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This is to certify that the

thesis entitled
VALIDATION OF A NUMERICAL MODEL FOR PREDICTION OF
MOISTURE CONTENT FOR BINARY MIXTURES OF CORN, OATS

AND WHEAT CEREALS IN SEMIPERMEABLE PACKAGING
presented by

CARLOS GUSTAVO CASTRO IZAGUIRRE

has been accepted towards fulﬁllment
of the requirements for

MS PACKAGING

degree in

 

C/léwy/J ﬁzofzz/

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6/01 C'JCIRC/DateDuepﬁs—p. 15

VALIDATION OF A NUMERICAL MODEL FOR PREDICTION OF MOISTURE
CONTENT FOR BINARY MIXTURES OF CORN, OATS AND WHEAT
CEREALS IN SEMIPERMEABLE PACKAGING

By

Carlos Gustavo Castro lzaguirre

A THESIS

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

MASTER OF SCIENCE

School of Packaging

2001

ABSTRACT

VALIDATION OF A NUMERICAL MODEL FOR PREDICTION OF MOISTURE
CONTENT FOR BINARY MIXTURES OF CORN, OATS AND WHEAT
CEREALS IN SEMIPERMEABLE PACKAGING

By

Carlos G. Castro

The application of mathematical modeling, which correlates the products’
moisture sorption characteristics, the packaging properties, and the storage
conditions, to two-component products was used to develop a computer
program. The experimental validation of the model was carried out with corn-
wheat, corn-oats and oats-wheat mixtures and with individually packaged
products. The mixtures were prepared at 1/2, 1/1 and 2/1 ratios and packaged
in LDPE and HDPE pouches.

The model estimates the components’ moisture contents with reasonable
accuracy for systems where the components have similar water activities. The
mixtures of components with very different water activity (corn-oats and oats-
wheat) presented an initial moisture exchange. During this early stage of the
storage, the moisture exchange was more important than the permeability. The
determination of the components' moisture content after this'moisture exchange
was critical to the successfully application of the computer model. The
correlation coefﬁcient (>90°/o), obtained from a regression analysis, shows that

model can be used to determine moisture gain of binary mixtures.

Copyright by
Carlos Gustavo Castro lzaguirre
2001

To my encouraging father, Julio Castro and my loving mother Imelda lzaguirre for
the enormous support given and the conﬁdence provided during my stay and

studies in the States.

ACKNOWLEDGMENTS

My gratitude to Dr. Theron Downes, my advisor, for providing the research
topic, his permanent advice, generous support and encouragement.

My appreciation to Dr. Ruben Hernandez, for his guidance, patience and
keen observations during the development of the computer program.

Thanks to Dr. Perry Ng (Department of Food Science and Human
Nutrition); for his time and his comments made to this manuscript.

Dr. Bruce Harte (Director of School of Packaging) for his permanent
appreciation and support during my studies at the School of Packaging.

Thanks also to the other professors, staff and fellow student at the School

of Packaging for their friendship that helps me to the culmination of my degree.

TABLE OF CONTENTS

List of Tables ...................................................................................... ix
List of Figures ..................................................................................... xii
Introduction .......................................................................................... 1

CHAPTER I - Literature Review

1.1. Deﬁnition of water activity .................................................................. 3
1.2. Sorption Isotherms ........................................................................... 6
1.3. Use of Moisture Sorption Isotherms ..................................................... 7
1.4. Equations for Sorption Isotherms ........................................................ 8
1.5. Equations for Multicomponent Isotherms ............................................. 10
1.6. Shelf Life Deﬁnition ........................................................................ 15
1.7. Shelf Life Models ........................................................................... 15

1 .7.1 . Generalities ....................................................................... 15

1.7.2. Single Products .................................................................. 16

1.7.3. Multicomponent Products ..................................................... 17
1.8. Mathematical Model Development ..................................................... 20

CHAPTER II - Material and Methods

2.1. Product — Package System .............................................................. 23

2.1.1. Food Product Samples ........................................................ 23

2.1.2. Package ........................................................................... 23
2.2. Moisture Content Determination ........................................................ 24
2.3. Moisture Sorption lsotherrns ............................................................ 25
2.4. Permeability of Packaging Material ................................................... 29
2.5. Model Validation Experiments .......................................................... 30

CHAPTER III - Results and Discussion

3.1. Initial Moisture Content .................................................................... 31
3.2. Moisture Sorption Isotherm ............................................................... 31
3.3. Film Permeability ........................................................................... 35
3.4. Package Permeability ..................................................................... 35
3.5. Validation 1 - Moisture Change in Cereal Packaged in HDPE 1.9 mil ........ 36
3.6. Validation 2 - Moisture Change in Cereal Packaged in LDPE 1.0 mil ........ 54
Conclusions ...................................................................................... 64
Recommedations ................................................................................ 65

vi

Bibliography ...................................................................................... 67

Appendices
Appendix A — Determination of Shelf Life Equations Using a Linear

and Non-linear Sorption lsotherrn ............................................. 72
Appendix B - Packaging Materials Characterization ................................... 79
Appendix C - Parameter Estimation of GAB Equation ................................ 82
Appendix D — Computer Program Validation ............................................ 84
Appendix E —Moisture Sorption lsotherrn Data for the Cereals ...................... 91
Appendix F — Experimental and Predicted Moisture Content ...................... 93
Appendix G - Detailed Data of Validation Experiments .............................. 103

vii

LIST OF TABLES

Table 1- Saturated salt solutions and their corresponding relative

humidities at 23°C .................................................................. 25
Table 2 - Linear, GAB and Cubic Sorption lsotherm Equations of

Com, Oats and Wheat Cereals determined at 23°C ....................... 34
Table 3 - Combinations of Cereals Used for the Experimental

Validation 1 ........................................................................... 36
Table 4 - Combinations of Cereals Used for the Experimental

Validation 2 ........................................................................... 54
Table 8.1 - Permeance (g/m2.day) and Permeability (g.mil/m2.day.mmHg)

at 23 °C for ﬂat LDPE samples ............................................... 79
Table 3.2 — Permeance (g/m2.day) and Permeability (g.mil/m2.day.mmHg)

at 23 °C for ﬂat HDPE samples ............................................... 80
Table 8.3 - Water Vapor Transmission Rate (g/day) and Permeability

(g.millm2.day.mmHg) at 23 °C for LDPE pouches ....................... 81
Table 8.4 - Water Vapor Transmission Rate (g/day) and Permeability

(g.mil/m2.day.mmHg) at 23 °C for HDPE pouches ....................... 81
Table 0.1 - aW and M (9/9) values used to obtain the cereal and raisin

isotherms at 20°C for the computer simulation .............................. 85
Table 0.2 — Conditions used in the computer simulation ............................. 86

Table E.1 - Equilibrium Moisture Content (Me, 919) of Com, Oats
and Wheat Cereals at Nine Different Water Activities ..................... 91

Table F1. - Experimental and Predicted Moisture Content (%) for 33/67
corn/wheat samples for validation with HDPE .............................. 93

Table F2. - Experimental and Predicted Moisture Content (%) for 50/50
corn/wheat samples for validation with HDPE .............................. 93

Table F3. - Experimental and Predicted Moisture Content (%) for 67/33
corn/wheat samples for validation with HDPE .............................. 94

Table F4. - Experimental and Predicted Moisture Content (%) for 33167
corn/oats samples for validation with HDPE .............................. 94

viii

Table F5. - Experimental and Predicted Moisture Content (%) for 50/50
corn/oats samples for validation with HDPE .............................. 95

Table F6. - Experimental and Predicted Moisture Content (%) for 67I33
corn/oats samples for validation with HDPE .............................. 95

Table F7. - Experimental and Predicted Moisture Content (%) for 33l67
corn/wheat samples for validation with HDPE ........................... 96

Table F8. - Experimental and Predicted Moisture Content (%) for 50/50
corn/wheat samples for validation with HDPE ........................... 96

Table F9. - Experimental and Predicted Moisture Content (%) for 67/33
corn/wheat samples for validation with HDPE ........................... 97

Table F10 - Experimental and Predicted Moisture Content (%) of corn, oats
and wheat samples for validation with HDPE ............................ 98

Table F11 - Experimental and Predicted Moisture Content (%) for 50/50
corn/wheat samples for validation with LDPE ........................... 99

Table F12 - Experimental and Predicted Moisture Content (%) for 50/50
corn/oats samples for validation with LDPE .............................. 99

Table F13. - Experimental and Predicted Moisture Content (%) for 50/50
oats/wheat samples for validation with LDPE ............................ 100

Table F14 - Experimental and Predicted Moisture Content (%) of corn, oats
and wheat samples for validation with LDPE ............................. 101

Table 6.1 - Initial weight (g) of components and pouches weight (9)
over time for 33l67 corn/wheat (Validation 1) ............................ 103

Table G.2 - Initial weight (g) of components and pouches weight (9)
over time for 33l67 corn/oats (Validation 1) ............................... 105

Table G.3 - Initial weight (g) of components and pouches weight (9)
over time for 33l67 oats/wheat (Validation 1) ............................. 107

Table 6.4 - Initial weight (g) of components and pouches weight (9)
over time for 50/50 corn/wheat (Validation 1) ............................ 109

Table G.5 — Initial weight (g) of components and pouches weight (9)
over time for 50/50 corn/oats (Validation 1) ............................... 111

Table G.6 — Initial weight (g) of components and pouches weight (9)
over time for 50l50 oats/wheat (Validation 1) ............................. 113

Table G.7 — Initial weight (g) of components and pouches weight (9)
over time for 67/33 corn/wheat (Validation 1) ............................ 115

Table G.8 - Initial weight (g) of components and pouches weight (9)
over time for 67/33 corn/oats (Validation 1) .............................. 117

Table G.9 - Initial weight (g) of components and pouches weight (g)
over time for 67/33 oats/wheat (Validation 1) ............................ 119

Table G.10 — Initial weight (g) of components and pouches weight (9)
over time for individually packaged corn (Validation 1) ................ 121

Table G.11 — Initial weight (g) of components and pouches weight (9)
over time for individually packaged oats (Validation 1) ................ 123

Table 6.12 - Initial weight (g) of components and pouches weight (9)
over time for individually packaged wheat (Validation 1) .............. 125

Table G.13 - Initial weight (g) of components and pouches weight (9)
over time for 50/50 corn/wheat (Validation 2) ........................... 127

Table 6.14 — Initial weight (g) of components and pouches weight (9)
over time for 50/50 corn/oats (Validation 2) .............................. 129

Table G.15 — Initial weight (g) of components and pouches weight (9)
over time for 50/50 oats/wheat (Validation 2) ........................... 131

Table G.16 - Initial weight (g) of components and pouches weight (9)
over time for individually packaged corn (Validation 2) ............... 133

Table G.17 - Initial weight (g) of components and pouches weight (9)
over time for individually packaged oats (Validation 2) ................ 135

Table 6.18 — Initial weight (g) of components and pouches weight (9)
over time for individually packaged wheat (Validation 2) .............. 137

LIST OF FIGURES

Figure 1 -WaterActivity- Stability Diagram ................................................ 5
Figure 2 - Schematic Representation of 3 (Moisture Sorption Hysteresis ............ 7
Figure 3 - Moisture Sorption lsothenn 'of Com Cereal at 23°C ....................... 31
Figure 4 - Moisture Sorption Isotherm of Oats Cereal at 23°C ........................ 32
Figure 5 - Moisture Sorption lsotherm of Wheat Cereal at 23‘C ..................... 32

Figure 6 - Experimental and Predicted Moisture Content Proﬁle of
37/67 Com/Wheat Mixtures for Validation 1 ................................. 39

Figure 7 — Experimental and Predicted Moisture Content Proﬁle of
50150 Corn/Wheat Mixtures for Validation 1 ................................. 40

Figure 8 - Experimental and Predicted Moisture Content Proﬁle of
'67/37 ComNVheat Mixtures for Validation 1 ................ p ................. 41

Figure 9 - Experimental and Predicted Moisture Content Proﬁle of
37/67 Com/Oats Mixtures for Validation 1 ................................... 42

Figure 10 — Experimental and Predicted Moisture Content Proﬁle of
50150 Com/Oats Mixtures for Validation 1 ................................... 43

Figure 11 - Experimental and Predicted Moisture Content Proﬁle of
67137 Corn/Oats Mixtures for Validation 1 .................................... 44

Figure 12 - Experimental and Predicted Moisture Content Proﬁle of
37167 OatsNVheat Mbttures for Validation 1 ................................. 45 '

