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thesis entitled

MODELING THE MOISTURE TRANSFER OF TWO-COMPONENT
FOOD PRODUCTS IN A FLEXIBLE PACKAGE

presented by

MARIA DE FATIMA FILIPE POCAS

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MODELING THE MOISTURE TRANSFER OF
TWO-COMPONENT FOOD PRODUCTS IN A FLEXIBLE PACKAGE

By

Maria de Fatima Filipe Poeas

A THESIS

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

MASTER OF SCIENCE

School of Packaging

1995

ABSTRACT
MODELING THE MOISTURE TRANSFER OF
TWO-COMPONENT FOOD PRODUCTS IN A FLEXIBLE PACKAGE
By
Maria de Fatima Filipe Pocas

Most deterioration reactions of foods are greatly affected by the food's moisture content. To
prevent spoilage of dry products a packaging system able to provide an adequate protection
against moisture uptake is necessary. Mathematical modeling is a useful technique for
shelf-er prediction at the packaging development and optimization stages. The application
of this technique to two-component foods was the main objective of this work. A
mathematical model correlating the products moisture sorption characteristics, the
packaging properties and the storage conditions was developed and a computer program
was prepared based on the model. The program selects the isotherm equation that best ﬁts
the experimental isotherms (Henderson, Chen, Oswin, Halsey or GAB) and calculates the
change in components' moisture content or the mixture shelf-life. Experimental validation
with breakfast cereal and powder chocolate packaged in two different packaging materials
was can-ied out. The model tends to overestimate the moisture content of the components,
in particular for the cereal and for longer storage periods. Deviations seem to be dependent
on the packaging material barrier, which affects the relative tendency of the components to

absorb moisture simultaneously.

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ACKNOWLEDGMENTS

I would like to thank Dr. Ruben Hernandez for providing the research topic and for advice,
support and encouragement. I specially thank him all the nice discussions. Special thanks
to Dr. Fernanda Oliveira for her guidance and for being my friend.
Give thanks to:
Dr. Theron Downes for the encouragement in following my way;
Dr. Perry Ng (Department of Food Science and Human Nutrition)
Staff from CEPA and CEQA (Escola Superior de Biotecnologia) for the support and
help on laboratory experiments;
Paulo Ramos from CIEI (Escola Superior de Biotecnologia) for his help on
programming;
Dr. Jovita Oliveira (Universidade do Minho) for her help on materials characterization;
Fundacao Luso-Americana para o Desenvolvimento (Portuguese-American
Foundation for Development) and Escola Superior de Biotecnologia da Universidade
Catdlica Portuguesa (Biotechnology College from Portuguese Catholic University), for
the ﬁnancial support.
Prof. Augusto Medina (Director of Escola Superior de Biotecnologia)
Dr. Bruce Hart (Director of School of Packaging)

PREFACE

This thesis is divided into three chapters. In Chapter I, a literature review on relevant topics
for the main subject is presented. Chapter H (Modeling the moisture content of two-
component food products in a ﬂexible package. Model development) and Chapter III
(Modeling the moisture content of two-component food products in a ﬂexible package.
Model validation) were prepared in article format. A Reference section is presented at the

end of each chapter.

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS
INTRODUCTION
CHAPTER I - Literature Review
Introduction
1. Review on Food Moisture Sorption Isotherm Equations
2. Review on Multicomponent Food Isotherm Equations
3. Review on Shelf-Life Models
Conclusions
References for Literature Review
CHAPTER II - Modeling the Moisture Content of Two-Component Food
Products in a Package. Model Development.
Abstract
Introduction
Mathematical Model Development
' Materials and Methods
Results and Discussion
Conclusions

References

Page

19
20
21
23
32

38
38

5‘"

CHAPTER III — Modeling the Moisture Content of Two-Component Food
Products in a Package. Model Validation.

