mixtures differ from food suspensions based on the size of the
individual solids. Large particulates are generally measured on a centimeter scale, come
in a variety of shapes and have only a small difference in density with the carrier fluid.
The carrier fluids are most often non-Newtonian, specifically pseudoplastic, and are
highly viscous (Lareo et al, 1997). Some studies on the heat transfer of fluid foods with
large particulates have been conducted. Sannervik et al (1996), for example, found that
the inner heat transfer coefficient increased with increasing food particulate concentration

in a tubular heat exchanger.

12

Bhamadipati and Singh (1990) investigated the flow behavior of frozen thawed
peas and dry soybeans in tomato sauce, using tube Viscometry. These particulates were
used as model foods rather than being an actual, commercial food product. Pressure
gradients and volumetric flow rates were used to determine the flow properties. Based on
their results, the power-law model best represents the flow behavior of solid-liquid
mixtures. Solids and particulate presence increases the consistency coefficient and
decreases the flow behavior index. The disadvantage of this technique is the large
amount of testing material required.

Rotational Viscometry was utilized by Pordesimo et al (1994) to evaluate solid-
liquid food mixtures at low shear rates. A very-large-gap parallel plate system was used
to determine rheological properties of edible compounds made to imitate liquid food
products with large particulates in the range of 0.32 cm to 0.95 cm. Effects of carrier
viscosity, particle size, particle concentration, and particle shape were investigated.
Pordesimo (1991) reviewed several proposed instruments and procedures to evaluate
coarse mixtures. Still, however, not enough is known about large-gap rotational
viscometers.

Martinez-Padilla et a1 (1999) used mixer Viscometry to evaluate the physical
properties of coarse food suspensions; specifically Mexican sauces. A shear-thinning
fluid with pepper and tomato seeds was analyzed using a helical ribbon, a tube
viscometer and a wide gap spindle. The helical ribbon best characterized the flow
behavior. The ribbon was better able to maintain a pseudo-homogenous flow and

required the smallest sample. The disc-shaped seeds were the largest (albeit still on the

13

small side of large particulate systems) particles used in combination with mixer
Viscometry. A
2.5. Concrete Rheology

In the concrete industry, many empirical tests exist to determine the flow
properties of fresh concrete (Bartos, 1992). Rheological information about concrete is
important because many aspects such as case of placement, durability and strength
depend on the flow characteristics. An obstacle for the analysis of fresh concrete is the
complexity of the composition. Particles found in concrete range from 1pm cement
grains to 10 mm coarse aggregates to even 100 mm particulates found in dams (Ferraris,
1999).

Tattersall (197 3).argues that since it has been accepted that. fresh concrete behaves
as a Bingharn plastic fluid, at least two shear rates are necessary for an accurate
characterization of its flow curve. Tattersall and Bloomer (1979), discussed the trials and
tribulations of developing an apparatus to test fresh concrete. The authors diverged from
historical usage and approached the problem using mixer Viscometry. The device
developed became the first and most widely known instrument to measure the flow
properties of concrete (Ferraris, 1999). A mixer (of interrupted helix form) that alloWed
concrete to fall back through the gaps and create localized mixing was fabricated.
Mathematical relationships were formed translating the raw data to rheological values.

Wallevik and Gjorv (1990) modified the apparatus and testing procedure of
Tattersall and Bloomer (1979) to produce more reliable results. The main drawbacks to
this apparatus were the required calibration, the large size of the apparatus making it not

test-site friendly, and the computations required to find results (Bartos, 1992). Versions

14

of this instrument are now commercially available as the BML Viscometer or the [BB
Concrete Rheometer (Ferraris, 1999).
2.6. Statistical Quality Control

Statistical quality control is used in many areas of the food industry, such as
product research and development, material control, production quality control and
product performance (Hubbard, 1990). When a process is in statistical control, the
distribution of data is attributed to stable and repeatable variation inherent in the process
(Bafna, 1995).

Dr. Walter A. Shewhart first developed control charts in 1924 as a graphical
device for the detection of unusual variation of data resulting from a repetitive process.
Control charts can be categorized by the type of application: for variables, attributes, or
individual points. Variables encompass any quality characteristic that can be measured,
while attributes are classified as either defective or nondefective. Rather than plotting
characteristics against time, as in variable and attribute charts; individual charts plot
against each specific observation (Puri et al, 1979). Upper and lower control limits are
put in place as the boundaries of acceptability. A common method is to use control
charts in pairs: one chart for the value of the variable, and one chart for the range or
spread of the values.

Bafna (1995) discussed the importance of rheological instruments in statistical
control. The variability of the instrument should less than or equal to one tenth of the
variability of the process it is monitoring. When monitoring viscosity, Bafna

recommended taking values from the highest and lowest shear rates and plotting them on

15

individual charts. The author also outlined six rules when using individual charts to 0
determine whether a process is out of control.

Mandel (1969) combined linear regression and control chart theory to construct
regression control charts as a means to analyze postal efficiency. Regression control
charts are applicable when controlling a variable that is linearly dependent upon the
magnitude of an independent variable. The chart is a linear plot of a variable with upper
and lower control limits running parallel with the control line. In the case of several
nonlinear relationships, a suitable transformation can make them linear (Chatterjee and
Price, 1977). The control limits can be set at any distance from the control line, but are
usually kept at 2 or 3 times the standard error of estimate. This decision is based upon
economics and experience of the management (Mandel, 1969). The Mandel (1969)

method was used in the current research.

16

CHAPTER 3
3. Theoretical Development
3.1. Mixer Viscometry
Applying dimensional analysis to mixer Viscometry with Newtonian fluids yields

the following empirical relationship:
Npo = —- [3.1]

This relationship is Widely accepted when applied in the laminar flow regime, and can be

used for non-Newtonian fluids. The Power number and impeller Reynolds number are

 

 

 

 

defined as
P
NPo = p523d5 [3.2]
and
2 .
NM = ‘ [3.3]
ju
Substituting Equations [3.2] and [3.3] into Equation [3.1] yields
5”, = ’2‘” [3.4]
d £2 ,0 d 52p
Using the definition of power,
P = M $2 [3.5]
Equation [3.4] simplifies to
M
= A 3.6
(139 ll [ ]

By replacing the Newtonian viscosity with an apparent viscosity (Equation [24]), that is

evaluated at an average shear rate given by

17

7.. = k '9 13-7]
Equation [3.6] becomes .

M
(13:2

 

= AK (k '52)"1 [3.8]

The mixer viscometer constant, k ', is exclusive to each mixer system.
3.2. Evaluation of Mixer Viscometry Constant (k ')
3.2.1. Slope Method
The slope method asSurnes a constant value for k'. Simplifying Equation [3.8]

and! taking the logarithm of each side yields

log", [5%) = logm(A) — (1 — n) logw(ki') [3.9]

k' is determined from the slope of the line, loglo (£375) vs. (1 — n) . Rieger and Novak

(1973) argued that if Equation [3.9] was not linear, then the average shear rate
assumption expressed by Equation [3.7] is not valid.
3.2.2. Matching Viscosity Method

This technique is a valuable alternative to the slope method for determining the
mixer viscometer constant. A power curve is first constructed using Newtonian fluids to
determine A. Then, a standard non-Newtonian fluid, in which the K and n values are
known, is mixed at a constant rate using the chosen impeller system and the resulting
Power Number is measured. Using the matching viscosity assumption (1] = p.) and

Equation [3.1], the apparent viscosity is defined by

,7 = (4252mm...)
A

 

[3.10]

18

Considering Equation [2.4], the average shear rate can be calculated:
1

. = 17:1
7. [K] [3.11]

When several iterations of the process have been conducted at different speeds, using
standard non-Newtonian fluids with well defined flow behavior indices, k'can be

calculated from Equation [3.7] as

. 7
k =—"— 3.12
9 [ ]

Using this method allows for k' to be evaluated as a function of angular velocity and the
flow behavior index.
3.2.3. Torque Curve Method

To determine k', Mackey et a] (1987) developed a method which was later
coined the torque curve method by Castell-Perez and Steffe (1990). Rearranging
Equation [3.6] yields

_ M _k"M
M352 :2

 

g [3.13]

where k", the mixer coefficient constant, is dependent solely on the system geometry.
Making the matching viscosity assumption and substituting Equation [2.4] into Equation

[3.13], yields an equation for k ':

were):

3.3. Determination of Fluid Properties

In laminar mixing, the relationship between torque and angular velocity is found from

Equation [3.8]

19

log,o(M) = log,o(d3AK(k )"")+nrog,o(rz) [3.15]
where n is the slope of the line. K can be determined by either of two methods. If the
values of d, A, k’, and n are known, then K can be calculated using the constant term
(loglo (d3AK (k ')"") of Equation [3.15]. The alternative method is to solve for K using

the following equation:

 

r2"! k "y
M,)( ,( D

K =K(
’ My Q:’(k')"’

x

) [3.16]

where x denotes the fluid with unknown properties and y designates the reference fluid
with known properties. This method eliminates the need for determining the value of A.