Figure 13 '- Experimental and Predicted Moisture Content Proﬁle oi
50150 OatsNVheat Mixtures for Validation 1 ................................. 46

Figure 14- Experimental and Predicted Moisture Content Proﬁle of
67137 Oats/Wheat Mixtures for Validation 1 ................................. 47

Figure 15- -Experimental and Predicted Moisture Content Proﬁle of
Com for Validation 1 ............................................................... 48

Figure 16 - Experimental and Predicted Moisture Content Proﬁle of
Oats for Validation 1 ............................................................... 49

xi

Figure 17 — Experimental and Predicted Moisture Content Proﬁle of
Wheat for Validation 1 ............................................................ 50

Figure 18 —- Experimental and Predicted Moisture Content Proﬁle of
50150 CornNVheat Mixtures for Validation 2 ................................ 58

Figure 19 - Experimental and Predicted Moisture Content Proﬁle of
50/50 Corn/Oats Mixtures for Validation 2 .................................. 59

Figure 20 — Experimental and Predicted Moisture Content Proﬁle
of 50150 OatsNVheat Mixtures for Validation 2 ............................ 60

Figure 21 — Experimental and Predicted Moisture Content Proﬁle of
Com for Validation 2 ............................................................. 61

Figure 22 - Experimental and Predicted Moisture Content Proﬁle of
Oats for Validation 2 .............................................................. 62

Figure 23 - Experimental and Predicted Moisture Content Proﬁle of
Wheat for Validation 2 ............................................................ 63

Figure D.1 - Moisture content proﬁle for different components’ weight ratio 87
Figure 0.2 - Moisture content proﬁle for different storage water activities ...... 88
Figure 0.3 - Moisture content proﬁle for different packaging barrier properties. 89

Figure 0.4 - Moisture content proﬁle for different total weight to packaging
area ratio .............................................................................. 90

xii

INTRODUCTION

Packaging of multi-component products where components have different
water activities has challenged food scientists and packaging engineers for
years. The difference in water activities is responsible for the moisture exchange
among the components and also controls the moisture transfer across the
package.

Mathematical models that relate these mass transfer mechanisms have
been created to facilitate package-product development and to replace tedious
actual testing. These shelf life models are desirable to reduce cost, diminish
labor, increase versatility and shorten the time of the product development
process.

This thesis worked with a general shelf life model developed by Pocas
(1995) who also prepared a DOS computer program with the proposed model. A
new windows program based on the model develop by Pocas (1995) was
produced to predict the time and moisture content of two-component products.
The program was designed for single and two-component products and included
linear and non-linear (GAB and Cubic) isotherms for its calculations. This new
software was validated with binary mixtures of corn, oats and wheat breakfast
cereals at different load ratios.

The corn, oats and wheat cereals were selected for this study because
cereals are an excellent example of consumers’ demand for variety, superior

quality and great taste.

The objectives of this study were:

A) To obtain moisture sorption isotherms for corn, wheat and cat cereals at
23°C.

B) To apply shelf life models; based on the linear, GAB, and cubic polynomial
moisture sorption isotherm equations; to ﬂexible packaging containing two
cereals.

C) To validate the shelf life model at 23°C.

D) To prepare a windows-based program that performs the models' calculations

for shelf life and moisture content.

Chapter 1

LITERATURE REVIEW

1.1. Deﬁnition of Water Activitv

Water activity is deﬁned as the ratio of the vapor pressures of solution
and solvent. In food science terms, water activity describes the availability of
the water in the food to participate in reactions. Water activity is used for
characterization of the state of water in foods and its availability for biological,
physical and chemical changes. It is a critical factor in physical, chemical and
biochemical phenomena taking place in the product. Therefore, water activity is
connected to the quality or shelf life of most foods. Water plays an important
part in the textural properties of several food products and also inﬂuences the
activity of microorganisms during the storage of food products under various
conditions. Water activity affects the rate of microbial growth, enzymatic
reaction, non-enzymatic browning, lipid oxidation, textural changes, aroma
retention, and it induces structural changes. (Troller and Christian, 1978;
lglesias and Chirife, 1982)

Three different binding mechanisms for water are found in food. Water is
bound to polar sites with ionic bonds at low water activities (Le Maguer, 1986).
This water is tightly bound and is unavailable to solvate reactants. The upper
limit of this ﬁrst binding mechanism is referred as the monolayer moisture (Le
Maguer, 1986). The second mechanism observed is the adsorption at the

multilayer. Hydrogen bonding governs the water adsorption in the multilayer

zone. The last mechanism present is the condensed water in capillaries. The
multilayer and the capillary mechanisms are observed at higher activities where
the mobility of water increases (Le Maguer, 1986; Labuza, 1975 cited by Nelson
and Labuza, 1994; Hernandez, 1999; and Pocas, 1995).

When water availability increases, the reaction rates also increase
because water acts as a reaction medium in which sufﬁcient reactant mobility
occurs to allow reactant interactions. Some reaction rates decrease as water
activity increases because some reaction species are diluted in the aqueous
phase. A main exception to this minimum-maximum relationship involves the
oxidation of unsaturated lipids where the reaction rate increases below the
monolayer due to the increased catalytic activity of metal ions when sufﬁcient
water is removed from the hydration sphere around these ions. (Nelson and
Labuza,1994)

Labuza (1971; cited by Nelson and Labuza, 1994) summarized in a plot
the reaction rate of various reactions and the moisture content as a function of
water activity. The plot is presented on the next page in Figure 1.

Nelson and Labuza (1994) made a comparison between the role of water
activity and the glass transition theory on physical, chemical and biochemical
reactions. The researchers stated that water activity essentially considers the
state of water in a food while glass transition theory generally considers the
state of a food matrix. This glass transition theory suggests that chemical
reactions are slower or do not occur at the glassy state, but will increase

substantially at the rubbery state. Finally the researchers stated that both

approaches help to understand the inﬂuence of water on rates of chemical

 

 

reactions.
Moisture
Content /
Relative Oxidation Moisture
Activity Reaction isotherm
Browning
Reaction
Microbial
Reaction
A
Enzymatic
Reaction
I
0 1 .00
Water Activity (a...)

Figure 1 — Water Activity - Stability Diagram

Source: Le Maguer (1986)

1.2. Sorptionﬁlsotherms

The water sorption isotherms of foods show the equilibrium relationship
between the moisture content of foods and the water activity (aw) at constant
temperatures and pressures (Troller and Christian, 1978; lglesias and Chirife,
1982). Water sorption isotherms are usually described as a plot of the amount
of water sorbed as a function of the water activity. The plot has generally, but
not in all cases, a sigmoid shape (lglesias and Chirife, 1982).

An important phenomenon present in most food’s sorption isotherms is
hysteresis. Kapsalis (1987) deﬁned hysteresis as the phenomenon where two
different paths exist between the adsorption and desorption isotherms. Due to
hysteresis, a much lower vapor pressure is required to reach a certain amount
of water by desorption than by adsorption. Hysteresis phenomenon is critical in
food stability because some foods are ﬁtted to a chosen aw by desorption while
others are ﬁtted to the desired aw by adsorption. (Labuza, 1984; Troller and
Christian, 1978; Kapsalis, 1987). A representation of the hysteresis

phenomenon is shown by Figure 2.

Moisture
Content

Desorption f

Adsorption

 

 

Water Activity

Figure 2 — Schematic Representation of a Moisture Sorption Hysteresis

Source: Kapsalis, 1987

1.3. Use of Moisture Sorption lsotherrns

The sorption data has numerous theoretical and practical applications in
food science and technology. Among the theoretical uses of sorption isotherms
are thermodynamics (sorption-desorption enthalpies and bound water),
structure investigations (speciﬁc surface area, pore volume/size distribution and
crystallinity). The practical applications of sorption data in food processing are

in drying, mixing, packaging, and storage (Gal, 1983).

In 1982, lglesias and Chirife presented a handbook of food isotherms
that compiled more than a thousand ,water vapor sorption isotherms of foods
and their components. The researchers also included a brief description of the
techniques for the use and calculation of isotherms. Among the uses mentioned
are prediction of microbial and physicochemical stability of foods, engineering
purposes related to concentration and dehydration, predicting sorption values,
determination of net heat of sorption and analyzing the behavior of food
mixtures.

1.4. Equations for Sorption Isotherms

Attempts to classify the several available sorption models have been
made by various researchers (Van Den Berg and Bruin, 1981; lglesias and
Chirife, 1978, Boquet et al, 1978 and Boquet et al 1979). Van Den Berg and
Bruin (1981) compiled and classiﬁed sorption models in four groups according
to their origins. The researchers presented the following categories:

(1) Monolayer sorption models

(2) Multilayer sorption and condensed ﬁlm models

(3) Sorption models from polymer science

(4) Empirical sorption models

Chirife and lglesias (1978) compiled and reviewed twenty three
equations for ﬁtting water sorption isotherms of food and food products. They
used the origin, range of applicability and use of the sorption isotherms as the

criteria for their analysis. The researchers not only found that some theoretical,

semi-empirical and empirical models are not equivalent, but that they also were
limited to speciﬁc ranges of water activity or types of food.

Boquet et al (1978) and Boquet et al (1979) continued the work started
by Chirife and lglesias (1978) selecting for their study eight two-parameter and
four three-parameter models to describe the sorption isotherms of various
foods. They grouped the food products as fruits, meats, milk products, proteins,
starchy foods and vegetables. The researchers concluded, based on its
versatility and excellent ability to ﬁt the experimental data for most types of
foods, that the Hailwood and Horrobin equation should be considered as the
“universal” isotherm. This three-parameter equation is mathematically
equivalent to the Guggenheim-Anderson-de Boer (GAB) equation and it works
well on a wide range of water activity (0.10-0.80). They also mentioned that
some two-parameter equations have equal or better ﬁtting abilities than the
three-parameter ones and the use of a third parameter might not be useful. The
recommended two-parameter equations were the Halsey and the Oswin
models.

The use of the GAB equation to construct sorption isotherms has been
also supported by Bizot (1991). The researcher prepared a computer program
capable of ﬁtting and plotting the isotherms from the experimental data and
used the transformed GAB equation to prepare it. The researcher also
emphasized that the GAB equation is the best alternative to determine primary
adsorption sites and to ﬁt an equation to experimental data. Spiess (Bizot,

1991) presented a discussion about Bizot’s article and pointed out that D'arcy-

Watt developed a ﬁve-parameter equation with application over the entire water
activity range (from zero to one), but for the application range, 0.2-0.8, the
model will be very difﬁcult to use and will not have any advantage over other
models.

Peleg (1993) took a different approach from the previous workers by
proposing an empirical double power law four-parameter equation. An equal or
slightly better ﬁt than the GAB model was obtained with the model proposed
when the model was validated with the following products: agar-agar,
carrageenan, gelatin, low methoxyl pectin, raisins, casein, potato starch,
dextrin, and coffee. Peleg used the Mean Square Error magnitudes of the GAB
and his empirical model to make his comparison. It is important to remark that
like the GAB model, Peleg’s model is only applicable up to an aW level about
0.90 and beyond this range (aW > 0.95) it can only be applied if aW is replaced
by a transform such as -In(1-aw).

The relative percent root mean square (%RMS) is widely used and
accepted to evaluate the ﬁtting goodness of the experimental data. Bizot
(1991) proposed the use of this relative per cent root mean square (%RMS) to

judge the quality of the ﬁt of the experimental data. The %RMS is expressed as:

 

2
EN; wi —w,’
w. x 100 (1)

%RMS =

 

N

Where N is the number of experimental points, W; is the experimental

water content, and w: is the calculated water content.

10

1.5. Equations for Multicomponent lsotherrns

When two or more products are packaged together in a permeable
package, a moisture transfer from the component with a lower water activity to
the component with a higher water activity is observed. A moisture ﬂow
between the package and the environment is also observed. The moisture
exchange among the products continues until an equilibrium water activity is
reached. This exchange causes the product with the lower water activity to gain
moisture while the component with the higher activity loses moisture. (Salwin
and Slawson, 1959; Gal, 1983; Labuza, 1984; Hong et al, 1986; and Kim et al,
1999). Therefore, it is critical to predict the equilibrium water activity in
multicomponent products.

A weighted-average hypothesis has been widely used by various
researchers to predict the water sorption behavior of a mixture from the

knowledge of its individual components.