Abstract

Introduction

Materials and Methods

Results and Discussion

Conclusions

References
APPENDIX A - Equations of Moisture Sorption Isotherms
APPENDIX B - Description of the Computer Program
APPENDIX C - Computer Simulated Results
APPENDIX D - Packaging Materials Characterization
APPENDIX E - Moisture Sorption Isotherms Data
APPENDIX F - Detailed Data of Validation Experiments

42
43

47
50
73
74
76
83
110
114
120
122

LIST OF TABLES

Table 1 - Moisture sorption isotherms equations used in the computer program
Table 2 - Conditions used in the computer simulation

Table 3 - Henderson equations ﬁtting experimental sorption data

Table 4 - Chen equations ﬁtting experimental sorption data

Table 5 - Oswin equations ﬁtting experimental sorption data

Table 6 - Halsey equations ﬁtting experimental sorption data

Table 7 - GAB equations ﬁtting experimental sorption data

Table 8 - Packaging materials permeance (g/m2 day mmHg) at 25° C

Table 9 - Validation l. Cereal and powder chocolate dry weights

Table 10 - Experimental moisture content (g/g) of components
as a function of storage time (days). Validation 1

Table 11 - Values of components moisture content (g/g) as a function of
storage time (days) predicted by the computer model at experiment 1 conditions

Table 12 - Validation 2. Cereal and powder chocolate dry weights

Table 13 - Experimental moisture content (g/ g) of components
as a function of storage time (days). Validation 2

Table 14 - Values of components moisture content (g/g) as a function of
storage time (days) predicted by the computer model at experiment 2 conditions

Page

32
33
55
55
56
56
57

58

61

68

68

68

Table C.l - Components moisture content as a function of time, for different
components weight ratio. Simulated results using set of data A from Table 2

Table C.2 - Components moisture content as a function of time, for different
storage water activity. Simulated results using set of data B from Table 2

Table C.3 - Components moisture content as a function of time, for different
packaging barrier properties. Simulated results using set of data C from Table 2

Table C.4 - Components moisture content as a function of time, for different total
weight to packaging area ratio. Simulated results using set of data D from Table 2

Table D.1 - Materials water vapor transmission rate (g/m2 day) at 25°C

Table D2 - Experimental data for packaging permeance determination
by the gravimetric method

Table D.3 - Materials water vapor transmission rate (g/m2 day) at 25°C.
Gravimetric method

Table E.l - Experimental moisture sorption isotherm of cereals, at 25° C
Table E.2 - Experimental moisture sorption isotherm of powder chocolate at 25° C
Table E.3 - Experimental moisture sorption isotherm of raisins, at 25° C

Table F.l - Initial weight of components and pouches weight over time
for experiment 1

Table F.2 - Initial weight of components and pouches weight over time
for experiment 2

110

111

112

113

114

116

117

120

120

121

122

126

LIST OF FIGURES

Figure l - Flow chart of the program sub-routine for shelf-life calculation

Figure 2 - Components moisture content as a function of time, for different
components weight ratio (runs 1, 2 and 3). Simulated results using
set of data A from Table 2

Figure 3 - Components moisture content as a function of time, for different
storage water activities (runs 1, 2 and 3). Simulated results using
set of data B from Table 2

Figure 4 - Components moisture content as a function of time, for different
packaging barrier properties (runs 1, 2 and 3). Simulated results using
set of data C from Table 2

Figure 5 - Components moisture content as a function of time, for different
total weight to packaging area ratio (runs 1. 2 and 3). Simulated results
using set of data D from Table 2

Figure 6 - Moisture adsorption and desorption isotherms of cereals at 25° C

Page

30

35

36

37

51

Figure 7 - Moisture adsorption and desorption isotherms of powder chocolate at 25° C 52

Figure 8 - Moisture adsorption and desorption isotherms of raisins at 25° C

Figure 9 - Validation 1. Experimental and calculated values of moisture
content for single packaged components

Figure 10 - Validation 1. Experimental and calculated values of moisture
content for the mixture 33/67

Figure 11 — Validation 1. Experimental and calculated values of moisture
content for the mixture 50/50

53

62

63

Figure 12 - Validation 1. Experimental and calculated values of moisture
content for the mixture 67/33

Figure 13 - Validation 2. Experimental and calculated values of moisture
content for single packaged components

Figure 14 - Validation 2. Experimental and calculated values of moisture
content for the mixture 50/50

Figure 15 - Powder chocolate moisture content vs. cereals moisture content.
Values from isotherm (individual sorption behavior) and values from

validation experiments (mixture sorption behavior)

Figure D.1 - Pouches with desiccant weight gain over time for packaging
permeance determination by the gravimetric method

Figure D.2 - Empty pouches weight gain over time for packaging
permeance determination by the gravimetric method

Figure D.3 - OPP ﬁlm observed at microsc0pe with phase contrast (x560)

Figure D.4 - PE/barrier film observed at microscope with phase contrast (x560)