If the value of k' is known, then rheological parameters may also be determined
by assembling a plot of apparent viscosity versus average shear rate. The average shear
rate is calculated using Equation [3.7]. Apparent viscosity is found by applying the
matching viscosity assumption and substituting the apparent viscosity for Newtonian
viscosity in Equation [3.13]:

k"M
=— 3.17
77 Q l l

Curve fitting programs can then easily characterize the fluid using an appropriate

rheological model.

20

CHAPTER 4

4. Materials and Methods
4.1. Equipment

The interrupted helical screw impeller was fabricated from stainless steel and
consists of 4 triangular blades (0.08 cm thick) joined to the shaft, pointing toward the
shaft, in a helical pattern (Figure 4.1 and 4.2). The initial impeller and cup system was a
1/3-scale replica of the design by Wallevik and Gjorv (1990), intended for testing fresh
concrete. Through preliminary trials, the cup diameter was increased to improve

movement of the particulate foods and reduce slip of particulates against container.

 

 

 

 

fir.—
0.4
+1594—
12.18
C 788
y”
’ 75° 2.71
V v
|1.88|

Figure 4.1. Interrupted helical screw impeller (all dimensions in cm).

21

 

1

3.2.01»

1 9.3 D

 

 

TV

27

t/
i

 

 

 

 

 

Figure 4.2. Interrupted helical screw impeller and container (all dimensions in cm).

Using an adaptor, the impeller was attached to a Haake VT550 Viscometer
(Haake, Paramus, NJ). The torque range of the instrument is 0.1 m Nm to 30 m Nm. A
rheological software program, RheoWinZ, controlled the VT550 and collected the raw
data: angular velocity and torque. The testing material was loaded into an 800ml
capacity glass beaker. A foam jacket was used to insulate the beaker and prevent
slippage on the test stand. The container was raised into testing position by a scissor
jack.

Samples for cold temperature testing were cooled in a kitchen refrigerator
(Kenmore, Hoffman Estates, IL) with temperatures varying by i1 °C. Heating of the

samples for hot temperature testing took place in a drying oven (Isotemp Oven, Fisher

22

Scientific, Itasca, IL) with a variation of :1 °C. Thermometers provided temperature
verification.

Using the Haake VT550, the W1 concentric cylinder system with a gap of 1mm
was chosen for evaluating non-particulate fluids. Properties were determined using
standard rheological methods (Steffe, 1996). The temperature was controlled using a
water bath (Haake F6, Paramus, NJ) to within :tO.1 °C. Densities of the Newtonian fluids
were determined with a 100 ml specific gravity cup.

A ‘11 inch square gap sieving pan was used to separate large particulates from the
testing foods. An electronic scale was employed to weigh both solid and liquid phases.
Particulate sizes were manually measured using a caliper (10.02 mm). The liquid phase
contained M: inch particulates able to pass through the sieve; therefore, a concentric
cylinder system was not appropriate to assess the rheological properties because of the
small gap size. A helical ribbon and W1 cup attached to the Haake VT550 was able to
successfully evaluate the fluids. The helical ribbon was 3.4 cm in height and 3.3 cm in
diameter. Agrawal (2001) determined the k" and k' values as 12566 rad m'3 and 1.38
rad", respectively, for this mixer viscometer system.

4.2. Experimental Materials

Home Harvest Pure Honey (United Wholesale Grocery Company, Grand Rapids,
MI) and Karo Light Corn Syrup (Bestfoods, Englewood Cliffs, NJ) were the Newtonian
fluids used to determine k " for the interrupted helical screw impeller system. All food
samples were purchased at a local grocery store.

Three standard power law fluids were used to determine k ': 2.5% and 2.0% (by

weight) hydroxypropyl methylcellulose (Dow Chemical Company, Midland, MI) and

23

1.0% guar gum (Sigma Chemical, St. Louis, MO). The hydroxypropyl methylcellulose
solutions were prepared by the hot/cold technique for aqueous media as directed by the
manufacturer. The guar gum solution was prepared by directly adding the powder to
room temperature deionized water.

The food products with particulates chosen for this investigation were Ragu Old
World Style Traditional pasta sauce (Lipton, Englewood Cliffs, NJ), Prego with Fresh
Mushrooms pasta sauce (Campbell, Camden, NJ), Chi-Chi’s Restaurante Fiesta Thick
and Chunky salsa (Hormel Foods, Austin, MN), and Del Monte Sweet Corn Cream Style
(Del Monte, San Fransisco, CA). Table 4.1 lists all the ingredients in each food product.
Dinty Moore Beef Stew (Hormel Foods, Austin, MN) and Bush’s Original Baked Beans
(Bush’s, Knoxville, TN) were initially explored but rejected as test subjects for reasons to

be discussed later.

Table 4.1. Ingredient list of the fluid foods with large particulates selected for testing.

 

Food Ingredients
Cream Corn Corn, water, modified food starch, sugar, salt (for flavor)

Prego Tomato puree (water, tomato paste), diced tomatoes, corn syrup,

vegetable oil (corn cottonseed, and/or canola), mushrooms, salt, spices
(Basil, Oregano and other spices), onion powder, dehydrated garlic,
citric acid, dehydrated parsley, spice extract.

Ragu Tomato puree (water, tomato paste), soybean oil, high fructose corn

syrup, salt, dried onions, extra virgin olive oil, Romano cheese (cow's
milk, cheese cultures, salt, enzymes), spices, natural flavor

Salsa Tomatoes, Jalapeno peppers, water, tomato paste, onions, vinegar,

salt, sugar, garlic powder, onion powder, spices, sodium benzoate (to
retard spoinlage after opening), citric acid, natural flavor

24

4.3. Data Collection Method
4.3.1. Phase Characterization

The particulate foods were emptied onto the Ms inch sieve in an even layer, enough
to cover the entire screen. A collection pan underneath the sieve caught the draining
fluid. Gravity and slight manual agitation of the sieve facilitated the separation of solid
and liquid components. When the drainage had abated, the two phases were ready for
analysis. Each phase was weighed separately. Three sieving trials were run using fresh
samples.

The solids portion was divided into the different groups of food present, such as
tomatoes, onions, and corn kernels. Ten of each type of food were randomly chosen and
measured in three directions: a, b, and c. a is the longest dimension, b is the longest
dimension perpendicular to a, and c is the longest dimension perpendicular to both a and
b. This method of characterizing the shapes was recommended by Mohsenin (1986).

Rheological pr0perties of the fluid portion were determined at room temperature
(23 °C) with the helical ribbon system. A steady-state shear rate ramp up from 1 s'1 to 27
s" and then back down from 27 s'1 to 1 s'1 was conducted for each sample. Two-second
equilibrating times were assigned to each data point. Three repetitions of each fluid food
were conducted.

4.3.2. Determination of Mixer Viscometry Constants (k " and k ')

The reference fluids included Newtonian fluids (corn syrup and honey) and non-
Newtonian fluids (methylcellulose and guar gum solutions). The flow properties of the
reference fluids were evaluated at room temperature (23 °C) using the MVl concentric

cylinder. Shear rates ranged from 10 s'1 to 100 s'1 for the corn syrup and 3 s'1 to 23 s‘1 for

25

the honey. The differing maximum shear rates were based on the torque capacity of the
instrument. The steady state test consisted of increasing and decreasing through the shear
rate ranges twice. Each ramp was divided into 10 steps with a 30 second equilibrium
time taken before a viscosity reading was recorded. Two repetitions of corn syrup and
honey were completed.