Mcal = 2 W1 * MI.— (2)
2 W,

Where Mca. is the moisture content if the mix, M, is the moisture content
of the product i before mixing and W, is the dry weight of component i.

This equation based in a mass balance assumes that water is
independently bounded to each product. In other words, at a given water
activity the moisture content of a mixture is equal to a weighted average of the

moisture content of each component at that water activity.

11

Attempts to predict water sorption behavior of a mixture from its
individual components has been researched by various investigators: Salwin
and Slawson (1959), Chuang and Toledo (1976), lglesias et al. (1980), Lang
and Steingberg (1980), Lang and Steinberg (1981), Lang et al.(1981), Hardy
and Steinberg (1984), Chinachoti and Steinberg (1985), Chinachoti and
Steinberg (1988), Nieto and Toledo (1989), Chinachoti, P. (1990), Leiras and
lglesias (1991), and Bakhit, RM. and Schmidt, SJ. (1992).

The shelf life studies mentioned above considered that no moisture
transfer occurred between the products and the environment and they used
linear sorption isotherm equations or equations with limited water activity range
of applicability (lglesias, et al, 1979).

Lang and Steinberg (1981) studied hand-mixed mixtures of starch,
casein, sucrose, salt propylene glycol, and ground beef in binary and ternary
combinations. They concluded that each component sorbs water independently
of the others. In other words, the predicted and measured values of moisture
content have shown good agreement because there are no interactions
present. The referred interactions are the ones that occurred at the molecular
level (eg. modiﬁcations of molecular bonds).

For multicomponent products obtained by physical mixing, it may be
assumed that mixtures sorb an amount of water equal to the weighed average
of the amount that components would sorb alone. This assumption implies that
water is independently bound to each product (weighed average basis) as

described by equation (2).

12

It has been proven that interactions among the mixture components
affect the moisture sorption of mixtures, creating an increase or decrease of
moisture content as compared to moisture content predicted by the weighed
average basis equation (lglesias et al, 1980; Hardy and Steinberg, 1984;
Chinachoti and Steinberg, 1985; Chinachoti and Steinberg, 1988; Leiras and
lglesias, 1991; Bakhit and Schmidt, 1992). The interactions observed are
caused by different mixing methods rather than simple physical mixing.
Examples of these mixing procedures are wet mixing followed by freeze-drying
and the order of the drying, before or after mixing.

lglesias et al (1980) worked with mixtures of non water soluble
biopolymers (proteins and carbohydrates) and found that the predicted values
of the moisture content of the mixtures were higher than the measured ones for
most of the samples that were run. The investigators proposed that the
polymer-polymer H-bonds that compete with polymer—water H-bonds are
responsible for decreasing the water sorption. Chinachoti and Steinberg (1985)
found the same type of interaction in mixtures of sodium chloride and starch
above water activities of 0.75.

Chinachoti and Steinberg (1988) worked with sucrose-protein mixtures
and found that the mixtures sorbed more water than calculated due to the water
binding with the proteins. Leiras and lglesias (1991) found that at high water
activities (aw>0.75) the experimental moisture contents were greater than
predicted and granted this difference to the solubilization of the salt and sugar

in cake mixtures.

13

Salwin and Slawson (1959) developed a model to predict moisture
transfer in combinations of dehydrated foods, from the knowledge of the
sorption isotherm of the individual components, dry weight of the components
and the relative humidity of each component. They assumed linear isotherms
between the initial and the equilibrium relative humidity. They worked over a
narrow range of relative humidity and found good agreement. Lang and
Steinberg (1981) reviewed and criticized Salwin and Slawson work and stated
that their linear approach over a narrow aw range (aw30.1 1) is not convenient.
They also emphasized that at higher relative humidities, the normal s-shaped
isotherms show more curvature and the assumption of a linear isotherm is no
longer valid. lglesias et al (1979) pointed out another major limitation in the
work done by Salwin and Slawson (1959). It does not allow the prediction of
equilibrium aW when there is simultaneous moisture exchange with the
environment.

lglesias et al. (1979) used the concept of additivity of isotherms. The
additivity of isotherms proposes that the amount of water sorbed at any given
water activity is derived by the weight percentage of each component times the
amount it would sorb alone. The researchers substituted the linear equation for
the BET equation and the range of work was 0.05-0.40 for the dehydrated
products tested. A very good agreement was obtained between samples of the

additive isotherm and the computer calculated values.

14

1.6. Shelf Life Deﬁnition

Marsh (Brody and Marsh, 1997) deﬁned shelf life as the time after the
production and packaging of the product for which it remains acceptable under
deﬁned environmental conditions. He emphasized that shelf life is a function of
the product, the package, and the environment through which the product is
transported, stored, and sold.

Product, package and environment are critical factors that affect shelf
life. While companies desire a shelf life that matches the distribution and use of
the company’s inventory, the consumers expect a shelf life that allows them to
fully use the product.

An overestimated shelf life requirement will increase costs due to
overpackaging. An underestimated shelf life requirement will increase costs in
wasted or discarded products, increased liability, or consumer dissatisfaction.
Therefore it is critical to deﬁne a reasonable shelf life which could be met with a
proper packaging design (Pocas, 1995; Marsh, 1997)

1.7. Shelf Life Models

1.7.1. Generalitiﬁ

A moisture transfer between the food product and the external
environment is observed in moisture-permeable packages and its rate is
controlled by the water vapor pressure difference between the package
headspace and the environment. When the product exhibits moisture diffusion

much faster than the diffusion across the packaging barrier, the food product

15

equilibrates with the headspace vapor pressure and the product’s moisture
content may be described by its isotherm. (Pocas, 1995)

An adequate shelf life can be achieved by controlling the moisture
exchange between the product and the storage environment with the proper
packaging material. Therefore, the shelf life determinations help to develop and
to optimize the packaging-product system. (Pocas, 1995)

The mathematical models connect the product’s characteristics, the
package properties and the environmental conditions. When a model is
validated and proven to be reliable, its use is preferred over other shelf life
estimation methods. Mathematical modeling is the most preferred shelf life
estimation due to its short time, low cost and as a package design tool. (Pocas,
1995; and Marsh, 1997).

1.7.2. mle Products

Shelf life modeling of single products was ﬁrst studied by Heiss (1958).
This researcher established a relationship between moisture sorption properties
of foods, the permeability of the ﬁlm and the shelf life of the product. Heiss
(1958) used F ick’s law of diffusion to develop his solution.

Heiss (1958) introduced basic concepts that served to calculate the shelf
life for moisture sensitive products. Further studies increased the complexity
and applicability of the models, but these studies were still focused on
packages of single products. For example, Labuza et al (1972) introduced
Oswin, Kuhn and Mizrahi, non-linear isotherms, into the model. Lee (1987) and

Lee et al (1996) developed a mathematical model for predicting the changes in

16

the moisture content of a packaged solid dosage form that takes into
consideration the effect of ﬂuctuating temperature and relative humidity during
prolonged storage. The model combines the sorption characteristics of the
product and the water vapor permeability of the package system as a function
of temperature.

Cardoso and Labuza (1983) worked with a single product, but they
developed a dynamic model to predict moisture transfer in packaged pasta.
They created a controlled unsteady state conditions (varying as sine wave) of
temperature and relative humidity.

1.7.3. Multicomponent Prgducts

For food mixtures, the moisture transfer from the component with the
higher to the lower water activity occurs until equilibrium of water activity is
reached. This equilibrium of water activity is responsible for the ﬁnal moisture
content of each component that directly inﬂuence the quality and shelf life of the
mixture (Hong et al, 1986; Gal, 1983; Labuza, 1984 and Pocas, 1995). In
consequence, predicting the equilibrium water activity of a mixture is critical to
formulate a mixed product.

When the diffusion coefﬁcient of the water in the packaging material is
much smaller than the diffusion of water within the product the transport through
the ﬁlm barrier controls the shelf life of the mixture (Pocas, 1995).

It is assumed that the water transferred through the package at any
water activity is distributed proportionally to each component as predicted by

their respective sorption isotherms. This weighted isotherm has been combined

17

with the shelf life models for single products (lglesias, 1979 and Pocas, 1995).
lglesias et al (1979) used a BET equation to describe the mixture sorption
isotherm in the water activity range of 0.05-0.40.

Hong et al (1986) predicted the moisture change of each component of a
mixture by using ﬁnite element modeling. They considered the moisture transfer
across the packaging material negligible. The researchers used the GAB
equation to describe the products” isotherm. Salwin and Slawson (1959) used
linear isotherm and also did not consider moisture transfer through the
packaging. Shelf life studies of multicomponent moisture sensitive products in
permeable packaging have been conducted primarily using linear and BET
isotherms.

Shelf life modeling of multicomponent foods has only focused on the
prediction of mixture sorption behavior from the sorption characteristics of
individual components and assumed no moisture transfer across the packaging
barrier. These studies reported the use of a linear sorption isotherm equation or
equations with limited range of activity.

Pocas (1995) developed a mathematical model and a computer program
to calculate the shelf life and to predict the change in moisture content over
storage time of a two component mixture packaged in ﬂexible packages. The
model used GAB (Bizot, 1983), Oswin (Oswin, 1946 in Pocas, 1995), Halsey
(Halsey, 1948 in Pocas, 1995), Henderson (Henderson, 1952 in Pocas, 1995)
and Chen (Chen, 1971 in Pocas, 1995) equations to ﬁt the experimental

sorption isotherm and the computer program included them. The importance of

18

this model is the consideration of the whole isotherm and not only the linear
part. The previous models mentioned considered only the linear part.

Pocas (1995) validated the program with mixtures at different weight
ratios of breakfast cereal and powder chocolate packaged in Oriented
Polypropylene (OPP) and Polyethylene (PE). It was reported that the model
tended to overestimate the component moisture content, especially the cereal
after longer storage periods. It was proposed that deviations are dependent on
the packaging material barrier, which affected the relative tendency of the
components to absorb moisture simultaneously. It was suggested that the
package introduced deviations because the model assumption of fast
equilibrium between the product’s moisture content and the package’s
headspace relative humidity is not met. Another proposed cause of this
difference was that the equilibrium moisture content of each component may be
affected by the presence of the other component (Pocas, 1995).

Pocas (1995) developed a more general mathematical model to
calculate the change in moisture content over storage time and the shelf life of
a two-component packaged mixture, using the GAB, Halsey, Henderson, Oswin
or the Chen equations, maintaining the individuality of each component and not
using one “weighed sorption isotherm”. This researcher also wrote a computer

program where simulation runs were carried out.

19

1.8. Mathematical Model Development
Labuza (1972) expressed the rate of water transport through a

permeable ﬁlm with the following equation:

dW P

—=—A - .

dt 1 (pt 13.) (3)
Where:

W is the weight of water transported across the ﬁlm, in g.

t is time, in days

P is the ﬁlm permeability coefﬁcient, in g-um/mz-day-mm Hg

l is the ﬁlm thickness, in um

po, pi are the vapor pressure of the water outside and inside of the
package, respectively, in mm Hg.

It is assumed that the packaging material controls the moisture exchange
between the product and environment. To consider this assumption valid the
condition of having a water diffusion coefﬁcient through the packaging material
much smaller than the water diffusion coefﬁcient in the air and within the
product must be met. It is also assumed the following: (1) the products’
moisture content is in equilibrium with the internal pressure, (2) there is a rapid
equilibrium between water and the food, (3) the internal pressure is determined

by the product equilibrium moisture content and the storage temperature.

20

For mixtures of binary products, the amount of moisture permeating
through the package is equal to the sum of the moisture changes in each
component.

Pocas (1995) developed a general equation for mixtures of two products
from the equations presented above. The researcher used the Henderson,
Chen, Oswin, Halsey linear and the GAB non-linear sorption isotherm
equations. A complete summary of the derivation for each component based on
moisture sorption data by linear regression and by second order polynomial
regression proposed by Pocas (1995) is presented in Appendix A.

To determine the shelf life of mixed products using the linear isotherm,

Pocas (1995) derived the following equation.

 

IA:

 

bB Mi dMA
P.A.ps

W +W —
[ A Bb MLaWO-aW(MA) (4)

A

 

 

Mia
t3 = 1 [WA EI'WB) I dMB
PHApS b3 M's aW0 - aw (MB) (5)

Where:

MA‘ and M31 are the initial moisture content of component A and B, respectively

tit, and t3 represents the time required to achieve the moisture content MA2 and
M32, respectively.

an, as, DA and be are coefﬁcients of the linear equation.