65

69

70

72

115

116

118

119

LIST OF SYMBOLS

A - packaging surface area

awo - external water activity

aw - internal water activity

A0, A1, A2 - parameters from non-linear moisture isotherms

b - slope of the linear moisture isotherms

EMC - equilibrium moisture content (dry basis)

IMC - initial moisture content (dry basis)

IR - infra red

I - film thickness

L - dimensionless number (ratio between moisture permeance in the food to the permeance
in the packaging material)

Mi - moisture content of producti (dry basis)

Mmix — moisture content of the mixture (dry basis)

OPP - oriented polypropylene

PE - polyethylene

PHbanier - polyethylene coextruded with a barrier material

P - ﬁlm permeability coefﬁcient

ps - water vapor saturation pressure

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

RH - relative humidity

R - relative percent root mean square of the difference between the experimental and
calculated values of moisture content

S - root mean square of the difference between the experimental and calculated values of
moisture content

t - time

U - average of relative percent difference between the experimental and calculated values of
moisture content

Wi - dry weight of component i

Yf - ﬁnal wet weight

Yi - initial wet weight

2 - mixture wet weight

INTRODUCTION

The control of moisture gain or loss during storage of packaged products is of prime
importance in the food industry for safety, marketing, economic and regulatory reasons.
Particularly for dry foods, the packaging system should be designed to provide protection
against moisture uptake. Shelf-life determination is required to develop and optimize the
packaging system. Mathematical modeling is useful for estimating shelf-life by reducing

the time and cost of experimental shelf-er determination.

The change in societies' life—styles has led to great developments in food products
processing and preservation, impelled by consumer demands for reduced time and effort
for meals' preparation. An increasing number of combined or multicomponent food
products is now marketed. Additionally, concern with environment protection and
economic constrains have led to a generalized trend in reducing packaging materials and
avoiding over-packaging without reducing products' protection or packaging user-

ﬁiendliness.

In moisture-sensitive multicomponent foods, moisture is transferred from products having
higher water activity to those with lower water activity. At equilibrium, all the products will
have the same water activity and dry products, such as breakfast cereal, may loose their
desirable crispness while semi-moist components, such as dried fruits, may dry out to

moisture content levels lower than the acceptable values.

In a moisture-permeable package, there is a moisture transfer between the food product and
the external environment. The rate of moisture transfer is governed by the difference
between the water vapor pressure in the package head-space and the water vapor pressure
in the environment. If the diffusion of moisture within the food product is fast compared to
the diffusion across the packaging banier, the food product reaches equilibrium with the
head-space vapor pressure and the product's moisture content may be described by its

isotherm.

Shelf-life modeling of single products has been reported. However, for multicomponent
foods, studies have 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. Nevertheless, shelf-life studies have been reported using a linear

sorption isotherm equation or equations with limited range of water activity.

The development of a more general mathematical model to predict the moisture change
over storage time and the shelf-life of two-component foods was the main goal of this
research. A computer program to perform the model calculations was prepared and
experimental validation was carried out. The model takes into consideration the whole
isotherm and not only a linear part of it: the Henderson, Chen, Oswin, Halsey and GAB
equations may be selected for the shelf-life calculations. Experimental validation of the
model was performed with mixtures of breakfast cereal and powder chocolate packaged

into different materials.

CHAPTER I

LITERATURE REVIEW

Introduction

Moisture content and water activity are critical parameters affecting the shelf life of most
foods: textural quality, chemical and biochemical reactions and microbial growth rates are

greatly affected by those parameters.

Water activity, describing the availability of water to play a role on physical, chemical and
biochemical reactions, has been used to explain the inﬂuence of moisture on reaction rates.
Recently, the glass transition theory from polymer science, has been introduced on food
preservation, particularly for intermediate and high moisture foods (Nelson and Labuza,
1994; Chirife and Pilar Buera, 1994). The relation between glass transition temperature and
food stability has been seen with increasing interest to help understanding the inﬂuence of

water on reactions of food deterioration or spoilage.

Moisture content and equilibrium water activity of a food product are related to each other
by the food sorption isotherm. Several equations have been used to mathematically
describe sorption data of different groups of food products. A review of those equations is
presented in this Chapter. The equations are listed in Appendix A. A review on the work
devoted to the prediction of moisture sorption behavior of mixed or multicomponent

products from individual component's behavior is also presented in this Chapter.

The control of moisture uptake or loss during storage is one of the major protection
functions of the food package. Fast and reliable methods for shelf life prediction are of
great interest as a tool for packaging development and optimization. Mathematical models
correlating the characteristics of the product, the package properties and the environmental

conditions are less time consuming and have lower cost than other techniques of shelf-life

determination. A review on shelf-life models developed for products, whose shelf-life may

be regarded as solely dependent on moisture content, is also presented.