Apart from the different shear rate ranges, the Newtonian data collection method
was repeated for non-Newtonian fluids. For 1.0% guar gum, the range was 20 s'1 - 150 s'
‘; for 2.0% Methylcellulose, 30 s‘1 — 250 s"; and 2.5% Methylcellulose, 10 s" — 70 s“.
The different shear rate ranges represent the obtainable torque ranges for each fluid.
Each fluid trial was duplicated with fresh samples.

The constant, k ", of the interrupted helical screw system was determined using
the Newtonian fluids at room temperature (23 °C). Approximately 500 ml of a reference
fluid was loaded into the glass beaker. The container was raised into position until the
top of the highest blade was just below the fluid surface (Figure 4.2). The impeller was
centered in the beaker using a ruler. A bubble balance was used to assure a level testing
surface. A steady state ramp up test ran from 1 rad s’1 to 30 rad s'1 and from 0.5 rad s'1 to
12 rad s'1 for the corn syrup and honey, respectively. The torque capacity of the Haake
VT550 was reached at the respective maximum angular velocity for each fluid. Each test
consisted of thirty steps with an acquisition time of thirty seconds for each torque
measurement. Two trials were conducted for each fluid.

The procedure to determine k ' of the interrupted helical screw system was carried
out at room temperature (23 °C). Samples were loaded in the same manner as for the k "

trials. The steady-state test for guar gum and 2.0% Methylcellulose consisted of 25 steps,

26

ramping up from 1 rad s'I to 30 rad s", in thirty second increments. While the protocol
was identical to the former two fluids, the maximum angular velocity for the 2.5%
. Methylcellulose was 20 rad 5". Two tests were executed for each fluid.
4.3.3. Particulate Food Flow Behavior
4.3.3.1. Room Temperature

The food products were tested at three different application temperatures: a cold
refrigerated temperature, ambient temperature, and a hot serving temperature. The
particulate foods were emptied from their original containers into a large, separate
beaker. Since large particulates may settle during storage and shipping, slow and gentle
manual mixing with a spoon for approximately 15 seconds was done to create a
homogenous mixture. Loading of the samples into the testing apparatus was completed
as outlined for k". Preliminary tests revealed that a pre-shearing phase to eliminate
slight time-dependent behavior was necessary for some foods. This pre-shear session
consisted of rotating the interrupted helical screw impeller for 100 seconds at 5 rad 8".

Table 4.2 notes which products and temperature settings required the pre-shear test.

Table 4.2. Fluid food products with particulates that did and did not require a pre-shear
phase.

 

Food Product Cold Room Hot
Cream Corn X X -

Prego X X -
Ragu - - -
Salsa X X X

 

X pre-shear; - no pre-shear

27

After the pre-shear, the particulate foods were all subjected to a steady state test:
3 rad 5" through 20 rad s"; and 20 rad 3'1 through 3 rad s". 30 torque measurements
were recorded in each direction with a 2 second equilibrating time for every point. The
presence of slip and particulate interaction were carefully monitored. Ten repetitions, the
minimum number to calculate a standard deviation (Bafna, 1995), were completed for
each brand of food using fresh samples each time.
4.3.3.2. Hot Testing

Samples were loaded in the glass beaker containers as done for the room
temperature trials and covered. The containers were placed into the oven, set at a
temperature of 90 °C. When the samples had reached a temperature comfortably over 80
°C, they were quickly transported to the Haake VT550. The temperature at the time of
testing was approximately 80 °C with a temperature drop of 3 to 4 °C throughout the
duration of the test. The setup and testing protocol was the same as that described for the
room temperature tests. A pre-shearing section was not conducted for cream corn,
Prego, or Ragu because no time-dependent behavior was evident from preliminary trials.
Ten trials of each food product were completed.
4.3.3.3. Cold Testing

Samples, already loaded into the testing containers, were placed in a kitchen
refrigerator. The samples were allowed to equilibrate to approximately 6 °C before being
tested. Temperature differences between the beginning and the end of the test were
maintained at less than 2 °C. The setup and testing protocol followed the room

temperature testing procedure. A pre-shear section was incorporated into the test for

28

cream corn, Prego and the salsa to eliminate time dependency. Ten replicates were made
of each product.

4.4. Data Analysis

4.4.1. Phase Characterization

To characterize the solid phase, averages of the measurements in each direction
were taken of each food type (onions, peppers, mushrooms, etc.). Torque and angular
velocity data from the helical ribbon system were used to evaluate the fluid phase.
Apparent viscosity was calculated using Equation [3.17] and Equation [3.7] was used to
calculate the average shear rate. The rheological parameters were determined by
regression analysis of apparent viscosity versus average shear rate plots using the power
law model (Equation [2.4]).

4.4.2. Determination of Mixer Viscometry Constants (k " and k ')

The RheoWin2 software automatically converted the data to viscosity and shear
rate readings for the concentric cylinder tests. Averages were taken of the Newtonian
viscosity readings for a representative value for each Newtonian fluid. Rheograms of
apparent viscOsity versus shear rate were made and regression analysis was performed to
determine the K and n values of the non-Newtonian fluids.

The raw data used from the interrupted helical screw impeller trials were torque
and angular velocity. Based on Equation [3.13], a plot of Newtonian viscosity times
angular velocity versus torque was constructed from the Newtonian fluid data. The slope
of the line was equal to k". k' was determined using Equation [3.14] for each of the
non-Newtonian standards. A plot of k' versus angular velocity was produced to show

any dependency on n and mixing speeds.

29

4.4.3. Particulate Food Flow Behavior

Using the newly determined mixer viscometer constants, apparent viscosities and
average shear rates were calculated with Equations [3.17] and [3.7], respectively. The
flow behavior of the particulate foods was characterized by a rheograrn of ln 1] versus ln
7,. Results were compared for temperature dependence and to the properties of the fluid

phase determined using the helical ribbon system.
4.4.4. Regression Control Charts
The general procedure to set up regression control charts is outlined by Mandel

(1969). In the current study, a linear plot of ln 77 versus 1n 7, was chosen as the quality

control condition. Ten trials of each food type at a certain temperature were averaged to

produce one characterizing control line. The standard error based on the predicted y is

se = "I -n(nl_—2)] "Z yz “ (Z Y)2 - [nznx§;(2?(2:(§):zy)]z [41]

Three times the standard error above and below the control line were drawn as the limits

 

of the regression chart.

3O

CHAPTER 5

5. Results and Discussion
5.1. Phase Characterization

The result of separating the fluid and solid phases of the particulate foods is
illustrated in Figure 5.1. Ragu pasta sauce contained the highest liquid portion by weight,
while salsa had the highest amount of solids. Table 5.1 lists the average measurements of
a (maximum dimension), b (maximum dimension perpendicular to a), and c (maximum
dimension perpendicular to a and b) for each food type in all the particulate food
products. Also included in Table 5.1 is the range of measurements taken for each
dimension. The tomato pieces in the salsa were the largest at nearly 2 cm. The largest
particulate in each product was close to 1 cm and above. Some of the dimensions of the
spices and small onion and garlic flakes were not measured because they were considered
insignificant.

Power law models best fit the flow behavior of the particulate food fluid phase.
The rheological parameters for each fluid phase measured using the helical ribbon are
listed in Table 5.2. The fluids of the cream corn and salsa had similar, low consistency
coefficient values. Prego and Ragu fluids had similar flow behavior indices; while the

cream corn fluid was the least shear-thinning.

31

100%

80%

60%

40%

20%

0%

 

F Liquids D Solids

 

 

 

 

 

Cream Corn Prego Ragu Salsa

Figure 5.1. Percentage by weight of solid and fluid phases in foods with particulates.

32

Table 5.1. Measurements a, b, and c and the ranges of each dimension of foodstuffs in
the fluid food products.

 

Food Product Average 3 Range* Average b Range* Average c Range*

 

(cm) (cm) (cm) (cm) (cm) (cm)
Cream Corn
-Kernel 1.00 0.33 0.81 0.32 0.44 0.20
Prego
-Tomato 1.48 0.65 1.23 0.93 0.68 0.77
~Mushroom 0.81 0.34 0.74 0.25 0.61 0.49
-Onion/Garlic 0.64 0.54 0.29 0.30
—Spice 0.90 1.04
Ragu
-Onion 1.24 1.20 0.35 0.22 0.19 0.14
Salsa
-Tomato 1.94 1.46 1.27 0.61 1.00 0.91
-Pepper 1.09 0.44 0.79 0.60 0.47 0.35
-Onion 0.99 0.36 0.83 0.45 0.36 0.26
-Seed 0.36 0.19 0.14 0.06 '

 

*Highest value - lowest value

Table 5.2. Power law, rheological parameters of the fluid phase of foods with
particulates at 23 °C determined by the helical ribbon system.