21

To determine the shelf life of mixed products using the non-linear
isotherm, the following equation was derivated by Pocas (1995).
1 Mi*
t :_ J‘WATWB'D(MA)
A .
P.A.ps M}, awo ' aw (MA)

 

dMA (6)

Mia
tB=——l——. j WB+WAB'D(MB) clMB <7)
P.A.ps M13 awo'aw (MB)

The relative percent root mean square of the difference between the
experimental and the calculated moisture content (R) was used to evaluate the

goodness of the ﬁt. The equation, previously presented is written below.

 

.. 2

 

" M , — M ;
%RMS: 2 x 100 (8)
I n

where Mi is the experimental moisture content Mi* is the calculated

 

 

 

moisture content and n is the number of experimental data points.

22

Chapter 2

MATERIALS AND METHODS

2.1. Product - Packgge Svstem

2.1.1. Food Product Samples

Three common breakfast cereals were obtained from a local store. The
following cereals were chosen, Corn Flakes, Shredded Wheat and Oats due to
their low sugar and salt contents.

The main ingredients in corn ﬂakes cereal are milled corn, sugar, salt,
malt ﬂavoring, and high fructose corn syrup. It was packaged in a polyethylene
bag which was placed into a carton. Shredded wheat has no salt or sugar
added and it also was packaged in a carton with an inner plastic bag. Oats also
has no salt or sugar added and it also was packaged in a carton cylinder with a
plastic cap.

Products were preconditioned before experiments. Products were stored
in a control environment at 23°C and 50% relative humidity for 48 hours. Then a
single product was stored in a glass container with nitrogen ﬂush.

2.1.2. Package

High Density Polyethylene and Low Density Polyethylene with 1.0 and
1.9 mil thickness, were supplied by a local converter. Materials were
conditioned at 23°C, 50% RH for 72 hours prior to testing. The characterization
of the packaging materials includes thickness and water permeability of the

ﬁlms. The characteristics are presented in Appendix B.

23

For the validation experiments three-side-seal pouches of these
materials were sealed using an impulse sealer. The dimensions of the pouches
were 17 cm x 10 cm. The integrity of the pouches was checked with a
polariscope and with manual tensile test. A quality seal was obtained when a
uniform and consistent color band was observed when placing the sample
between two polarized lenses. In the manual tensile test, the seals were slowly
pulled apart while holding the two sides of the sealed sample. Ripping of the
material before the seal suggests a quality seal.

2.2. Moisture Content Determination

Moisture content of cereals was determined by Gravimetric Method: 5 g
of product was placed in an aluminum dish and dried in vacuum oven (Precision
Scientiﬁc Model 524) at 75°C and 30 mm Hg until constant weight. The
moisture content was reported on percent wet basis, Mw. The percent moisture

content (dry basis), M, was determined as

M = —” (9)

This method was developed at School of Packaging (Michigan State
University) and is used on the Permeability and Shelf Life Lab Manual. For

more information see the Bibliography.

24

2.3. Moisture Sorption Isotherms

Moisture sorption isotherms were determined gravimetrically at 72°C by
equilibrating cereal samples (3 replicates) at nine different relative humidity
values, ranging from 5% to 88% RH. The relative humidity was created inside
closed containers with saturated solutions and was monitored with a calibrated
hygrometer (Hydrodynamics, lnc., Silver Spring, MD) at the beginning and end
of the experiment. Table 1 presents the saturated salt solutions and their
corresponding measured relative humidity.

Table 1: Saturated salt solutions and their corresponding relative

 

 

 

 

 

 

 

 

 

 

 

humidities at 23°C
Saturated Salt Solution Relative Source
Humidity, %
Lithium Bromide 5.3 Sigma, MO
Lithium Chloride 11.2 J,T. Baker, NJ
Potassium Acetate 25.1 J,T. Baker, NJ
Magnesium Chloride 33.0 J,T. Baker, NJ
Potassium Nitrite 47.8 Columbus Chemical Industries, Inc., WI
Sodium Nitrate 61.5 J,T. Baker, NJ
Sodium Chloride 76.0 Columbus Chemical Industries, Inc., WI
Ammonium Sulfate 80.8 EM Science, NJ
Potassium Nitrate 87.8 Columbus Chemical Industries, Inc., Wl

 

 

 

25

 

Water activity can be easily calculated from the relative humidity values

presented on Table 1 by

RH
a:—

10
w 100 ( )

About 4 grams of cereal were weighed into a Petri dish (55 mm
diameter). Three replicates and two controls (empty Petri dish) were placed into
the closed containers (speciﬁc relative humidity). Samples were weighed on AE
160 Meter Analytical Balance at pre-determined time intervals. This procedure
was performed until a constant weight was found. The equilibrium moisture
content, expressed as dry basis, was calculated based on moisture change of a
sample at equilibrium.

The equilibrium moisture content (dry basis), M, was calculated by

equation 11.

M=[we(Mi_l)-1]x1oo (11)
w

 

where M = equilibrium moisture content, % dry basis
M; = initial moisture content, % dry basis
We = weight at equilibrium, 9

W, = initial weight, g

26

Experimental moisture sorption isotherm was ﬁt with GAB, and cubic

polynomial equations. Parameters in equation were estimated as the following:

GAB Equation

__M_= CKaW (12)
Wm (l-kanI-kaw +Ckaw)

Where:
Wm = water content corresponding to saturation of all primary adsorption

sites by one water molecule (formerly called the monolayer in BET theory)
C = Guggenheim Constant = c’ exp[(H. - Hm)/RT]

k = factor correcting properties of the multilayer molecules with respect to

the bulk liquid: k =k’ exp [(H. - Hq)/RT]
H. = heat of condensation of pure water vapor

Hrn = total heat of sorption of the ﬁrst layer on primary sites

H, = total heat of sorption of the multilayer water molecules

In order to estimate parameters, the equation was transformed into a

quadratic form as

91 = aaf +ﬂaw +7
(13)

 

 

27

 

_;_Z=1 _
ﬁ‘wbc) wc(C 2) (15)

 

The quadratic regression was performed by MS Excel. GAB constants C,

Wm, and k were calculated by equations 17, 19, and 20, respectively. The

details for obtaining these equations are presented in Appendix C.

 

 

 

C = 6:: 62—461
2 (17)
where
,62
9=4+ 18
(”)7 ( )
I
w... = -—(c-2>
[’C (19)
k = 1

Cubic Polynomial Equation
M = k1aw3 + kzaw2 + kaaw +t)c

The polynomial regression was performed by Microsoft Excel 97-SR1.

28

The goodness of ﬁt for each isotherm was evaluated based on the

minimum value of percent root mean square, RMS.

Zn: |:Mexp _Mcalc:|
i=1 M
x100

 

 

 

where Mexp = experimental moisture content, % dry basis, Mcaic =

calculated moisture content, %dry basis, and N =number of data point.

2.4. Penitegapilitv of Packaging Material

Water vapor transmission rate of packaging ﬁlms was determined by an
infrared sensor method (based on ASTM F1249-90), using a PERMATRAN
W3/31 (Mocon Inc, Minneapolis, USA). Six replicates per material were tested
at 23°C with 50% of relative humidity as the driving force. The relative humidity
was obtained with water vapor in one side chamber of the cell and nitrogen
ﬂush in the other side chamber. The actual value of permeability was found by
dividing the transmission rates of the material by the driving force as indicated
in Appendix B.

Water vapor transmission rate of the pouches was also determined by
the gravimetric method (ASTM D3079). Three pouches of each material (17 cm
x 10 cm) ﬁlled with desiccant, were stored at 23°C and 50%relative humidity
and weighed every 4 days, until there was a constant increase of weight. Three
empty pouches were also stored to evaluate the moisture sorption on the

material.

29

2.5. Model Validation Experiments

To validate the model, two experiments were carried out. For the ﬁrst
experiment, mixtures of two cereals (corn-oats, oats-wheat; and corn-wheat)
were packaged in 17 cm x 10 cm pouches of HDPE and stored at 23°C and
50% relative humidity. Mixtures of different ratios of cereal to cereal were
prepared: 1/2, 1/1 and 211. Pouches were weighed daily during the ﬁrst week
and then weekly during the following 8 weeks, two of those pouches of each
mixture were tested for moisture content determination of each product. A
similar procedure was employed for pouches with single product.

For the second validation experiment, mixtures of cereals in a ratio of 111
were packaged in LDPE pouches (17 cm x 10 cm) and stored at the same
conditions. Pouches were weighed daily during the ﬁrst week and aftenNards
weekly for the following 8 weeks. Pouches with a single product were also
treated with same procedure.

Initial moisture content was determined for each experiment with the

procedure described above.

30

Chapter 3

RESULTS AND DISCUSSION

3.1. Initial Moisture Content
The initial moisture content (dry basis) of corn, oats and wheat
determined and used for plotting the moisture sorption isotherms were:

Corn: 3.18 i 0.07 9 H20] 9 100 dry product
Oats: 10.68 i 0.08 9 H20/ 9 100 dry product
Wheat: 4.95 i 0.107 9 H201 g 100 dry product

3.2. Moisture Sorption lsfotherms
The plot of the moisture sorption isotherms for corn, oats and wheat

cereals at 23°C isotherms are presented in Figures 3, 4 and 5 respectively.

 

 

‘ 0.30 I

i 0.25 .__.- . ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2’
C)
..- 0.20 f
C
‘9 015
C . ~»—— . — --
O
2:, 0.10 ,_.__-‘- /
3
E 0.05 /
O
2 0.00 I . ,
0.00 0.25 0.50 0.75 1.00 -
. wateractivity
I +Corn
‘ .-

 

 

Figure 3 - Moisture Sorption lsotherm of Com Cereal at 23°C.

31

 

 

 

 

 

 

 

l d
J "3 0.15 --
E
l a
I § 0.10
l a
i 3
J g 0.05 .
2
I 0.00 . , .
1 0.00 0.25 0.50 0.75 1.00
J wateractivity
J J—g—Oats‘

 

 

 

 

 

 

 

 

 

 

 

 

l
s; 0.20 ___.-__ . . _ L
I g /
J E _L
O
o
J 2
3
J .2
O
2
J 0.00 , , .
0.00 0.25 0.50 0.75 1.00
wateractivity
J r——————vi
l

{+Wheat J

 

Figure 5 - Moisture Sorption lsotherrn of Wheat Cereal at 23°C.

32

 

 

 

The data used to construct the graphs are presented in Appendix E. The
same data was used to calculate the Linear, GAB and Cubic Sorption lsotherm
Equations. The equations for the cereals tested were calculated with MS Excel

and they are presented in Table 2.

33

a nae. so: 9: aged 0 eon: Leos; 8v ”6 22¢ Soc 90 aged m. new: ado Q ”a 23 so: mi

858 m new: :80 E .wEBQ _mEoEEono 05 __m 8: Lo: 2o “was; new mﬁmo .500 L8 8:960 80:: or; C

 

 

 

 

 

886 u am Name u «m. 58.0 H mm
25.0 + 388.? E86 + 3831? #86. £88.?
«seamen? ”£986 n s. “.6886 l ”328.0 u s_ N385? ”£886 u s. 225
Bad u um 83.0 u E 88.0 n E I
3.: 43+ 8.~+
33.3.. «some? n s: so 352+ «58.0- u 2:6 :83: NERD- u s: so m5
886 u «m 83o u mm
886 H mm Q E
E 55.0 + 382.0 n s. 88.0 + gnome; u s. 28.0 + 2333 u _2 C .85..
«mos; 9.3 500 .5395

 

 

 

 

.008 6 852.560 50:2, ocm mLmO _Eoo Lo mcozmscm E558. cozeom 05:0 cam 95 .89.: l N 2an

 

34

3.3. Film Permeabilitv

The permeability of four HDPE and four LDPE ﬁlm samples was
determined with ASTM F-1249-90. The conditions were set at: 50%RH and 23
°C. Permeability results, obtained from 4 repetitions, are presented below and
the details are presented in Appendix B.

LDPE Film: 9.54E-05 :t 7.85E-06 g.millin2.day.mmHg

HDPE Film: 5.31 E-05 : 4.91 E-07 g.mil/in2.day.mmHg

3.4. Package Permeability

Package permeability was also measured to see the effect of the seals.
The permeability values obtained from the LDPE and HDPE samples’
transmission rates by the Gravimetric Method are presented below.