1. Review on Food Moisture Sorption Isotherm Equations

Water binding to food products takes place by the following mechanisms: (i) adsorption as
a monolayer to speciﬁc sites by molecular forces, (ii) multilayer absorption consisting of
water molecules hydrogen bonded and (iii) absorption with free water in the interstitial
pores. These mechanisms correspond to different ranges of equilibrium water activity
(aw). Monolayer adsorption corresponds to aw up to ca. 0.3, at which most deterioration
reactions have a minimum rate. The second mechanism corresponds to the medium range
of aw in the sorption isotherm that is often a straight line in this range. At high aw, free

water is capable of acting as a solvent and microbial growth may occur.

Most foods' sorption isotherms show hysteresis behavior, i.e., the moisture content is
lower on equilibrium by adsorption than by desorption. This has important implications
with respect to food stability, since foods adjusted to the desired aw by desorption rather

than by adsorption, may deteriorate more rapidly because of their higher moistrrre content.

A large number of equations have been proposed to describe the moisture sorption
behavior of foods. Some are based on theoretical principles and some are proposed due to
its ﬁtting capability to experimental data. The models can be classiﬁed into kinetic models
based on a molecular monolayer of water, kinetic models based on multilayer sorption and
a condensed ﬁlm, models imported from the polymer literature and empirical models

(Peleg, 1993).

Chirife and Iglesias (1978) reviewed the equations existing in the literature and compiled
twenty-three equations, discussing its origin, range of applicability and use. Some of these
equations were mathematically equivalent and some were limited to a speciﬁc range of aw

or type of foods.

Boquet et al. (1978) and Boquet er al. (1979) evaluated equations with two and three
parameters for ﬁtting experimental data of moisture sorption of fruits, meats, milk
products, proteins, starchy foods and vegetables. The authors studied the following two-
parameter equations: Bradley, Caurie, Halsey, Henderson, Iglesias and Chirife, Kuhn,
Mizrahi and Oswin equations. The Halsey and the Oswin models were appointed as the
more versatile ones (Boquet et al., 1978). The three-parameter equations studied were the
Brunauer-Emmet—Teller (BET), Chen, Hailwood and Horrobin and Young and Nelson
equations. The Hailwood and Horrobin equation, which is mathematically equivalent to the
Guggenheirn-Anderson-de Boer (GAB) equation, was considered very versatile (Boquet et
al., 1979). It was also noted that some of the simpler two-parameter equations give, in
some cases, ﬁts of comparable or even better accuracy than some of the three-parameter

equations, pointing out that the use of a third-parameter may not be always worthwhile.

Lomauro et al. (1985a) and Lomauro er al. (1985b) compared the accuracy of the Halsey,
Oswin, Iglesias and Chirife equations (two parameters) and the GAB equation (three
parameters) to describe moisture sorption of several types of foods (fruits, vegetables and
meat products, milk, coffee, tea, nuts, oilseeds, spices and starchy foods). They concluded
that the GAB equation gives a very good ﬁt over a wide range of aw (up to 0.9), for most
food isotherms exhibiting a sigmoid shape curve. The equation also gives a better
evaluation of the amount of water tightly bound by the primary sorption sites (Bizot,
1983), which is related to the physical and chemical deterioration in dehydrated foods
(Chirife and Iglesias, 1978).

Saravacos et al. (1986) used the D'Arcy-Watt equation (ﬁve parameters) to ﬁt experimental
data of raisin's isotherms at various temperatures. The best ﬁt over a wide range of aw (0.1
- 0.9) was obtained with the ﬁve-parameter D'Arcy-Watt equation as compared to the

Halsey and GAB equations.

An empirical double power law four-parameter equation was proposed by Peleg (1993).
Its ﬁtting capabilities to sorption data of different food products, including raisin, were
compared with the GAB equation. Better results were obtained with the double power law

equation than with the GAB.

The criteria commonly followed to evaluate the goodness of ﬁt of the experimental data, is
the average of relative percent difference between the experimental and calculated values of

moisture content (U ). expressed as

n . .
magenta <1)

where Mi is the experimental moisture content, Mi* is the calculated and n is the number

of experimental data points.