 

 

Food K n R2
(Pa 8“) (-)

Cream Corn 3.2 0.43 0.981

Prego 23.8 0.17 0.997

Ragu 18.8 0.19 0.993

Salsa 3.4 0.29 0.987

 

33

5.2. Mixer Viscometry Constants (k " and k ')

The pr0perty values of the standard fluids are listed in Table 5.3. A graphical
representation of Equation [3.13] as Newtonian viscosity times angular velocity versus
torque was constructed (Figure 5.2) utilizing the Newtonian standards. The mixer
coefficient constant (k"), equal to the slope, was found to be 3047.4 rad rn’3 with a R2
>0.99. This value is unique to the specific geometry of the interrupted helical screw/cup

system used in this study.

Table 5.3. Rheological parameters of the standard fluids at 23 oC used to evaluate
k" and k'.

 

 

Standard Fluid p. K n
(Pa 8) (Pa 8") 0
Honey 7.5 1.00
Corn Syrup 2.3 1.00
1.0% Guar Gum 7.6 0.29
2.0% Methylcellulose 9.9 0.54
2.5% Methylcellulose 16.8 0.59

 

34

100

 

 

 

 

 

 

 

 

*3 0 Corn Syrup X Honey , I

53. 80 ~ '

.é‘ .

.8. , .3 5'

§ 60 - .5 .9?

g Q . " ' Slope = 3047.4

* (i " .4.) r

b x ‘

8 20 ,_ . o O

8 . '

s ,
O 1 1 1 1 1 1
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Torque , uNm

Figure 5.2. Viscosity times angular velocity versus torque for the interrupted helical
screw impeller with Newtonian standard fluids for the determination of the mixer
coefficient constant, k" at 23 °C.

k' was determined using Equation [3.14] for each non-Newtonian standard fluid.
The data show that k' varies with angular velocity and n (Figure 5.3). However, when
focusing on data from 3 to 30 rad s", the k' values become relatively independent of
angular velocity. A value of 1.6 rad" was determined for k' by plotting the average
shear rate versus the angular velocity for each material. The slope of the regressed line
for all the data was taken as the mixer viscometer constant. This finding is comparable to
other studies (Qiu and Rao (1988), Rao and Cooley (1984), and Lai et al (2000)). An
approximate value of k' is acceptable because it is used to estimate the average shear
rate. The actual shear rate varies widely during mixing. The suitability of this value was

verified against a conventional rheometer using ketchup. Table 5.4 compares the

35

regression curves of the ketchup data for each instrument. The match is not exact but

adequately close because the k' value is an estimate.

 

 

 

 

 

 

 

 

10
A 1.0% Guar Gum (n = 0.29)
8 _ B D 2.0% Methylcellulose (n = 0.54)
0 2.5% Methylcellulose (n = 0.59)
'7 6 'o
-o
8 o a
.34 _ fl
4 g B
o B a
2 30 38330403550“. 5°05 u u a
” u u a a
A 5 585 0200555055.}
0 l l I l l
0 5 10 15 20 25 30

Angular Velocity, rad s’1

Figure 5.3. Mixer viscometer constant, k', versus angular velocity for the interrupted
helical screw impeller using non-Newtonian standard fluids at 23 °C.

Table 5.4. Comparison of the interrupted helical screw impeller and concentric cylinder
using ketchup at 23 °C.

 

Instrument K n R2
(Pa 8“) (-)
Interrupted Helical Screw Impeller 27.1 0.23 0.979

Concentric Cylinder 23.8 0.22 0.993

5.3. Particulate Food Flow Behavior
Figure 5.4 shows a typical plot of the raw data scatter for one run using the
interrupted helical screw impeller and Prego sauce at the cold temperature (8 °C). The

resulting trend showing torque to be linearly related to angular velocity was found for all

36

the products with particulates. Each product exhibited a high level of variation in torque
response most probably due to the impeller blades coming in contact with different
particulates. Variation between tests was attributed to the slightly different composition

of particulates in each test batch.

 

Cold Prego

6

Torquex10,Nm
moofia’a‘o
o 8 8 § § § §

 

 

l l l i

0 5 10 15 20 25
Angular Velocity, rad s’l

 

Figure 5.4. A typical raw data set from one trial using the interrupted helical screw
impeller with Prego sauce at 8 °C.

Using the value of k' and Equation [3.7], the average shear rate range for testing
the fluid foods with particulates was 4.8 s‘1 to 32 s". By taking the logarithm of each side

of Equation [2.4], a linear relationship between apparent viscosity and average shear rate

is formed:
ln 77=ln K+(n—l)ln 70 [5.1]
1n 7] versus In 70 was plotted for cream corn, Prego, Ragu, and salsa (Figures 5.5 — 5.8).

The regressed lines for all three temperatures appear on each figure. The upper range of

37

the angular velocity (17.1 rad s'l - 20 rad s") for the salsa trials at hot temperature was
eliminated from analysis because excessive slip (a violation of a basic assumption) was

observed at the wall of the container. Data results were no longer linear for those

 

 

 

 

 

 

 

 

conditions.
2.5
. 0 Cold U Room A Hot
w o
5?. 2 ' o 0 Cream Corn
. E o

5‘ 9 ° 0
'5 2 R O 0 O
.E A D D O 0 o
> A A D D 0
‘E AAEDDDD °°°°°o
g l P Abbagnnunng 0%
Q. A AA 0
2‘ AAAAZZDQE'
5 0 5 ‘ “MM

0 l l l

1.5 2 2.5 3 3.5

In Average Shear Rate, 5’1

Figure 5.5. 1n 11 versus 1n ya for cream corn at cold (5 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

38

P
Ln

 

 

 

 

 

 

 

 

o
D o 0 Cold 0 Room A Hot
0 o

5: 2 ‘ a 0
>2 A D 3 ° .0 Prego
3.: A D D o
m 0
o 1 5 .. A '3 :1 ° 0
8 A °n°°
> A no °o¢
0.5 A an O
t: A CH3 00°

1 _ A DD 00
g A A A ”DDCGWO
& A A A
< “AAA
5 0.5 ' A AAA

0 L 1 4

1.5 2 2.5 3 3.5

In Average Shear Rate, 5'1

Figure 5.6. ln 7] versus ln 7, for Prego at cold (8 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

 

 

 

 

 

 

 

 

1.8
o 0 Cold 0 Room A Hot
8 0 °
N D o o
9" l 2 r U o Rag“
5: A U D O 0
'8 A D o o
8 A D 0 ° 0 o
> 0.6 ‘ A D a 0 o
G A A Dan °°o
:a A A an 000°
< 0 * A A A
.5 AAAA
AAA
-06 . . 4
1.5 2 2.5 3 3.5

In Average Shear Rate, s'1

Figure 5.7. 1n 1] versus ln ya for Ragu at cold (7 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

39

E"
U!

 

 

 

 

 

 

 

 

0 Cold 0 Room A Hot
0
23 2 - ° .
9* 0 ° 0 Salsa
>1 n
.5 a a
g 1.5 - o o
E A D :1 ° ° 0
c: a o
1 _ A D u °o°
g A A ”a 0°00
D. A Dunn °°OQ
2‘ A A A an 00
5 0.5 - A A A A
A A A A
AAAAA
0 1 1 1 AL
1.5 2 2.5 3 3.5

In Average Shear Rate, 3‘1

Figure 5.8. 1n 11 versus 1n ya for salsa at cold (7 °C), room (23 °C) and hot (80 °C)
temperatures using the interrupted helical screw impeller.

All products exhibited similar slopes over the temperatures studied, and the lowest
temperature trial always produced the highest apparent viscosity readings. Table 5.5 lists
the regressed K and n values at each temperature for all four products. The temperatures
listed are average values. The n values do not appear to be a strong function of

temperature. As the temperature increases, the consistency coefficient decreases for all

food products except for cream com.