LDPE Film: 5345-05 i 5.05505 g.millin2.day.mmHg

HDPE Film: 4.20E-05 i 1.16E-06 g.mil/in2.day.mmHg

The package permeability values of LDPE and HDPE were
approximately 33% and 21% lower than the ones obtained from the ﬁlm
samples. This difference between the ﬁlm-sample and pouch permeability is
within reasonable range. An explanation for this difference lies on a higher ﬁlm
permeability determination due to a higher vapor pressure differential, a higher
temperature or a miscalibrated sensor in the Permatran. A lower storage
relative humidity or a lower storage temperature could be responsible for the
lower pouch-permeability values reported. The storage relative humidity and
temperature were monitored and they were in the range i 3%. The Moisture

Gain vs Time plot for the pouches (Appendix B) showed straight lines,

35

indicating good agreement. The pouch-permeability values also indicate that
good seals were achieved because the pouches’ permeability values were
always lower than the ﬁlm samples. Due to this difference in permeability value
between the ﬁlm (also known as ﬂat-ﬁlm) and gravimetric method, the latter
value was selected and used in the calculation carried by the computer

program.

3.5. ﬁlidation 1 - Moisture Charge in Cereal Pa_cﬂlged in HDPE 1.9 mil

The experimental validation for the computer model was carried out by
monitoring the change in moisture content over time of each component of the
packaged mixtures. Table 3 summarizes the combinations used for the
Experimental Validation 1.

Table 3 - Combinations of cereals used for the Experimental Validation 1

 

 

 

 

 

Experiment 33167 50150 67/33 100
1 corn/wheat corn/wheat corn/wheat corn
2 corn/oats corn/oats corn/oats cats
3 oats/wheat oats/wheat oats/wheat wheat

 

 

 

 

 

 

Because oats presented an initial water activity of approximately 0.47-
0.49 and the values for corn and wheat ranged near 0.17-0.20; it was expected
that moisture exchange between oats and corn or cats and wheat would be
more important than the permeability through the package during the early
phase of he experiment. Therefore, in addition to the mixtures described in the
table above, a 30-gram mixture (ratio 1:1) of com (14.63 g dry product) and
oats (13.50 g dry product) was placed in a glass jar to determine the time

required until moisture equilibrium is reached in the absence of permeability.

36

Equilibrium, the time when the hygrometer sensor attached to the metal lid did
not report any further change, was reached in 48 hours. The readings of this
closed environment were performed every 12 hours. After forty-eight hours the

sensor showed a constant reading (38.5 :I: 1.0 %RH).

Corn at an initial moisture content of 0.0284 9 H2019 dry product and
oats at 0.1206 9 H2019 were placed in the glass jar. The glass jar was opened
after 192 hours (8 days), and corn and oats were separated. Then their
moisture content was determined. The ﬁnal moisture content of corn and cats
were 0.0491 9 H2019 dry product and 0.1027 g H2Olg dry product respectively.

A mass balance was performed to corroborate the numbers obtained.
The mass balance was as follows:

Initial Water Mass: 0.0284 9 H2019 dry corn * 14.63 g dry corn + 0.1206
g H2O/g dry oats * 13.50 g dry oats = 2.04 9 H2O

Final Water Mass: 0.0491 g H2O/g dry corn * 14.63 g dry corn + 0.1027
9 H2019 dry oats * 13.50 g dry oats = 2.10 9 H2O

The most important conclusion from this ancillary experiment is that in
closed systems moisture exchange takes approximately 48 hours. This
consideration will be helpful to support the discussion of the following
experiments and in the application of the computer model.

Figures 6, 7 and 8 show the percent moisture change proﬁle of 33167,
50150 and 67/33 corn/wheat samples. Figures 9, 10 and 11 present the percent
moisture change proﬁle of 33167, 50/50 and 67133 corn/oats pouches. Figures

12, 13 and 14 plot the percent moisture change proﬁle of 33167, 50/50 and

37

67133 oats/wheat samples. Finally, the percent moisture change proﬁle for
corn, oats and wheat is presented in Figures 15, 16 and 17.

The experimental and predicted values of the percent moisture content
as a function of storage time for the cereal combinations (Table 3) are
presented in Appendix F. Detailed tables of the individual pouches’ weight gain

values for all these combinations are presented in Appendix G.

38

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In the corn and wheat mixtures, it was observed that both cereals started
to pick up moisture immediately because the cereals had lower initial water
activity (0.17-0.20) in comparison with storage relative humidity (50%RH). The
moisture transfer between corn and wheat was expected to be small because
their initial water activities taken from their respective isotherms were close
(corn = 0.17, oats = 0.20).

The experimental and predicted values showed good agreement for the
corn and wheat mixtures (Figures 6-8). The percent difference between these
values was lower than 10% with the exception of mixture of 33167 corn-wheat
(Figure 6). A difference in the order of 10-26% was noticed from the third week.
It is important to mention that the difference was above 20% (20-26%) only
during weeks 5-7 (Figure 6). The experimental values for the 33l67 corn/wheat
samples were slightly lower than the predicted ones for most of the samples.
The 50/50 and 67l33 corn/wheat samples also show this behavior.

In the individually packaged products (Figures 15-17), single packaged
corn (Figure 15) showed a difference between the experimental and predicted
values greater than 10% from the sixth week of storage. The difference range
for weeks 6-9 was 10-23%. Again, the experimental values were lower than the
predicted ones. The difference in the single packaged oats and wheat (Figures

16 and 17) was lower than 4% and 12%, respectively.

51

The difference (greater than 10%) found in the samples of corn-wheat
(33l67) and corn could be caused by errors in the moisture content
determination of those samples. The com samples were mixed in a large plastic
bag and then immediately nitrogen-ﬂush packaged in glass jars. The initial
moisture content was determined from samples before placing the cereal in the
jars and perhaps the batch did not have homogenous moisture content.

The lower rate on the moisture transfer could possibly attributed to a
lower storage relative humidity, to the pouches’ lower transmission rate or to the
pouches’ lower surface available for moisture transfer. It is proposed that
samples of individually packaged corn and 33l67 com-wheat showed the
deviation because of a lower storage relative humidity or lower temperature
during the storage.

Experimental errors associated with the weighing, component
separation, moisture determination or modiﬁcation of the corn (e.g. oxidation)
could also be responsible for the higher values of moisture content predicted by
the model as compared to the values that were experimentally determined.

Pocas (1995) pointed out that the relative resistance to moisture transfer
within the food components to the packaging material plays an important role to
the effectiveness of the model. The researcher used corn cereal and chocolate
powder and found that com alone or packaged (in PP and PE) with the powder
presented similar deviations in the order of 20—30%. The researcher remarked
that the corn moisture content when packaged together with the powder

chocolate reached equilibrium at lower values than the predicted at longer

52

storage periods. Individually packaged corn as well as the powder chocolate did
not reach equilibrium during the storage period.

In the corn-oats and oats-wheat, oats was selected because it had a
much higher initial water activity (about 0.45-0.48), which was close to the
storage relative humidity. It was expected that oats would gain moisture from
the storage environment very slowly as shown by the oats isotherm (Figure 4)
and the individually packaged oats samples (Figure 16).

Oats would also transfer moisture to the other component (corn or
wheat) much faster during the first days as demonstrated in the glass-jar
experiment. After this time of dramatic moisture exchange, a temporal
equilibrium will be reached and oats will present lower moisture contents while
the other cereal (corn or wheat) will have higher moisture content values. For
most of the cases the transitory equilibrium was reached in one or two days.

To account for this moisture exchange event (“temporal equilibrium”), the
lowest experimental moisture content (from oats) was used to deﬁne the initial
point where permeation through the package became more important than the
components’ moisture exchange.

After making the corrections, it was observed that the predicted and
experimental moisture content values for corn-oats and oats-wheat presented a
good agreement. The difference between these values was less than 13% for

all the combinations of corn-oats and oats-wheat.

53

In addition to the percent difference between the experimental and
predicted values, a regression analysis was performed to determine the positive
relationship between the predicted and experimental values. The regression
analysis was selected because it is the most suitable statistical method to
compare observed and predicted values. The regression analysis was done by
plotting the experimental values in the X-axis and the predicted values in the Y-
axis. If the model predicts perfectly the experimental data a straight line should
be expected and its correlation coefﬁcient will be 1, but this hypothetical
condition does not occur. Therefore, the correlation coefﬁcient is a good
indicator of the relationship between the experimental and predicted values.

All combinations used on the validation with HDPE, with the exception of
the oats individually packaged (84%), presented correlation values greater than
90%. This indicates that the model described accurately the systems used.

3.6. Validation 2 — Moisture Change in Cereals Packaged in LDPE 1 mil

 

An additional experimental validation for the computer model was carried
out with a lower barrier packaging material. Monitoring the moisture content
change of each component of the packaged mixtures over time was performed
similarly to Validation 1. Table 4 summarizes the combinations used for the
Experimental Validation 2.

Table 4 - Cereal combinations used for the Validation 2

 

 

 

 

Experiment 50/50 0/1 00
1 corn/wheat /corn
2 corn/oats loats
3 oats/wheat /wheat

 

 

 

 

 

54

Figures 18, 19 and 20 show the percent moisture change proﬁle of 50l50
corn/wheat, corn/oats and oats/wheat samples. The percent moisture change
proﬁle for corn, oats and wheat is presented in Figures 21, 22 and 23.

The experimental and predicted values of the percent moisture content
as a function of storage time for the cereal combinations (Table 4) are
presented in Appendix F. Detailed tables of the individual pouches’ weight gain
values for all these combinations are presented in Appendix G.

For the validation with LDPE, the predicted and experimental moisture
content values for individually packaged cereals present good agreement. All
the samples showed a difference smaller than 10% with the exception of
individually packaged wheat where the difference range was 6-1 3%.

The combinations of corn-oats and oats-wheat also present good
agreement between the experimental and predicted values. The samples also
showed the initial moisture exchange. Therefore, a similar treatment was
applied to determine the initial moisture content to be entered into the computer
program.

A regression analysis was also performed to determine the relationship
between the predicted and experimental values. All combinations used on the
validation with LDPE, with the exception of the oats individually packaged,
presented correlation values greater than 90%. This indicates that the model
has a high and signiﬁcant relationship with what is observed in the experiments.

A correlation value was not available for oats because the predicted moisture

55

content value was constant during the storage. This reﬂect that the software did
not account for the relative humidity variation in the storage room.

Both sets (validation with HDPE and LDPE) clearly indicate the
importance of the consideration of initial moisture exchange in the application of
the model. The time required for moisture exchange seems to be less important
than the internal moisture equilibrium reached.

The moisture content can be calculated from the products’ isotherms or
determined experimentally in a glass jar. The resulting moisture content (from
the above experiment) for the component with the lower water activity will be
the lowest moisture content to be used in the computer program. For the
component with the higher water activity, the outcoming moisture content will be
the lowest moisture content to be entered in the computer program.

To ﬁnd the resulting moisture content after the internal moisture
exchange from the components’ isotherms, the isotherms need to be expressed
as water activity as a function of moisture content. The resulting water activity
range is deﬁned by the water activities of the components. The components
also reach an equilibrium condition where the water activity is the same for
each component. Therefore, selecting a moisture content for each component
and replacing in its isotherms. This procedure is done until the moisture content

values give the same water activity value.

56

Another way to ﬁnd the resulting moisture content is to place the
components in a glass jar and monitor the moisture headspace until equilibrium
is reached. Then open the jara determined the moisture content of each
component. This procedure was used and described earlier in this chapter.

Permeation through the package is present at all times, but the
approximation discussed in the above paragraph could be used as a good
approximation. Deﬁning what is the minimum water activity difference between
the components that will make the moisture exchange between products
predominant over the permeation through the package is important.

In multicomponent products packaged in low-permeability packaging, the
moisture exchange between the products is more noticeable than if they were
packaged in high-permeability materials. This is because a low permeability

packaging material will simulate glass.

57

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CONCLUSIONS

1. A model developed using the GAB (Guggenheim-Anderson-deBoer)

equation to predict moisture content in binary mixtures was validated

2. For products with a large difference in water activity, the internal moisture

exchange is more important than the permeability during the ﬁrst days of

storage.

3. The model accuracy was greatly improved when the initial moisture

exchange is accounted.

64

RECOMENDATIONS

Further reﬁnement of the model should focus on the following:

1. Determining the minimum water activity difference between components that
makes the moisture exchange between products predominant over the
permeation through the package

2. Incorporating the moisture exchange between the components in the model
for a more accurate prediction when they present very different water
activity,

3. Studying the effect of the temperature on the moisture exchange as well as

the moisture permeated during the storage.