Boquet et al. (1978) suggested the use of the root mean square of the deviations (S),

I n 2
S = 91-20% ‘ Mi*) (2)
l

to compare the ﬁtting abilities of the different equations when applied to the same

expressed as

experimental data.

The relative percent root mean square (R) has also been used (Bizot, 1983), expressed as

n
_ I ._ .,
R_q/n21:|M—W‘flml x100 (3)

which combines both concepts described above.

A list of the equations to describe the isotherms referred to above is presented in the

Appendix A.

2. Review on Multicomponent Food Isotherms Equations

In packages of multicomponent food products, a transfer of moisture occurs not only
between the products and the environment, but also between the components. At
equilibrium, all components will have the same aw and the ﬁnal moisture content of each
component will inﬂuence the quality and shelf-life of the mixed product (Hong et a1, 1986;
Gal, 1983; Labuza, 1984). The prediction of equilibrium aw is therefore very important

when formulating a moisture sensitive multicomponent food.

The prediction of water sorption behavior of a mixture from the individual components has
been studied by several authors: Iglesias et al . (1980), Chinachoti and Steinberg (1985),
Chinachoti and Steinberg (1988), Leiras and Iglesias (1991), Lang and Steinberg (1980),
Lang and Steinberg (1981), Nieto and Toledo (1989) and Lang et al. (1981). Water is
assumed to be independently bonded to each product as described by equation (4):

2 wiMi

“”37

(4)

where Mmix is the moisture content of the mixture, Mi is the moisture content of product i

before mixing and Wi is the dry weight of component i.

Interactions between the mixture components may result in either a decreased or an
increased water sorption by the mixture as compared to the moisture content predicted by
equation (4), particularly in mixtures prepared by any method other than by simple

physical mixing, such as wet mixing followed by freeze-drying.

The predicted values of moisture content of mixtures of protein and carbohydrates were
almost always higher than the measured ones (Iglesias et al., 1980), but mixtures of
sucrose-protein sorbed more water than the calculated (Chinachoti and Steinberg, 1988). In
both cases, mixtures were obtained by freeze-dehydration of water solutions or

suspensions of the components.

Solubilization of components such as salt and Sugar, may also yield to deviations from the
predicted behavior, as found in cake mixes, specially at high aw where experimental
moisture contents were greater than the predicted (Leiras and Iglesias, 1991). Interactions
involving hydrogen bonds between the components competing with hydrogen bonds with
water may explain the lower sorption of mixtures of sodium chloride and starch that
showed a decreased water sorption at aw above 0.75 as compared to the expected values

obtained from the mass balance (Chinachoti and Steinberg, 1985).

Mixtures of starch, casein, sugar, salt, propylene glycol and ground beef in binary and
ternary combinations prepared by hand mixing, have shown a good agreement between the
predicted values of moisture content calculated by equation (4) and the measured values

(Lang and Steinberg, 1980).

10

In an attempt to include interaction parameters Nieto and Toledo (1989) applied an
empirical approach using a factorial design of 4x3 levels of combinations of NaCl, non-fat
dry milk and lard added to minced ﬁsh to produce a ﬁsh sausage. Although with good
agreement between the experimental and predicted values, the regression equation was

limited to the factors and respective levels used in the validation experiment.

Lang et al. (1981) followed a thermodynamic approach, using an enthalpy balance, rather
than a mass balance described by equation (4). The hypothesis tested was that the total
partial enthalpy change for the water of a mixture is equal to the sum of the partial enthalpy
changes for the water of the individual ingredients at the same aw. This was tested for

starch, casein, sucrose and starch-casein and starch-sucrose combinations.

Salwin and Slawson (1959) derived an equation to calculate the equilibrium relative
humidity of a dehydrated mixture from the dry weight of the components, the initial
relative humidity for each component and the slopes of the isotherms. Linear isotherms
between the initial and the equilibrium relative humidity were assumed. They found good
agreement between the calculated and the experimental ﬁnal moisture content, although
they were working over a narrow range of relative humidity. This is appointed as a major
drawback, because at higher relative humidity, the normal s-shaped isotherms show more
curvature and therefore the assumption of linear isotherm is no longer valid (Lang and

Steinberg, 1981).

Iglesias et al. (1979) assumed the concept of additivity of the components' isotherms,
calculating a mixture isotherm from the weight percentage of each component times the
amount it would sorb alone. The merit lies on the use of a non-linear isotherm. The BET

equation is used with applicability in the range of aw from 0.05 to 0.40.