40

Table 5.5. Rheological parameters for foods with particulates at cold, room, and hot
temperatures using the interrupted helical screw impeller.

 

Fluid Food K n R2 Temperature
(Pa 8“) (-) (°C)

Cream Corn
~Cold 23.8 0.35 0.854 5
-Room 17.9 0.36 0.871 23

-Hot 20.4 0.26 0.979 80
Prego

-Cold 40.3 0.19 0.978 8
-Room 38.3 0.17 0.959 23
-Hot 21.8 0.18 0.984 80
Ragu

-Cold 15 .9 0.26 0.969 7
-Room 13.7 0.24 0.959 23
-Hot 10.1 0.20 0.988 80
Salsa

-Cold 30.8 0.20 0.957 7
-Room 22.6 0.23 0.932 23
-Hot 10.9 0.28 0.877 80

 

Figure 5.9 is a graphical representation of the logarithm of Equation [2.5]. An
intermediate average shear rate of 18.88 s’1 was chosen to compare apparent viscosities at
each temperature. Apparent viscosity is clearly dependent on temperature. The slope
(activation energy) and y-intercept (constant A) were determined by regression analysis
of these plots and compared in Table 5.6. Looking at the energy activation terms, salsa’s

apparent viscosity changes the most with temperature.

41

1.4

 

1.2

I

1.0 -
0.8 +
0.6 -
0.4 -
0.2 -

1n Apparent Viscosity, Pa 8

0.0 F

 

-0.2 ‘

 

X Cream Corn
El Prego

0 Ragu

A Salsa

 

 

 

 

0.0025 0.003

Figure 5.9. 1n 1] versus 1/T at 18.88 s'1 for each fluid food with particulates using the

interrupted helical screw impeller.

Table 5.6. Activation energy and A values for each fluid food with particulates using the

interrupted helical screw impeller.

. 0.0035
l/T, 1/K

 

 

Product Eo/R A R2

Cream Corn 561 0.45 0.879
Prego 898 0.15 0.995
Ragu 840 0.09 0.999
Salsa 1057 0.07 0.997

 

Figure 5.10-12 depicts regression lines of each product at cold, room and hot

temperatures respectively on a 1n 1] versus ln 7“ plot for comparison. Ragu pasta sauce

was consistently the least viscous. Prego, Ragu, and salsa had similar slopes; while

42

0.004

 

cream corn intercepted the salsa and Prego lines at cold temperature and only the salsa
line at room temperature. At the cold and room temperatures, Prego was the most

viscous of the food products. For the hot temperature, the cream corn was more viscous

 

 

 

 

 

 

 

thanPrego.
2.5 t
2 E] XCream Corn UPrego ORagu ASalsa
m E]
a“: 2 ” X z; U C]
a? K 5 £30 9
.53 0 X
§15_ ° 0 “Aggggg
S 0 0 A R’v
E: 000
5 05 P °°°°°W
0 1 l 1

 

 

1.5 2 2.5 3 3.5
In Average Shear Rate, 3’1

Figure 5.10. 1n 1] versus ln 70 of fluid food products with large particulates at cold
temperature (5-8 °C) using the interrupted helical screw impeller.

43

E"
m

 

 

El [XCreamCorn DPrego ORagu ASalsaJ
_ El
195

N
C]

1n Apparent Vrscosrty, Pa s
c
O Ur t—
<>
0
0
0
0
0 OX
0 DX
DX
DX
DX
DX
X
' DX
395
if

3
6
u
u
m
D<

 

 

I
.O
U!

 

p—0
U1
N

2.5 3 3.5
In Average Shear Rate, 3'1

Figure 5.11. 1n 7] versus 1n 7a of fluid food products with large particulates at room
temperature (23 °C) using the interrupted helical screw impeller.

 

 

 

 

 

 

 

 

2
fi XCream Corn DPrego ORagu ASalsa

m a 6
53 1.5 - E 6
>2 A 6 x x
g 1 . A A '3 :1 x xx
.E 0 A DC] XXX
> . <> 0 A A UUUDXX
a 0 AAA
23 A
8 ° 0 o o AAAAA .
< O

-05 . . , 00M

1.5 2 2.5 3 3.5

In Average Shear Rate, 5'1

Figure 5.12. 1n 11 versus 1n 70 of fluid food products with large particulates at hot
temperature (80 °C) using the interrupted helical screw impeller.

Table 5.7 contrasts the power law parameters for the whole fluid food and the
fluid phase analyzed by the helical ribbon at room temperature (23 °C). Similar shear
rates were selected for each instrument (4 s'1 to 27 s“) for a fair comparison. Relatively
speaking, there is a large increase in the consistency coefficient that corresponds with the
loading of particulates for all products except Ragu. The similarity of the results reflects
the small amount of particulates in the fluid initially, and therefore, small effect in the
fluid. Based on the flow behavior indices, the fluid phase appears to be less shear-
thinning than the complete product with the particulates included. These findings are in

agreement with past investigations (Bhamadipati and Singh, 1990).

Table 5.7. Comparison of the rheological parameters of whole fluid food products with
large particulates at room temperature (23 °C) using the interrupted helical screw impeller
to the fluid phase at room temperature (23 °C) using a helical ribbon.

 

Fluid Food K n R2

(Pa 8“) (-)
Cream Corn 18.5 0.34 0.854
Cream Corn Fluid 2.8 0.47 0.955

Prego 38.9 0.16 0.952
Prego Fluid 22.3 0.19 0.993

Ragu 14.2 0.22 0.953
Ragu Fluid 17.7 0.21 0.980
Salsa 23.8 0.21 0.936
Salsa Fluid 3.09 0.33 0.965

 

45

Preliminary trials of Bush’s Baked Beans and Dinty Moore Beef Stew were
unsuccessful. The baked beans exhibited high particle—to-particle interaction and
appeared to move as a whole entity rather than moving as discrete particles, which
indicates excessive slip. Another issue of concern with the beans was the observation of
particle degradation during testing. Also, the beef stew particulates (the largest tested in
this investigation) became jammed between the impeller and side of the beaker.

5.4. Regression Control Charts

1n n were plotted against In in for each food product with large particulates at

each temperature. Figure 5.13, a plot for Prego pasta sauce at cold temperature, is an
example of typical results. All ten repetitions are represented in the figure. Linear
regression produced an average control line and the upper and lower control limits for
each figure. Due to the wide spread of the data, the control limits are based on three
times the standard error rather than two. This allows for a lower risk of false alarms.
Table 5.8 compares the standard errors for each food product at each temperature. The
lower average standard error values correspond to the food products with lower
percentages of solids by weight. Temperature did not affect the standard errors in a
consistent manner.

One trial from cream corn and Ragu at room temperature appear separated from
the rest of the data pool. When reviewing the circumstances of the tests, no extraordinary
conditions were recorded; therefore, these outlying test trials were included in the

analysis.

46

 

 

 

 

 

ColdPrego

‘0 2.5 -
«3
a.
3;; 2 -
o
.8
> 1.5 ~
7%
‘3. 1 .
o.
<
E 0.5 -

O r r r

1.5 2 2.5 3 3.5

In Average Shear Rate, 3'1

Figure 5.13. 1n 11 versus ln 7“ for Prego sauce at cold temperature (5 °C) using the
interrupted helical screw impeller.

47

Table 5.8. Comparison of standard errors for each fluid food with large particulates at
each temperature.

 

 

Fluid Food Standard Error of 1n 1] Data
Cream Corn

-Cold 0.142
-Room 0.131
-Hot 0.057
Average 0.1 10
Prego Hot

-Cold 0.064
~Room 0.091
-Hot 0.056
Average 0.070
Ragu

-Cold 0.071
-Room 0.083
-Hot 0.048
Average 0.067
Salsa

-Cold 0.090
-Room 0.1 10
-Hot 0.130
Average 0.1 10

 

5.5. Statistical Quality Control Protocol

Using the interrupted helical screw impeller, a quality control program can be
established for fluid food products with large particulates. Based on steady-state shear
ramp tests similar to this study, regression control charts can be produced. The number

of trials on acceptable product samples to establish the control line and control limits is a

48

management decision based on the variance of the product. Recommended values differ
between authors (Bafna, 1995; Hubbard, 1990).