65

BIBLIOGRAPHY

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Mixed and Freeze-Dried NaCI/Casein Mixtures. Journal of Food Science.
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(2) Berens, A. R. 1989. Transport of Plasticizing Penetrants in Glassy
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(3) Bizot, H. 1991. “Using the “G.A.B.” Model to Construct Sorption Isotherms”
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(4) Brody, A. L. and Marsh, K. S. 1997. The Wiley Encyclopedia of Packaging
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(8) Chinachoti, P. and Steinberg, MP. 1988. Interaction of Sucrose with
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(9) Chuang, L. and Toledo, RT. 1976. Predicting the Water Activity of
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67

(10) Gal, S. 1983. “The Need for, and Practical Applications of, Sorption Data”
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(11) Hardy, J.J. and Steinberg, MP. 1984. Interaction Between Sodium
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(12) Hernadez, R.J. 1999. Shelf Life and Permebility, Class Material. School of
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(13) Heiss, R. 1958. Shelf Life Determinations. Modern Packaging. Vol 31. No
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(14) Hong, Y.C., Bakshi, AS. and Labuza, T.P. 1986. Finite Element Modeling
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(17) Kapsalis, JG. 1987. “Inﬂuences of Hysteresis and Temperature on
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(18) Kim, 8.8., Kim, S.Y., Kim, D.W., Shin, 8G. and Chang, KS. 1999.
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(20) Labuza, T.P. 1984. Moisture Sorption: Practical Aspects of lsotherm
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(21) Labuza, T.P., Mizrahi, S. and Karel, M. 1972. Mathematical Models for
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(22) Lang, K.W. and Steinberg, MP. 1980. Calculation of Moisture Content of a
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(24) Lang, K.W., Whitnay, R. McL., and Steinberg, MP. 1981. Mass Balance
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(25) Le Maguer, Marc. 1986. “Mechanics and Inﬂuence of Water Binding on
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Rockland, LB. and Beuchat, LR. 1986. Marcel Dekker, Inc.

(26) Lee, CH. 1987. Temperature Dependency of the Equilibrium Sorption
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Sensitive Pharmaceutical Tablet. MS Thesis. Michigan State University.

(27) Lee, C.H.; Hernandez, R.H.; Giacin, JR. and Lee, M. 1996. Modeling the
Temperature Dependency of the Shelf Life of a Packaged Moisture
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(28) Leiras, M. C. and lglesias, H. A. 1991. Water vapour sorption isotherms of
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(29) Mannheim, C. M.; Liu, J. X. and Gilbert, G. S. 1994. Control of Water in
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69

(31) Nieto, MB. and Toledo, RT. 1989. A Factorial Approach to Modeling aW of
a Multicomponent Food in the High Moisture Range (aw 0.90-1.00).
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(34) Salwin, H. and Slawson, V. 1959. Moisture Transfer in Combinations of
Dehydrated Foods. Food Technology. December, 1959.

(35) School of Packaging. 1999. Permeability and Shelf Life - Lab Manual.
Michigan State University

(36) Troller, J.A. and Christian, J.H.B., 1978. Water Activity and Food.
Academic Press.

70

APPENDICES

APPENDIX A

DETERMINATION OF SHELF LIFE EQUATIONS USING A LINEAR AND
NON-LINEAR SORPTION ISOTHERM

Pocas (1995) presented the following procedure to deduce the shelf life
equation for mixed products packaged in permeable packages using linear and

non-linear isotherms.

Moisture exchange is governed by the following equation.

%zli'A(Po'Pi) (I)

Where:

W: is the weight of water transported across the ﬁlm

t: is time

P is the ﬁlm permeability coefficient

I is the ﬁlm thickness

p0, pi are the vapor pressure of the water outside and inside of the
package, respectively

Moisture distribution in two products is controlled by the following
equaﬁon.

dW = WA dMA + W3 dMB (II)

Where:

WA, We are the dry weights of components A and B, respectively

72

dMA, dMB are the change in moisture content of component A and B
respectively, in g/g dry weight.
Combining the equations (I) and (II)

WA dMA + W3 dMB = E A ps (awo — aw) dt (III)
|

Where:

ps is the water vapor pressure at the storage temperature

awe, aW are the external and internal water activity, respectively

MA and M3 are products’ equilibrium moisture content at aW

MA and M; are related to the aW through the sorption isotherm equations.

Integrating equation (III) gives a relationship between time and moisture
content of each component.

Linear sorption isotherms

The simpliﬁed case is when the moisture sorption isotherms of the
components are represented by a linear equation within the water activity range
under consideration:

MA = aA + bx aW (IV)

M3 = a3 + b3 aW (V)

Where aA, a3, bA and be are coefﬁcients if the linear equation.

Derivating
dMA = daW .bA (VI)
dMB = daW . b3 (VII)

Dividing equations (7) and (8) and rearranging the terms:

dMA . be = dMB. bA (VIII)

73

Combining equation (8) with equation (3) and integrating gives:

_ 1 bB M3: dMA
t"'PA [WA+WB—] I - (M ) (IX)
- ’ps A M; awo aw A

 

 

 

 

1 b Mi* dM
tB = [WA —A + WE] I B (X)
P-A-Ps b3 M}, awo "aw (MB)
Where:

MA‘ and MB1 are the initial moisture content of component A and B,

respectively

tA, and t3 represents the time required to achieve the moisture content

MA2 and M32, respectively.

The analytical integration of equations 9 and 10 gives:

 

 

 

 

l
tA= (W .b +w,,.bB)1n[awo aW(M;):| (XI)
Rips awo'aw( MA)
a a (M‘)
t = W .b W .b 1n “’0 W B (X")
B P.A.ps( A A+ B B) [awo: -aw( (M3)]
Where:

aw(MA) and aw(MB) represent the head-space water activity, in equilibrium
with the components’ moisture content. Superscripts 1 and 2 refer respectively

for initial and ﬁnal moisture content conditions.

74

Non-linear sorption isotherm

When the linear equation does not represent accurately the sorption
isotherm, the whole isotherm needs to be considered in the model and a
numerical integration of equation (3) will be necessary.

Assuming that the sorption isotherm equations of components A and B
are described by,

MA = f(aw) (XIII)

M3 = f(aw) (XIV)

Where f(aw) and g(aw) are the sorption equations for component A and B,
respectively.

Considering the inverse functions of the isotherms, aW can be expressed

as a function of the components’ equilibrium moisture content, MA and MB,

respectively:
aw = f‘ (MA) (XV)
aw = 9" (Me) (XVI)

It is assumed that the moisture content between the two products is in

equilibrium and therefore:

MA = fl 9" (M3)] (XVII)
and
Me = g I r‘ (MAM (XVII)

Therefore dMB can be expressed as a function of dMA:

dMB = D dMA (XIX)

75

Where the function D is deﬁned as:

___ dMB = dlglf "(Mull
[KM A) “ dMA dMA (XX)

The expression of dMA as a function of dMB gives:

dMA d "MB
D(MB)EdM = [figd 1x: )1] (XXI)

The function D can be obtained analytically or numerically.
Equation (Ill) rearranged can then be integrated to calculate the shelf life

or to predict the moisture content over storage time.

1 ”A wA + WB.D(MA)

 

 

 

 

t = . dM (xxn)
A P-A-Ps M; awo 'aw (MA) A
t _ I M wB +WA.D(MB) (N
B - P A - _ (M ) a (XXIII)
- ~Ps M13 awo aw B

where:

P = ﬁlm permeability coefﬁcient

I = ﬁlm thickness

A = package surface area available for the moisture transfer

p3 = water vapor pressure at the storage temperature

76

WA, W3 = dry weights of components A and B
dMA, dMB = change in moisture content of component A and B
respectively
awo = external water activity
aw(MA), aw(MB) = head-space water activity, in equilibrium with the
moisture content of component A and B, respectively
MA‘, ME, M31 and M32 = initial and ﬁnal moisture content of component A
and B respectively
tm t3 = time required to component A and B to achieve the moisture
content MAZ, M32 respectively
D(MA), D(MB) = functions of MA ,MB relating the slopes of the
components isotherms at each aw.
Pocas stated also the following assumptions for the model that she
developed:
(1) The shelf life of the mixture depends solely on the moisture content change
of the components
(2) The storage temperature and relative humidity are constant
(3) The amount of water vapor in the package head-space is negligible
compared with the products’ moisture content
(4) Both components of the mixture reach fast equilibrium with the package’s
head space relative humidity
(5) The components do not show hysterisis behavior on moisture sorption

isotherms

77

(6) The transfer of water through the package is always at a steady state
(7) The packaging material controls the rate of water transfer
(8) Moisture is independently bonded to each component according to its

sorption isotherm.

78

APPENDIX B

PACKAGING MATERIALS CHARACTERIZATION

1. Film Thickness

Ten measurements of ﬁlm thickness were performed to verify the value
provided by the manufacturer. The average values are presented below.

LDPE Film: 1.15 i 0.09 mil

HDPE Film: 1.85 i 0.09 mil

2. Materials water vapor transmission rate (g/m2.day) and permeability
(g.miI/m2.day.mmHg) at 23°C. Infrared Sensor Method.
Four ﬂat samples were tested to determine the penneance and
permeability of the ﬁlms. Results are compiled below.
Table B1 — Permeance (g/m2.day ) and Permeability

(g.millm2.day.mmHg) at 23°C for ﬂat LDPE samples.

 

 

 

 

 

 

 

 

Sample Permeance, g/mz.day Permeability, g.millmz.day.mmHg
1 1 .350 8.80E-05
2 1.531 1.02E-04
3 1 .536 . 9.80E-05
4 1.395 9.29E-05
Average 1.453 9.52E-05
Std. Dev. 9.48E-02 6.08E-06

 

 

 

79

 

Table 32 — Permeance (g/m2.day ) and Permeability

(g.miI/m2.day.mmHg) at 23°C for ﬂat HDPE samples.

 

 

 

 

 

 

 

 

Sample Permeance, g/m2.day Permeability, g.miI/mz.day.mmHg
1 1.350 8.80E-O5
2 1.531 1.02E-04
3 1.536 9.80E-05
4 1.395 9.29E-05
Average 1 .453 9.52E-05
Std. Dev. 9.48E-02 6.08E-06

 

 

 

3. Materials water vapor transmission rate (g/m2.day) and permeability

(g.mil/m2.day.mmHg) at 23°C. Gravimetric Method.

Four pouch samples were tested to determine the transmission rate and

permeability of the ﬁlms. The results are compiled in the next page.

80

 

Table B3 - Water Vapor Transmission Rate (g/day) and Permeability

(g.mil/m2.day.mmHg) at 23°C for LDPE pouches.

 

 

 

 

 

 

Sample Transmission Rate, 9/ day Permeability, g.mi|/mz.day.mmHg
1 0.0324 6.15E-05
2 0.0286 5.44E-05
3 0.0370 6.64E-05
4 0.0396 7.13E-05
Average 0.0327 6.34E-05
Std. Dev. 0.0042 6.05E-06

 

 

 

 

 

Table 84 - Water Vapor Transmission Rate (g/day) and Permeability

(g.millm2.day.mmHg) at 23°C for HDPE pouches.

 

 

 

 

 

 

 

 

Sample Permeance, glm7.day Permeability, g.mi|/mz.day.mmHg
1 0.0115 4.15E-05
2 0.0120 4.34E-05
3 0.0121 4.13E—05
4 0.0119 3.87E-05
Average 0.01 1 9 4.20E-05
Std. Dev. 0.0003 1.16E-06

 

 

 

Experimental data for packaging permeance determination by the

gravimetric method.

81

 

 

APPENDIX C

PARAMETER ESTIMATION OF GAB EQUATION

The Guggenheim-Anderson-deBoer (GAB) equation (Eq. C1) was

transformed into quadratic form to easily estimate GAB parameters.

M = CKaw (C1)
W (l-kaw)(1—kaw+Ckaw)

m

 

 

 

 

W CKa 2 2
—'“———“’=1-k +Ck —k ,+k2 -Cl(2
M aw aw a“ aw aw (02)
3w— : i[l—1)aw2+—1—(1—3]aw+ 1 (03)
M Wm C Wm C Wka
Assigning
k 1 1
= — ——1 = l-C C4
a “(C ) Wmc( ) ( )
1 2 1
= — 1—— = — C—2 C5
5 W..[ C] Wmc( ) ( )
— 1 (06)
Y Wka
Eq. C3 is rewritten as:
aw 2
— = ora w + a w+y 07
M r3 < >

Eq. C7 was plotted as aW vs awlM (X vs Y) and from the quadratic

regression the constants a, [3 and 7 were obtained. The value of these

82

constants is used to calculate the GAB constants: C, Wm, and k. The
calculations are presented below.