11

The estimation of equilibrium aw of mixtures may, according to the models used, raise
calculation difﬁculties. Peleg and Normand (1992) developed a method for aw estimation
using the easy-to-use mathematical software "MathCAD" package. The method is also
based on a combined weighted isotherm, and determines the mixture aw as the root of the
relation Mmix - 2 Mi = 0, where Mmix is the mixture moisture content (a function of aw)
and Mi is the initial moisture content of component i. The method was developed for a
closed system (there is no moisture exchange with the environment) and allows for each

component to have a different sorpu'on isotherm equation.

3. Review on Shelf-Life Models

The interest in the development of shelf-life models for moisture sensitive products has
been recognized for long time. However, most studies have focused on packages of single
products. After the concepts introduced by Heiss (1958), other studies on shelf-life
modeling have followed, releasing some of the assumptions originally made and

increasing the complexity and applicability of the models.

Heiss (1958) discussed the relationship between moisture sorption properties of foods, the
packaging ﬁlm permeability and the shelf-life of the product and developed a solution
based on Fick's law of diffusion. The model was modiﬁed by Karel (1967) assuming a
linear isotherm and later by Labuza, Mizrahi and Karel (1972) who introduced the non-
linear isotherms Oswin, Kuhn and Mizrahi, on the model. Clifford et al. (1977) reported a
shelf-life model taking into consideration the moisture in the package head-space and
assuming a linear isotherm. Peppas and Khanna (1980) developed a model using the
Nemst-Plank diffusion equation combined with the non-linear isotherms BET, Halsey,

Oswin and Freundlich. The model was further extended to packaging systems where the

12

polymeric ﬁlm is appreciably swollen by the diffusing water. Kim (1992) developed a
model and a computer program for predicting the shelf-life of a packaged pharmaceutical
tablet based on the unsteady state mass transfer of water through the package and within
the tablet and used the method of ﬁnite differences to solve the model. The inﬂuence of
temperature on the system was introduced by Lee (1987) considering its effect on the
permeability coefﬁcient and by Kirloskar (1991) considering its effect on the sorption

isotherm.

All the above referred studies have, as one of the assumptions, constant storage
temperature and relative humidity. Cardoso and Labuza (1983) developed a dynamic
mathematical model to predict moisture transfer for packaged pasta under controlled
unsteady state conditions of temperature and relative humidity. The inﬂuence of storage
temperature and relative humidity varying as sine wave, was considered on packaging

permeability and on pasta isotherm.

Although moisture transfer in a combination of foods has been studied by several authors
as previously referred, a much less amount of work has been devoted to the case where the
mixture is packaged in a moisture permeable package and to its implication on the shelf-life
of the product. In multicomponent foods, it is assumed that the amount of water sorbed at
any aw is equal to a weighted average of the moisture each component would absorb alone
and a mixture isotherm could be derived. This approach was followed by Iglesias er al.,
1979 using the BET model to describe the mixture sorption isotherm. However, this
model is only applicable in the aw range 0.05 - 0.40. Furthermore, no experimental

validation of the model was presented.

Hong, Bakshi and Labuza (1986) developed a computer-aided model using the ﬁnite

element method to predict moisture transfer in a multicomponent mixed system during

13

storage, but no moisture transfer across the container barrier was assumed. The GAB
equation was used to describe the products isotherm. The model derived by Salwin and
Slawson (1959), previously referred, assumes linear isotherms and does also not consider

moisture transfer through the packaging.

Conclusions

Among the equations proposed to describe the moisture sorption isotherms of foods, the
GAB gives the best results for a great variety of foods and over a wider range of aw. The
Halsey and the Oswin equations also represent well the experimental data of several types
of foods.

Moisture sorption of dried mixtures may be inﬂuenced by interactions between
components, by the method of mixing and by whether drying is carried out before or after
mixing. As a ﬁrst approach and in the case of 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.

Shelf-life studies of moisture-sensitive foods in permeable packaging have only focused on
single products and have considered only either linear or the BET isotherms in the case of

multicomponent products.

References for Literature Review

Bizot, H. 1983. Using the GAB Model to Construct Sorption Isotherrns. In W
W- R. Jowitt, F. E. Escher, B. Hallstrom, H.F.T. Meffert,
W.E.L. Spiess and G. Vos (eds.) Applied Science Publishers, Ltd, Essex.