Personnel can run a test on the product and compare results to the established
control chart. The management would decide the frequency of the testing. The most
thorough assessment would be to run the same steady state ramp up—and—down test and
compare the regressed curve to the control chart. Occasional outlying points, caused by
random particulates colliding with the'impeller blade may be eliminated from the data
p00] using residual analysis. If the result lies within the limits, then the product is in
accordance with accepted values. A test result that intersects a control line indicates a
problem with the flow behavior index; whereas, a test line that runs parallel to the control
line but outside the control limits, indicates an unacceptable value of K. The protocol for
actions to be taken when a product is found to be out of specification is a management
decision, that may involve reformulation or disposal.

Another quality control test option using the regression control chart is to
determine the apparent viscosity at two different shear rates and see if the points are
located within the control limits. This test would only give a general indication of how
the product behaves because it is based on only two points. Adding more apparent
viscosity point tests would make the quality control procedure more laborious, but may
be necessary with some products. Single point testing is generally unacceptable with
shear-thinnin g products.

This type of test and regression control chart for quality control purposes is aimed
at batch processes rather than continuous. This type of chart is not as suitable to follow

the progress of a process with time because the chart represents only one test result.

49

Separate tests could be run at different points in the processing of the product. Another
use for regression control charts is in product development of fluid foods with large
particulates. The results can be compared with acceptable rheological parameters of

competing products.

50

CHAPTER 6
6. Summary and Conclusions

A mixer viscometer impeller modeled after an impeller used to evaluate the
rheological properties of fresh concrete was successfully designed and constructed.
Using Newtonian fluids, it was characterized by a mixer coefficient constant (k") value
of 3047.4 rad m’3. The mixer viscometer constant (k') was determined with non-
Newtonian fluids to be 1.6 rad'l over the angular velocity range of 3 — 30 rad s'l.

The interrupted helical screw impeller was effectively used to evaluate the
rheological behavior of fluid foods with large particulates. Apparent viscosity
measurements were obtained and power law parameters were found using regression
analysis for cream corn, salsa, a smooth pasta sauce and a chunky pasta sauce at typical
application temperatures: cold (6 °C), room (23 °C), and hot (80 °C). The largest
particulates in each food ranged from approximately 1 cm to 2 cm in the longest
direction.

There was variation within a single test and between tests due to the positioning
and quantity of particulates in the samples. However, a definite trendcould be
determined: higher particulate loading resulted in higher standard error values. Apparent
viscosity was found to decrease with increasing temperature. For cream corn, Prego, and
salsa, K was larger for the whole product versus only the fluid phase. The chunky pasta
sauce was the most viscous, followed by cream corn, salsa, and then the smooth pasta

sauce at room temperature.

Regression control charts of 1n 7] versus ln ya were made for all the food products

investigated at each temperature. The control line and control limits represent the

51

acceptable range of flow behavior for each product. Such charts can be established in
food manufacturing facilities for quality control purposes. Fluid foods with large
particulates can be tested using the interrupted helical screw impeller and compared to a
regression control chart. This is a valuable discovery to the food industry because
currently no standardized test exists to assess objective parameters of such foods. The
ability to quantitatively test rheological properties of fluid foods containing large
particulates is also important for process design calculations involving pipeline design,

mixing and pumping.

52

CHAPTER 7

7. Future Research

The following topics are recommended for future study:

1. Expanding the pool of large particulate fluid foods analyzed to include items such

as fruit preserves and chunky soups.

2. One specific brand was chosen to represent each type of food considered in the
current study. Evaluating different brands, of similar large particulate products
for comparison of rheological parameters is suggested.

3. In this study, the amount of solids in the fluid foods affected the rheological
parameters. Future study correlating particulate loading (size, shape and volume)

with changes in flow behavior is recommended.

4. Determining the range of sizes and loading of particulates appropriate for the

interrupted helical screw impeller in this study.
5. Studying the effect of different gap sizes.

6. Constructing a permanent temperature control device for the testing container.

53

7.

10.

Beef stew contained particulates that were of a size inappropriate for this study.
A scaling investigation is suggested to address extraordinarily sized particulates.
First, a basis for sealing must be determined. The author suggests scaling on a
geometrical basis. Next, a relationship must be developed between the
particulates in question and the impeller system for sealing. lrnportant factors
must be established, such as blade size and gap size, so if distortion is necessary,
those design factors will not be sacrificed. Torque capacity of the instrument may

become an important issue with large impellers.

The quality control plan for this study was aimed at batch processes, and therefore
did not lend itself to monitoring historical trends in results. A method is needed
to measure the progress with time of the rheological parameters of fluid foods

using statistical quality control applications.

Multivariate quality control was investigated for monitoring K and n values;
however, the process involved complex statistical analysis inappropriate for
typical food plant environment. Designing a software program to easily carry out
multivariate quality control calculations would greatly simplify the process. This

technique may be useful in some applications.

Using rheological data found by the interrupted helical screw impeller system to

model pipeflow problems found in aseptic processing systems.

54

APPENDIX:
Typical experimental data for the interrupted helical screw impeller

55

Table A.1. Interrupted helical screw impeller data to determine k" using Newtonian

 

 

fluids at 23 °C.
Fluid Angular Velocity Torque x 1045 Viscosity
(rad/s) (Nm) (Pa 5)
Corn Syrup 1.04 722 2.3

2.07 1454
3.10 2188
4.14 2930
5.17 3660
6.21 4400
7.24 5146
8.26 5860
9.30 6568
10.40 7310

1 1.40 8030
12.40 8802
13.40 9510
14.50 10260
15.50 1 1000
16.60 1 1760
17.60 12510
18.60 13270
19.70 14060
20.70 14840
21.70 15640
22.80 16390
23.80 17220
24.80 18000
25.90 18870
26.90 19660
27.90 20490
29.00 21250
30.00 22040

56

Table A.1. (cont’d)

 

 

Fluid Angular Velocity Torque x 1043 Viscosity
(rad/s) (Nm) (Pa 3)
Honey 0.42 1068 7.5

0.83 2082
1.25 3180
1.65 4236
2.07 5300
2.48 6314
2.90 7390
3.31 8410
3.73 9466
4.14 10480
4.55 1 15 10
4.96 12560
5.38 13600
5.79 14580
6.21 15650
6.62 16640
7.04 17650
7 .43 18620
7.86 19660
8.26 20630
8.70 21720
9.09 22650
9.51 23670
9.94 24680
10.40 25680
10.80 26690
1 1.20 27580
1 1.60 28660
12.00 29520

 

57

Table A2. Interrupted helical screw impeller data to determine k' using non-Newtonian
fluids at 23 °C.

 

 

Fluid . Angular Velocity Torque x 10'6
(rad/S) (N m)
1% Guar Gum 0.03 74
1.28 1300
2.53 1900
3.78 2310
5.03 2630
6.27 2880
7.53 3090
8.77 3290
10.00 3470
l 1.30 3650
12.50 3820
13.80 4010
15.00 4180
16.30 4370
17.50 4550
18.80 4740
20.00 4930
21.20 5120
22.50 5320
23.80 5530
25.00 5750
26.30 5960
27.50 6190
28.70 6430
30.00 6670

58

Table A2. (cont’d)

 

 

Fluid Angular Velocity Torque x 106
(rad/s)- (N m)
2.0% Methylcellulose 0.03 24
1.28 1370
2.53 2470
3.78 3440
5.03 4340
6.27 5160
7 .53 5920
8.77 6640
10.00 7320
l 1.30 7970
12.50 8590
13.80 9200
15.00 9770
16.30 10300
17.50 10900
18.80 1 1500
20.00 12000
21.20 12500
22.50 13100
23.80 13600
25.00 14100
26.30 14600
27.50 15100
28.70 15600
30.00 16100

59

Table A2. (cont’d)

 

 

Fluid Angular Velocity Torque x 1045
(rad/S) (N m)
2.5% Methycellulose 0.03 90
0.87 2480
1.70 4320
2.53 5990
3.36 7450
4.19 8800
5.03 10100
5.85 1 1200
6.69 12300
7 .53 13400
8.35 14400
9.19 15300
10.00 16200
10.80 17100
11.70 17900
12.50 18800
13.30 19500
14.20 20300
15.00 21000
15.80 21700
16.70 22400
17.50 23000
18.30 23700
19.20 24300
20.00 24900

 

60

Table A3. Interrupted helical screw impeller data for cream corn.