Substituting Eq C4 into Eq C5 gives

 

 

 

 

 

___a(C-2) (CB)
ﬁ(C-1)
Substituting Eq CB into Eq CS gives
L = _ay (C-2)C (C9)
Wm B (C -1)
Substituting Eq 09 into Eq C5 gives
2 2
t3 = (C -4C +4) (C10)
(-a);' (C -1)
P 2
Assigning: X =
Ga)r
Eq C10 can be rewritten as
c2 — (4+X) c + (4+X) = 0 (C11)
‘3 2
Assigning: 6 =4+X=4+

(-a) 7

Eq. C11 can be solved as:

6:46-46
2

C:

 

This quadratic solution presented gives two mathematical solutions for C,
but the solution of C that gives positive values for all GAB constants is correct.

Parameter Wm and k can be obtained by subsitution of C into Eq CS and C6

83

APPENDIX D

COMPUTER PROGRAM VALIDATION

1. Model Development

The model used to create the computer program was developed by
Pocas (1995). The researcher worked with the Henderson, Chen, Oswin,
Halsey and GAB moisture sorption isotherms for modeling the moisture of two
component food products. The researcher also prepared a DOS computer
program where immediate calculations were done. The model prepared by
Pocas (1995) was discussed in Chapter 2 and is explained in detail in Appendix
A.

A windows-based program was prepared to calculate the shelf life of
two-component food products using the model developed by Pocas (1995) for
linear and non-linear isotherms. In addition, the computer program prepared in

this research has the option to work with a single product.

2. Model Validation

The data used to verify the operational characteristics of the computer
program were taken from Pocas’ (1995) work. The results obtained with the
new computer program were compared with the ones reported by Pocas (1995)

and a difference of :t 1.25% was found. Therefore, it was concluded that the

computer program was accurate in its calculations.

84

The Halsey and GAB equations for cracker and raisin at 20°C,
respectively, included in the literature by Pocas (1995), were used to generate
the data that were entered in the computer program. The data entered to build

the moisture sorption isotherm are presented in the next page.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cracker Raisin
aw M aw M
0.10 0.0510 0.10 0.0260
0.18 0.0600 0.18 0.0466
0.28 0.0700 0.28 0.0712
0.37 0.0800 0.37 0.0964
0.45 0.0900 0.45 0.1222
0.52 0.1000 0.52 0.1489
0.58 0.1100 0.58 0.1765
0.63 0.1200 0.63 0.2050
0.68 0.1300 0.68 0.2344
0.71 0.1400 0.71 0.2645
0.74 0.1500 0.74 0.2953
0.77 0.1600 0.77 0.3265
0.79 0.1700 0.79 0.3582
0.81 0.1800 0.81 0.3901
0.83 0.1900 0.83 0.4222
0.84 0.2000 0.84 0.4543
0.89 0.2500 0.89 0.6123
0.92 0.3000 0.92 0.7597

 

 

 

Table D1 — aw and M (9/9) values used to obtain the cereal and raisin
isotherms at 20°C

The program was run with the same four sets of data presented by
Pocas (1995). The runs were designed to understand how the program can
facilitate the analysis of the components’ weight ratio, storage water activity,
packaging barrier properties and total weight to the packaging area ratio in the
storage stability curves prediction. The conditions used for the computer

simulation are presented in Table D2.

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Run cracker raisin total aw l, mil P, Area,
wt, 9 wt, 9 wt, 9 g.millin2.day.mmHg in2
Set A: To evaluate the inﬂuence of components weight ratio
10 20 30 0.80 0.985 3.81E-05 69.75
15 15 30 0.80 0.985 3.81E-05 69.75
20 10 30 0.80 0.985 3.81E-05 69.75
Set B: To evaluate the inﬂuence of Storage water actvity
15 15 30 0.80 0.985 3.81E-05 69.75
15 15 30 0.75 0.985 3.81E-05 69.75
15 15 30 0.70 0.985 3.81E-05 69.75
Set C: To evaluate the inﬂuence of packaging barrier properties
15 15 30 0.80 0.985 6.35E-05 69.75
15 15 30 0.80 0.985 3.81E-05 69.75
15 15 30 0.80 1.182 3.81E-05 69.75
Set D: To evaluate the inﬂuence of total weight to packaging area ratio
15 15 30 0.80 0.985 3.81E-05 69.75
20 20 40 0.80 0.985 3.81E-05 69.75
3 25 25 50 0.80 0.985 3.81 E-05 77.50

 

 

 

 

 

 

 

 

Table D2 - Conditions used in the computer simulation

The initial moisture content of the cracker and raisin are 0.077 gig and

0.090 g/g respectively and the temperature selected was 20°C. The isotherms

were obtained at the same temperature.

86

 

Figures 01 - D.3 show the moisture content proﬁle generated by the
computer model for the conditions presented in Table D2. Values in Table D2

and Figures 0.1 — 0.3 are equivalent to the ones presented by Pocas (1995).

 

 

 

 

 

 

l 0.30 "T _' f —‘ ' ‘ ‘7
' Run 3 (10 g)
i 0'25 Raisin RU" 2 (15 9)
3, Run 1 (20 g)
E: 0.20 .

3 ’A’ R 3 (20 )
= ‘ Cracker U0

3 o 15 / / g
a - /.g—=‘/"‘" Run1(109)
,9 0.10 _ / / "

o /_, -

2
t 0.05 . _
1 SET A- components weight ratio
? 0.00 , . ,

 

 

0 50 100 150 200 250 300 350 400
1 time, dew

 

 

Figure 0.1 - Moisture content proﬁle for different components weight ratio.

Note: Predicted values using set data A from Table D2.

From Figure 0.1, it is observed that increasing the ratio of the lower
moisture component (Run 3) causes a higher moisture uptake of the mixture.

This information would be useful to study the inﬂuence of mixture formulation in

shelf life.

87

 

 

 

 

 

 

 

0.30
Run 1 (80%) l
0.25 .. Raisin
Run 2 (75%)
‘3 0.20 Run 3 (70%)
C
3 v"
5 0.15 . /;é* Cracker Run 1 (80%)
2’, / Run 2 (75%)
3?; 0.10 - ’ , .5; 5:: =5 "— Run3(70%)
'5
s
. 0-05 SETB-Storage relative humidity
l .
I .
l 0.00 , . T I I I I . l
o 50 100 150 200 250 300 350 400

time, days

i... ._ l

Figure 02 - Moisture content proﬁle for different storage water activities.

Note: Predicted values using set data B from Table 0.2.

From Figure D.2, it is observed that higher relative humidity storage
conditions (Run 1) increase the moisture uptake. Knowing the highest and
lowest expected storage relative humidity, the upper and lower limits of
moisture uptake could be predicted and then the selection of the necessary

package barrier can be made.

88

9
w
o

“‘—l

 

     
   
 
 

 

 

 

 

. . Run 1 (15512)
Raism
0.25 Run 2 (25853)
‘5) Run 3 (31024)
.7 0.20
5
E Cracker Run 1 (15512)
0 0.15 - .
0 Run 2 (25853) l
o
" "‘ Run 3 31024
3?, 0.10 , ( )
n5 1
5 I
0.05 . . ,
SET C - Packaging barrier properties (l/P)
0.00 ‘
0 50 100 150 200 250 300

time, days

 

Figure D.3 - Moisture content proﬁle for different packaging barrier
properties(l/P).

Note: Predicted values using set data C from Table 0.2.

400

From Figure D.3, it is observed that the lower the packaging resistance

to moisture transfer (Run 1); deﬁned as the ration thickness/Permeability (l/P),

the higher the moisture uptake. This information could be used to deﬁne the

lower and the upper limits of packaging barrier properties when selecting ﬁlm

material or ﬁlm thickness.

89

‘ 0.30

 

 

 

 

 

 

0.25 . . ' Run 1 (0.43) .
Raism Run 2 (0.57)

g 0.20 , - '. Run 3 (0.65)
a ‘I
c ’
3 / Run 1 (0.43)
5 0.15 / C k
0 / / '30 9’ Run 2 (0.57)
“I / —‘
5 egg"!!! Run 3 (0.65)
g 0.10 a / / I ’2' a!!! '
E

0.05 -

SET D - Total weight to packaging area ratio (g/sq.in)
0.00 , , , , , . .
0 50 100 150 200 250 300 350 400

5 time, days J'

 

Figjre D.4 - Moisture content proﬁle for different total weight to packaging area
ratio.
Note: Predicted values using set data D from Table D2.

From Figure D.4, it is noticed that increasing the ratio total weight to the
packaging area (Run 3) would reduce moisture pickup of each component for a
selected time.

It is important to mention that the model assumes that the mixed
products are in equilibrium at all times and it also assumes that moisture is
independently bonded to each product because there are no interactions
among the products. The validity of the model assumptions would make the
predictions accurate and the computer program a useful tool for packaging
design and optimization.

The computer program validation was performed with the data presented

in tables D1 and 0.2.

90

MOISTURE SORPTION ISOTHERM DATA FOR THE CEREALS

APPENDIX E

 

 

 

 

 

 

 

 

 

 

 

Point Water Activity Corn Oats Wheat
1 0.053 0.0153 0.0268 0.0293
2 0.112 0.0268 0.0488 0.0388
3 0.251 0.0401 0.0720 0.0548
4 0.330 0.0516 0.0851 0.0673
5 0.478 0.0801 0.1042 0.0954
6 0.615 0.1135 0.1228 0.1171
7 0.760 0.1645 0.1357 0.1420
8 0.808 0.2046 0.1503 0.1654
9 0.878 0.2819 0.1810 0.2166

 

 

 

 

 

Table E.1: Equilibrium Moisture Content (Me, gig) of Corn, Oats and

Wheat at Nine Different Water Activities.

91

 

APPENDIX F

MOISTURE PROFILE FOR THE EXPERIMENTAL AND PREDICTED CERAL
MIXTURES

Table F1 - Experimental and Predicted Moisture Content (%) of 33l67 corn-wheat samples
for validation with HDPE (Each table value is the average of two determinations)

 

Day Ex mental Predicted % Difference
Corn Corn Wheat
2.25 .38 2.25 .38 0
2.33 4.43 2. 4. 1
2.1 4.38 2.40 4.53 3
4.56 2.45 4.58 1
2.49 4.68 2.50 4.63 1
2.57 4.85 2.55 4.68
2.58 4.79 2.60 4.78 0
60 4.85 2. 4.83 0
. 3. . 8 1
. 3. .
.33 . .80 .83
3. . 4.10 6.1
3. . 4.40 6.38
3.74 . 4.70 6.58
4.24 . 4. 6.83
4.58 . 5.20 6.98
Corn Wheat
Correlation Coefﬁcient 0.9821 0.9810
Signiﬁcance <0.0001 <0.0001

Table F2 - Experimental and Predicted Moisture Content (%) of 50l50 corn-wheat samples
for validation with HDPE (Each table value is the average of two determinations)

 

Day Ex mental Predicted % Difference
Corn Wheat Corn
2.67 4. 1 2.67 .71 0 0
2.80 4. 2. 4.8 1
2.87 4.98 2.82 4.86 2 2
91 4. 2. 4.91 1 1
.18 .96
3.10 . .
3. . 3. .06
3.34 5.40 3.12 5.16
3.68 5. 3. .51
3. 4 5. 3.87 .8
4.20 6.27 4.22 6.11
4.34 6.41 4.52 6.41
4. 6. 4.82 6.61
4.68 6.89 .07 6.86
4.89 6. 5 7.01
.20 .22 .52 .21
Corn Wheat
Correlation Coefﬁcient 0.9913 0.9895
Significance <0.0001 <0.0001

93

Table F3 - Experimental and Predicted Moisture Content (%) of 67/33 corn-wheat samples

for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Corn Wheat Corn Wheat Corn Wheat