Boquet, R.; Chirife, J .; Iglesias, H. A. 1978. Equations for Fitting Water Sorpu'on
Isotherrns of Foods. II. Evaluation of Various Two-Parameter Models. Journal
of Food Technology. Vol. 13, pp. 319-327

Boquet, R.; Chirife, J.; Iglesias, H. A. 1979. Equations for Fitting Water Sorption
Isotherrns of Foods. 111. Evaluation of Various Three-Parameter Models. Journal
of Food Technology. Vol. 14, pp. 527-534.

Cardoso, G.; Labuza,T.P. 1983. Prediction of Moisture Gain and Loss for Packaged
Pasta Subjected to a Sine Wave Temperature/Humidity Environment Journal of
Food Technology, Vol.18, pp. 587—606.

Clifford, W.H.; Gyeszly, S.W.; Manathunya,V. 1977. Packaging Development and
Systems. Sept/Oct, pp.29-32.

Chinachoti, P.; Steinberg, M. P. 1985. Interaction of Sodium Chloride with Raw Starch
in Freeze-Dried Mixtures as Shown by Water Sorption. Journal of Food Science.
Vol. 50, PP. 825-839.

Chinachoti, P.; Steinberg, M. P. 1988. Interaction of Sucrose with Gelatin, Egg Albumin
and Gluten in Freeze-Dried Mixtures as Shown by Water Sorption. Journal of
Food Science. Vol. 53, No 3, pp. 932—939.

15

Chirife, J.; Iglesias, H. A. 197 8. Equations for Fitting Water Sorption Isotherrns of
Foods. Part I - a review. Journal of Food Technology. Vol. 13, pp. 159-174.

Chirife, J .; Pilar Buera, M. 1994. Water Activity, Glass Transition and Microbial
Stability in Concentrated/Semimoist Food Systems. Journal of Food Science.
Vol. 59, No 5, pp.921 - 927

Gal, S.l983. The Need for, and Practical Applications of, Sorption Data. In M
W. R. Jowitt, F. E. Escher, B. Hallstrom, H.F.T. Meffert,
W.E.L. Spiess and G. Vos (eds). Applied Science Publishers, Ltd, Essex.

Heiss, R. 1958. Shelf Life Determinations. Modern Packaging. Vol.31, pp.119, 125,
172-175.

Hong, Y. C.; Bakshi, A. S.; Labuza, T. P. 1986. Finite Element Modeling of Moisture
Transfer During Storage of Mixed Multicomponent Dried Foods. Journal of
Food Science. Vol. 51, No 3, pp. 554-558.

Iglesias, H. A.; Chirife, J.; Boquet, R. 1980. Prediction of Water Sorption Isotherrns
of Food Models from Knowledge of Components Sorption Behavior. Journal
of Food Science. Vol. 45, pp. 450-457.

Iglesias, H. A.; Viollaz, P.;Chirife, J. 1979. Technical Note: A Technique for
Predicting Moisture Transfer in Mixtures of Packaged Dehydrated Foods. Journal
of Food Technology. Vol. 14, pp. 89-93.

Karel, M. 1967. Use-tests Only Real Way to Determine Effect of Package on Food
Quality. Food in Canada Vol. 27, pp.43.

Kim, J .N. 1992. An Application of the Finite Difference Method to Estimate the Shelf
Life of a Packaged Moisture Sensitive Pharmaceutical Tablet. MS. Thesis.
Michigan State University.

l6

Kirloskar, M. 1991. Shelf Life Prediction of a Packaged Moisture Sensitive Solid Drug
Product Over a Range of Temperature and Relative Humidity Values. MS.
Thesis. Michigan State University.

Labuza, T.P.; Mizrahi, S.; Karel, M. 1972. Mathematical Models for Optimization of
Flexible Film Packaging of Foods for Storage. Transactions of the ASAE. Vol.
15. pp-150-155.

Labuza, T. P. 1984. Moisture Sorption - Practical Aspects of Isotherrn Measurement
and Use. American Association of Cereal Chemistry, St Paul, Minnesota.

Lang, K. W.; Whitney, McL.; Steinberg, M. P. 1981. Mass Balance Model for
Enthalpy of Water Binding by a Mixture. Journal of Food Science. Vol. 47, pp.
1 10-1 13.

Lang, K. W.; Steinberg, M. P. 1980. Calculation of Moisture Content of a Formulated
Food System to any Given Water Activity. Journal of Food Science. Vol. 45,
pp. 1228-1230.

Lang, K. W.; Steinberg, M. P. 1981. Predicting Water Activity from 0.30 to 0.95 of a
Multicomponent Food Formulation. Journal of Food Science. Vol. 46, pp.
670-67 2.