 

 

 

Angular Velocity Torque x 10'6
(rad/S) (Nm)

5 °C 23 °C 80 °C
3.0 8530 6860 65 80
3.6 9430 6860 6730
4.2 10400 7050 6320
4.8 10700 7120 6600
5.3 1 1200 7660 6890
5.9 11500 8520 7170
6.5 11600 8120 6830
7.1 12700 8430 7740
7 .7 12300 8850 7980
8.3 12600 8920 7950
8.9 13200 9150 7750
9.4 13300 9260 8200
10.0 13500 9100 8280
10.6 14200 9990 8040
1 1.2 13900 9590 8370
l 1.8 13900 9760 8500
12.4 14300 9660 8780
13.0 13700 10300 8950 .
13.6 14500 10800 9140
14.1 14800 11100 8810
14.7 14900 10300 9140
15.3 15400 10300 9140
15.9 15500 11400 9210
16.5 16000 11400 8820
17.1 15700 11600 9010
17.7 16300 11700 9310
18.3 16100 11900 9060
18.8 16600 12300 9600
19.4 16100 11800 9630
20.0 16500 12500 10200

61

Table A3. (cont’d)

 

 

 

Angular Velocity Torque x 10'6
(rad/s) (Nm)

5 °C 23 °C 80 °C
20.0 16100 12000 10200
19.4 15600 12200 10500
18.8 15900 11300 10000
18.3 15600 11800 9660
17.7 15100 11500 10200
17.1 15100 11100 9140
16.5 15000 10600 9130
15.9 14700 10900 9460
15.3 14600 9860 8660
14.7 14500 9820 8600,
14.1 13700 9830 8960
13.6 13200 9630 8390
13.0 13300 10500 8400
12.4 12900 8870 7580
11.8 13000 9140 7950
1 1.2 12900 8570 8620
10.6 13000 8970 8800
10.0 12200 8680 8060
9.4 12100 8570 7970
8.9 11900 7870 7310
8.3 11100 8010 7170
7.7 10500 7830 7170
7 .1 10600 7780 7380
6.5 9880 7250 7250
5.9 9620 6800 7200
5.3 9470 6860 6710
4.8 8890 6680 6770
4.2 8860 6410 6470
3.6 8420 6620 6420
3.0 7990 61 10 6010

 

62

Table A.4. Interrupted helical screw impeller data for Prego.

 

 

 

Angular Velocity Torque x 104‘
(rad/s) (Nm)
8 °C 23 °C 80 °C

3.0 10900 11200 5420
3.6 11500 10900 5620
4.2 11400 11600 5870
4.8 11700 11600 6020
5.3 12000 1 1800 6180
5 .9 12200 12200 6290
6.5 12500 12100 6290
7.1 12400 12500 6620
7 .7 12900 12500 6920
8.3 13100 12600 7170
8.9 13500 12500 7290
9.4 13700 13000 7400
10.0 13500 13100 7590
10.6 13500 13100 7520
11.2 13700 13300 7610
11.8 13800 13600 8080
12.4 14300 13200 7720
13.0 13900 13400 7900
13.6 14200 13700 7890
14.1 14500 13800 8040
14.7 14900 14200 8030
15.3 15200 14200 8160
15.9 15500 14100 8170
16.5 15500 14100 8290
17 . 1 15600 14300 8350
17.7 15500 14200 8550
18.3 16000 14600 8440
18.8 15900 14400 8580
19.4 16300 14500 8790
20.0 16000 14600 8940

63

Table A.4. (cont’d)

 

 

 

Angular Velocity Torque x 104
(rad/S) (Nm)
8 °C 23 °C 80 °C

20.0 16100 14700 8850
19.4 16000 14800 8180
18.8 15700 14600 8550
18.3 15900 14300 8450
17.7 15500 14200 8320
17.1 15800 14200 8220
16.5 15200 14000 8050
15.9 15000 14000 7980
15.3 14700 13900 8010
14.7 14900 13700 7890
14.1 14300 13600 8050
13.6 14200 13800 7890
13.0 14200 13500 8110
12.4 14600 13200 8110
11.8 13800 13400 7830
11.2 14300 12900 7570
10.6 13600 13000 7680
10.0 13600 12900 7660
9.4 13600 12900 7480
8.9 13500 12600 7420
8.3 13400 12600 7360
7 .7 13400 12500 7360
7.1 13400 12300 7430
6.5 12900 12300 7180
5.9 12600 12000 7020
5.3 12600 12100 6860
4.8 l 1800 l 1600 6910
4.2 1 1900 11600 6720
3.6 12000 11000 6630
3.0 11400 11400 6320

 

Table A5. Interrupted helical screw impeller data for Ragu.

 

 

 

65

Angular Velocity Torque x 104‘
(rad/s) (Nm)
7 °C 23 °C 80 °C
3.0 5490 4110 3080
3.6 5610 4220 3120
' 4.2 5790 4380 3170
4.8 5900 4510 3170
5.3 6040 4550 3240
5.9 6160 4640 3270
6.5 6270 4750 3320
7.1 6450 4810 3410
7.7 6610 4860 3460
8.3 6630 4950 3510
8.9 6800 5020 3620
9.4 6820 51 10 3620
10.0 6980 5170 3720
10.6 7110 5180 3800
11.2 7210 5330 3830
1 1.8 7330 5450 3800
12.4 7380 5500 3860
13.0 7510 5600 3930
13.6 7570 5690 4010
14.1 7750 5710 4050
14.7 7830 5800 4060
15.3 7890 6030 4170
15.9 8030 6050 4220
16.5 8040 6030 4260
17.1 8160 6250 4230
17.7 8310 6410 4320
18.3 8400 6550 4360
18.8 8460 6720 4430
19.4 8530 6660 4430
20.0 8590 6620 4520

Table A5. (cont’d)

 

 

 

Angular Velocity Torque x 10'6
(rad/s) (Nm)
7 °C 23 °c 80 °C

20.0 8660 6540 4530
19.4 8520 6580 4460
18.8 8490 6440 4380
18.3 8450 6320 4320
17.7 8290 6370 4320
17.1 8260 6310 4250
16.5 8210 6350 4160
15.9 8140 6200 4180
15.3 8060 6110 4090
14.7 7890 5950 4080
14.1 7820 6220 4000
13.6 7700 5980 3980
13.0 7700 5750 3920
12.4 7510 5630 3890
1 1.8 7450 5550 3920
11.2 7330 5500 3850
10.6 7260 5500 3780
10.0 7190 5400 3760
9.4 7010 5370 3710
8.9 6970 5300 3730
8.3 6920 5230 3640
7.7 6840 5140 3590
7.1 6680 5090 3590
6.5 6480 5080 3470
5.9 6380 4960 3450
5.3 6270 4900 3470
4.8 6140 4660 3360
4.2 5960 4670 3340
3.6 5730 4470 3220
3.0 5610 4270 3170

 

66

Table A6. Interrupted helical screw impeller data for salsa.