0 2.77 4.49 2.77 4.49 0 0
1 2.93 4.63 2.87 4.59 2 1
2 2.91 4.74 2.92 4.64 0 2
3 3.10 4.68 2.97 4.69 4 0
4 3.20 4.76 3.02 4.79 6 1
5 3.32 4.81 3.12 4.84 6 1
6 3.34 4.95 3.17 4.89 5 1
7 3.40 5.08 3.22 4.94 5 3
14 3.58 5.30 3.62 5.34 1 1
21 3.87 5.60 3.97 5.69 2 2
28 4.18 5.74 4.32 5.99 3 4
35 4.39 6.02 4.62 6.29 5 5
42 4.48 6.11 4.87 6.54 9 7
49 4.68 6.41 5.12 6.74 9 5
56 4.93 6.35 5.37 6.94 9 9
63 5.37 6.56 5.57 7.14 4 9

Corn Wheat

Correlation Coefﬁcient 0.9912 0.9942

Signiﬁcance <0.0001 <0.0001

Table F4 - Experimental and Predicted Moisture Content (%) of 33l67 corn-oats samples

for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Cor_r_I Oats Corn Oats Corn Oats
0 2.67 10.50
1 3.11 8.61
2 3.59 8.23 3.59 8.23 0 0
3 3.92 8.33 3.64 8.28 7 1
4 4.13 8.68 3.69 8.33 11 4
5 4.19 8.69 3.74 8.33 11 4
6 4.27 8.88 3.79 8.38 11 6
7 4.36 9.04 3.84 8.43 12 7
14 4.52 9.16 4.14 8.58 8 6
21 4.67 9.33 4.44 8.78 5 6
28 4.90 9.58 4.69 8.93 4 7
35 5.18 9.77 4.94 9.08 5 L
42 5.46 9.92 5.14 9.18 6 7
49 5.77 10.04 5.39 9.33 7 7
56 5.95 10.31 5.59 9.43 6 9
63 6.44 10.45 5.79 9.53 10 9
Corn Oats
Correlation Coefﬁcient 0.9827 0.9812
Signiﬁcance <0.0001 <0.0001

94

 

 

 

 

Table F5 - Experimental and Predicted Moisture Content (%) of 50/50 corn-oats samples
for validation with HDPE (Each table value is the average of two determinations)

 

Ex mental Predicted % Difference
Corn Oats Corn Oats Corn Oats
0 2.77 10.50
1 3.31 8.08
2 3.28 8.09
3 3.43 8.32
4 3.56 8.04
5 3.65 .98
6 3.65 8

7 3.76 .92 3.76 .92 0

14 3.80 8.20 4.11 8.1 8

21 3.98 8. 4.41 .42 11

28 4.77 8.51 4.66 8.62 2

4.71 .59 4.91 8. 4

5.21 8. 5.16 8.92 1

5.40 8.88 5.36 9. 1

.63 9.06 5.56 9.1 1

5. 9 .66 9 3

Corn Oats
Correlation Coefﬁcient 0.9759 0.9884
Signiﬁcance <0.0001 <0.0001

Table F6 - Experimental and Predicted Moisture Content (%) of 67l33 corn-oats samples
for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Corn Oats Corn Oats Corn Oats

0 2.77 10.50

1 3.28 6.70

2 3.32 5.71 3.32 5.71 0 0

3 3.36 6.15 3.42 5.81 2 6

4 3.41 6.48 3.47 5.86 2 10

5 3.45 6.69 3.47 5.96 1 11

6 3.49 6.68 3.52 6.01 1 10

7 3.60 7.02 3.57 6.11 1 13
14 3.96 7.04 3.92 6.51 1 7
21 3.99 7.20 4.22 6.91 6 4
28 4.06 7.58 4.52 7.26 11 4
35 4.43 7.42 4.77 7.61 8 3
42 4.66 7.77 5.02 7.86 8 1
49 5.32 8.22 5.22 8.11 2 1
56 5.22 7.75 5.47 8.36 5 8
63 5.66 7.92 5.62 8.51 1 7

Corn Oats
Correlation Coefﬁcient 0.9774 0.9169
Signiﬁcance <0.0001 <0.0001

95

Table F7 - Experimental and Predicted Moisture Content (%) of 33l67 oats-wheat samples

for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Oats Wheat Oats Wheat Oats Wheat
0 10.62 4.49
1 7.35 5.46

2 6.39 5.52 6.39 5.52 0 0
3 6.90 5.58 6.49 5.57 6 0
4 6.88 5.77 6.54 5.62 5 3
5 6.86 5.82 6.59 5.67 4 2
6 7.03 5.75 6.64 5.72 6 1
7 7.02 5.80 6.69 5.77 5 1
14 7.35 6.11 7.09 6.07 3 1
21 7.50 6.51 7.44 6.32 1 3
28 7.62 6.84 7.74 6.57 2 4
35 7.80 7.10 7.99 6.77 2 5
42 7.83 7.36 8.24 6.97 5 5
49 7.98 7.71 8.44 7.17 6 7
56 8.15 7.85 8.64 7.32 6 7
63 8.34 8.10 8.84 7.47 6 8

Oats Wheat

Correlation Coefﬁcient 0.9756 0.9975

Signiﬁcance <0.0001 <0.0001

Table F8 - Experimental and Predicted Moisture Content (%) of 50l50 oats-wheat samples

for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Oats Wheat Oats Wheat Oats Wheat
0 10.62 4.60
1 8.38 6.52
2 8.11 6.46
3 7.85 6.54 7.85 6.54 0 0
4 8.19 6.52 7.90 6.59 4 1
5 8.04 6.56 7.95 6.64 1 1
6 7.95 6.60 8.00 6.64 1 1
7 7.99 6.56 8.05 6.69 1 2
14 8.37 6.74 8.30 6.89 1 2
21 8.74 6.88 8.50 7.09 3 3
28 8.83 6.95 8.70 7.29 1 5
35 9.05 7.28 8.85 7.44 2 2
42 9.17 7.67 9.05 7.59 1 1
49 9.25 7.79 9.15 7.74 1 1
56 9.35 7.91 9.30 7.84 1 1
63 9.59 8.26 9.40 7.99 2 3
Oats Wheat
Correlation Coefﬁcient 0.9857 0.9751
Signiﬁcance <0.0001 <0.0001

96

 

 

Table F9 - Experimental and Predicted Moisture Content (%) of 67/33 oats-wheat samples

for validation with HDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Oats Wheat Oats Wheat Oats Wheat
0 10.62 4.49
1 9.13 6.32

2 8.53 6.41 8.53 6.41 0 0
3 8.85 6.57 8.58 6.46 3 2
4 8.81 6.65 8.63 6.51 2 2
5 9.13 6.55 8.63 6.51 5 1
6 9.07 6.58 8.68 6.56 4 0
7 9.39 6.88 8.68 6.61 8 4
14 9.80 7.06 8.88 6.81 9 4
21 9.55 7.11 9.03 7.01 5 1
28 9.66 7.14 9.13 7.21 5 1
35 9.82 7.24 9.28 7.36 6 2
42 10.07 7.59 9.38 7.51 7 1
49 10.26 7.83 9.48 7.66 8 2
56 10.21 7.80 9.58 7.76 6 1
63 10.66 8.04 9.68 7.91 9 2

Oats Wheat

Correlation Coefﬁcient 0.9472 0.9793

Signiﬁcance <0.0001 <0.0001

97

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Table F11 - Experimental and Predicted Moisture Content (%) of 50/50 corn-wheat samples
for validation with LDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Corn Wheat Corn Wheat Corn Wheat

0 3.43 5.70 3.43 5.70 0 0
1 3.49 5.79 3.63 5.85 4 1
2 3.63 5.88 3.78 6.00 4 2
3 3.80 6.06 3.93 6.10 3 1
4 3.89 ' 6.26 4.08 6.20 5 1
5 3.98 6.40 4.18 6.35 5 1
6 4.07 6.54 4.33 6.45 6 1
7 4.17 6.66 4.48 6.55 8 2
14 5.19 7.51 5.23 7.15 1 5
21 5.57 7.66 5.83 7.55 5 1
28 6.21 8.24 6.28 7.90 1 4
35 6.36 8.24 6.63 8.15 4 1
42 6.79 8.38 6.88 8.35 1 0
49 7.10 8.58 7.13 8.55 0 0
56 7.32 9.05 7.28 8.65 0 4
63 7.68 9.12 7.43 8.75 3 4

Corn Wheat

Correlation Coefficient 0.9966 0.9945

Signiﬁcance <0.0001 <0.0001

Table F 12 - Experimental and Predicted Moisture Content (%) of 50/50 corn-oats samples
for validation with LDPE (Each table value is the average of two determinations)

 

Day % Difference
Corn Oats Corn Oats Corn Oats
0 3.31 10.86
1 4.50 9.59
2 4.82 9.49
3 4.97 9.42
4 5.03 9.36
5 5.08 9.29
6 5.13 9.19
7 5.16 9.06 5.16 9.06 0 0
14 6.09 9.76 5.76 9.41 5 4
21 6.28 9.84 6.21 9.66 1 2
28 6.77 10.03 6.61 9.86 2 2
35 7.21 10.20 6.86 10.01 5 2
42 7.45 10.41 7.11 10.11 5 3
49 7.74 10.55 7.26 10.21 6 3
56 7.95 10.52 7.41 10.26 7 3
63 8.15 10.58 7.56 10.31 7 3
Corn Oats
Correlation Coefficient 0.9934 0.9845
Significance <0.0001 <0.0001

99

Table F13 - Experimental and Predicted Moisture Content (%) of 50/50 oats-wheat samples
for validation with LDPE (Each table value is the average of two determinations)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Day Experimental Predicted % Difference
Oats Wheat Oats Wheat Corn Oats
0 10.74 5.04

1 9.27 7.21 9.27 7.21 0 0
2 9.53 7.34 9.32 7.31 2 0
3 9.61 7.42 9.37 7.36 3 1
4 9.52 7.39 9.42 7.46 1 1
5 9.64 7.67 9.47 7.51 2 2
6 9.70 7.71 9.52 7.56 2 2
7 9.58 7.44 9.57 7.61 0 2
14 9.95 8.26 9.77 7.96 2 4
21 10.13 8.53 9.97 8.26 2 3
28 10.39 8.98 10.07 8.46 3 6
35 10.50 9.11 10.17 8.61 3 5
42 10.56 9.35 10.27 8.76 3 6
49 10.42 9.31 10.32 8.81 1 5
56 10.62 9.50 10.37 8.91 2 6
63 10.66 9.68 10.42 8.96 2 7

Oats Wheat

Correlation Coefficient 0.9838 0.9940

Significance <0.0001 <0.0001

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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101

APPENDIX G

DETAILED DATA OF VALIDATION EXPERIMENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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N000.00 0000.00 0000.00 0000.00 0000.00 0000.00 00

0000.00 0000.00 000?: 0N00.00 0000.00 0000.00 0

N000.00 0000.00 0000.00 0000.00 00N0.00 0000.00 0

000000 0000.00 0000.I00 000E; 0000.00 0000.00 0

0000.00 0000.00 0000.00 0000.00 0000.00 0

N000.00 0000.00 0000.00 0N0.000 NO0N.00 0

0000.00 0000.00 0000.00 NO0N.00 0

00NN.00 000N.00 0W00.00 0N00.00 0

0NON.00 00NN.00 00N0.00 N

0000.00 00N0.00 0000.00 0

00 0 0 0 0 0 N 0 canon.

>00 >00 >00 >00 >00 >00 >00 >00 + 00.0 00002. canon.

 

 

137

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N000.00 0000.00 00N0.00 000N.00 NNON.00 000N.00 0000.00 N0

000N.00 0000.00 0000.00 N000.00 0000.00 0000.00 0000.00 00

0000.00 0F000.00 0000.00 000N.00 000N.00 0NON.00 0000.00 00

01000.00 0000.00 0000.00 00F00.00 0000.00 0000.00 0000.00 0N

0000.00 0N00.00 0000.00 N000.00 0000.00 N000.00 0N

0000.00 0000.00 000r0.00 0N00.00 000N.00 000N.00 0N

0000.00 0000.00 0000.00 0000.00 0000.00 0N

00NN.00 0000.00 N000.00 0000.00 00N0.00 0N

00N0.00 00.00.00 00N0.00 0000.00 0N

0000.00 0000.00 N0F00.00 0N00.00 0N

0000.00 0000.00 0N00.00 NN

NON0.¢ 0N00.00 0N00.00 0N

0.0r00.00 NNON.00 0N

0000.00 00N0.00 00

0|00N.00 00

N000.00 00

00

00

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00

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0

00 00 00 N0 00 0N 0N

>00 >00 >00 >00 >00 >00 >00 00:00

8.02.08 - So 2000

 

138

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