 

 

 

Angular Velocity Torque x 104‘
(rad/s) (Nm)
8 °C 23 °C 80 °C

3.0 8540 7920 3380
3.6 8050 7910 3860
4.2 8370 7090 4290
4.8 8510 8000 4670
5.3 8910 .8340 3940
5.9 85 80 7960 4130
6.5 9380 8380 4130
7.1 9620 8680 4200
7.7 8840 8590 4550
8.3 8530 8880 4460
8.9 9480 8580 4560
9.4 10000 9340 4580
10.0 9590 9100 4520
10.6 10100 9940 4430
1 1.2 9860 9020 4710
11.8 10200 9320 5570
12.4 10700 9170 5100
13.0 10500 9850 5350
13.6 10300 9620 5020
14.1 10800 11200 5040
14.7 11200 10100 5710
15.3 10500 9860 5740
15.9 10800 10100 5280
16.5 10800 11300 5980
17.1 11100 10400 5750
17.7 12000 10800 6210
18.3 1 1600 1 1600 6420
18.8 11000 12100 6640
19.4 11200 11900 7220
20.0 11200 1 1700 7520

67

Table A6. (cont’d)

 

 

 

Angular Velocity Torque x 1045
(rad/s) (Nm)
8 °C 23 °C 80 °C

20.0 11600 11700 7490
19.4 11000 11700 6960
18.8 1 1200 11000 7040
18.3 11100 11400 6770
17.7 10500 10300 6590
17.1 10400 10500 6360
16.5 10200 10800 6080
15.9 10500 9990 5990
15.3 9930 9850 5650
14.7 10100 10200 5590
14.1 10100 10300 5390
13.6 10100 9730 5590
13.0 10100 9980 5300
12.4 10300 9490 5330
11.8 10100 9130 5150
1 1.2 9490 9690 5290
10.6 9530 9030 4870
10.0 8900 8790 4860
9.4 9010 8860 4530
8.9 8850 9390 4380
8.3 8530 8800 4280
7.7 8440 8720 4390
7.1 9120 8300 4.110
6.5 8260 8210 4020
5.9 8170 8170 4020
5.3 7880 8440 3930
4.8 7490 7620 4290
4.2 7470 7730 4000
3.6 7500 7750 3380
3.0 6950 7610 3690

 

68

LIST OF REFERENCES

AGRAWAL, Eva. 2001. Evaluation of fluid foods using a helical ribbon viscometer.
MS. Thesis. Department of Food Science and Human Nutrition, Michigan State
University, East Lansing, MI, USA.

BAFNA, S. S. 1995. The application of statistical process control to rheological
measurements. Journal of Applied Polymer Science. 57, 1233-1244.

BARTOS, P. 1992. Fresh concrete: properties and tests. El Sevier, Amsterdam.

BRIGGS, J.L. and STEFFE, J.F. 1996. Mixer viscometer constant (k’) for the
Brookfield small sample adapter and flag impeller. Journal of Texture Studies 27,
671-677.

BHAMADIPATI S. and SINGH R.K. 1990. Flow behavior of tomato sauce with or
without particulates in tube flow. J. Food Proc. Eng. 12, 275-293.

CASTELL-PEREZ, ME. and STEFFE, J .F. 1990. Evaluating shear rates for power law
fluids in mixer Viscometry. Journal of Texture Studies 21 , 439-453.

CASTELL-PEREZ, ME. and STEFFE, J .F. 1992. Using Mixing to evaluate rheological
properties. In: Rao, M.A. (editor). Viscoelastic Properties. Elsevier Applied Science
Publishers Ltd., Barking, England.

CASTELL-PEREZ, M.E., STEFFE, J .F. and MORGAN, R.G. 1987. Adaptation of a
Brookfield (I-IBTD) viscometer for mixer Viscometry studies. Journal of Texture
Studies 18, 359-365.

CANTU-LOZANO, D., RAO, MA. and GASPARE'ITO, GA. 2000. Rheological
properties of noncohesive apple dispersion with helical and vane impellers: effect of
concentration and particle size. Journal of Food Process Engineering 23, 373-385.

CHATTERJEE, S. and PRICE, B. 1977. Regression Analysis by Example. John Wiley
& Sons, New York.

DUCLA, J.M., DESPLANCHES, H. and CHEVALIER, J .L. 1983. Effective viscosity
of non-Newtonian fluids in a mechanically stirred tank. Chem. Eng. Commun. 21,
29-36.

EDWARDS, M.F., GODFREY, J .C. and KASHANI, M.M. 1976. Power requirement
for the mixing of thixotropic liquids. Journal of Non-Newtonian Fluid Mechanics. I ,
309-322.

69

FERRARIS, CF. 1999. Measurement of the Rheological Properties of high
Performance Concrete: State of the art Report. Journal of Research of the National
Institute of Standards and Technology. 104, 461-477.

HUBBARD, MR. 1990. Statistical Quality Control for the Food Industry. Van
Nostrand Reinhold, New York.

HUGELSHOFER, D., WINDHAB, E]. and WANG, J. 2000. Rheological and
structural changes during the mixing of suspensions and emulsions. Applied
Rheology. 10, 22-30.

LAI, K.P., STEFFE, J .F. and NG, P.K.W. 2000. Average shear rates in the rapid Visco
analyser (RVA) mixing system.

LAREO C., FRYER P.J., BARIGOU M. 1997. The fluid mechanics of two-phase solid-
liquid food flows: A review. Trans. Institution of Chemical Engineers. 75( C), 73-
105.

MACKEY, K.L., MORGAN, R.G. and STEFFE, J.F. 1987. Effects of shear-thinning
behavior on mixer Viscometry techniques. Journal of Texture Studies 18, 231-240.

MANDEL, B]. 1969. The regression control chart. Joumal of Quality Technology I, 1-
9.

MARTINEZ-PADILLA L.P., CORNEJO-ROMERO L., CRUZ-CRUZ C.M., JAQUEZ-
HUACUJA C.C., BARBOSA-CANOVAS G.V. 1999. Rheological characterization

of a model food suspension containing discs using three different geometries. J.
Food Proc. Eng. 22, 55-79.

METZNER, AB. and OTTO, RE. 1957. Agitation of non-Newtonian fluids. A.I.Ch.E.
Journal 3, 3-10.

MOHSENIN, N. N. 1986. Physical properties of plant and animal materials, 2nd Ed.
Gordon and Breach, Science Publisher, Inc. New York.

NAGATA, S. 1975. Mixing: Principles and Applications. John Wiley and Sons, New
. York.

PATANKAR, NA. and HU, H.H. 2001. Rheology of a suspension of particles in
Viscoelastic fluids. J. Non-Newtonian Fluid Mech. 96, 427—443.

PORDESIMO, L0. 1991. Flow behavior of coarse solid-liquid food mixtures. Ph.D.
Thesis. The Pennsylvania State University, University Park, PA, USA.

PORDESIMO L.O., ZURITZ C.A., SHARMA MG. 1994. Flow behavior of coarse
solid-liquid food mixtures. J. Food Eng. 21, 495-511.

70

PURI, S.C., ENNIS, D., MULLEN, K. 1979. Statistical Quality Control for Food and
Agricultural Scientists, G. K. Hall & Co., Boston, MA.

QIU, CG. and RAO, M.A. 1988. Role of pulp content and particle size in yield stress of
apple sauce. Journal of Food Science 53, 1165-1170.

RAO, M.A. 1975. Measurement of flow properties of food suspensions with a mixer.
Journal of Texture Studies 6, 533-539.

RAO M.A. 1987. Predicting the flow of properties of food suspensions of plant origin.
Food Technology 41, 85-88.

RAO, M.A. and COOLEY, H]. 1984. Determination of effective shear rates in

rotational viscometers with complex geometries. Journal of Texture Studies 15, 327-
335.

REGER, F. and NOVAK, V. 1973. Power consumption of agitators in highly viscous
non—Newtonian liquids. Trans. Instn. Chem. Engrs. 51 , 105-111.

SANNERVIK J., BOLMSTEDT U., TRAGARDH C. 1996. Heat transfer in tubular
heat exchangers for particulate containing liquid foods. J. of Food Eng. 29, 63-74.

SCHUBERT H. 1987. Food particle technology. Part 1: Properties of particles and
particulate food systems. J. of Food Eng. 6, 1-32.

SESTAK, 1., ZIT NY, R. and HOUSKA, M. 1986. Anchor-agitated systems: power
input correlation for pseudoplastic and thixotropic fluids in equilibrium. AIChE
Journal. 32,155-158.

STEFFE, J .F. 1996. Rheological Methods in Food Process Engineering, 2nd Ed.
Freeman Press. East Lansing, MI.

STEFFE, J .F. and FORD, W. 1985. Rheological techniques to evaluate the shelf-

stability of starch-thickened, strained apricots. Journal of Texture Studies 16, 179-
192.

TA'ITERSALL, OH. 1973. The rationale of a two-point workability test. Magazine of
Concrete Research 25, 169-172.

TATTERSALL CH. and BLOOMER SJ. 1979. Further development of the two-point

test for workability and extension of its range. Magazine of Concrete Research 31,
202-210.

WALLEVIK OH. and GJORV DE. 1990. Modification of the two-point workability
apparatus. Magazine of Concrete Research 42, 135-142.

71

WILDEMUTH, CR. and WILLIAMS, MC. 1984. Viscosity of suspensions modeled
with a shear-dependent maximum packing fraction. Rheologica Acta 23, 627-635.

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