Tee, CH. 1987. Temperature Dependence of the Equilibrium Sorption Isotherrn and
Its Utility in Shelf Life Simulation of a Packaged Moisture Sensitive
Pharmaceutical Tablet. MS. Thesis. Michigan State University.

Leiras, M. C.; Iglesias, H. A. 1991. Water Vapour Sorption Isotherrns of Two Cake
Mixes and Their Components. International Journal of Food Science and
Technology. Vol. 26, pp. 91-97.

17

Lomauro, C. J.; Bakshi, A. S.; Labuza, T. P. 1985a. Evaluation of Food Moisture
Sorption Isotherrn Equations. Part I: Fnrit, Vegetable and Meat Products.
Iebensminel-Wissenschaft-und-Technologie. Vol. 18, pp. 111-117.

Lomauro, C. J .; Bakshi, A. S.; Labuza, T. P. 1985b. Evaluation of Food Moisture
Sorption Isothenn Equations. Part 11: Milk, Coffee, Tea, Nuts, Oilseeds, Spices
and Starchy Foods. Lebensmittel-Wissenschaft—und-Technologie. Vol. 18, pp.
1 18-124.

Nelson, K.A.; Labuza, TR 1994. Water Activity and Food Polymer Science:
Implication of State on Arrhenius and WLF Models in Predicting Shelf Life.
Journal of Food Engineering. Vol.22, pp. 271 - 289.

Nieto, M. B.; Toledo, R. T. 1989. A Factorial Approach to Modeling aw of a
Multicomponent Food in the High Moisture Range (aw 0.90 - 1.00). Journal of
Food Science. Vol. 54, No 4, pp. 925-930.

Peleg, M.; Normand, M. D. 1992. Estimation of the Equilibrium Water Activity of
Multicomponent Mixtures. Trends in Food Science & Technology. Vol. 3, No
7, pp. 157-160.

Peleg, M. 1993. Assessment of a Semi-empirical Four Parameter General Model for
Sigmoid Moisture Sorption Isotherrns. Joumal of Food Process Engineering.
Vol.16, pp. 21-37.

Peppas, N. A.; Khanna, R. 1980. Mathematical Analysis of Transport Properties of
Polymer Films for Food Packaging. H. Generalized Water Vapor Models.
Polymer Engineering and Science. Vol. 20, No 17, pp. 1147-1156.

Salwin, H.; Slawson, V. 1959. Moisture Transfer in Combination of Dehydrated Foods.
Food Technology. Vol. 13. pp.715-718.

 

18

Saravacos, G.D.; Tsiourvas, D.A.; Tsami, E. 1986. Effect of Temperature on the Water
Adsorption Isotherrns of Sultana Raisins. Journal of Food Science. Vol.52, No. 2,
pp. 381-383.

Schuchmann, H.; Roy, 1.; Peleg, M. 1990. Empirical Model for Moisture Sorption
Isotherrns at Very High Water Activities. Journal of Food Science. Vol. 55,
No.3, pp. 759-762.

CHAPTER II

MODELING THE MOISTURE CONTENT
OF TWO-CONIPONENT FOOD PRODUCTS IN A FLEXIBLE PACKAGE
MODEL DEVELOPMENT

20

Abstract

Water plays a predominant role in the physical and chemical properties of foods, as well as
in the mechanisms controlling their deterioration. Moisture-sensitive products packaged in
plastic containers are expected to change their moisture content during storage and
distribution. The impact of the exchange of water through the packaging material in most

cases determines the product's shelf life.

The development of mathematical models correlating the characteristics of a product, the
packaging material properties and the environmental conditions is desirable not only as a
means to reduce the time and cost of shelf-life determinations but, perhaps more

importantly, as a tool for packaging design.

Shelf-life models have been developed in the past for a single product. Studies of
multicomponent food however, have also been reported. Most of these studies included
solely the prediction of water sorption behavior of a mixture from the individual
component's behavior. In the case of shelf-life estimation, a linear isotherm equation or

equations with limited water activity range of applicability were used.

In this work, a computer shelf-life program for ﬂexible packaging containing two
moisture-sensitive food products was developed. The computer program allows to select
from GAB, Oswin, Halsey, Henderson and Chen equations to ﬁt the experimental
moisture sorption isotherm of the products. Computer simulated results of products

storage stability are presented.

21

Introduction

Controlling moisture content of a product is a major concern in preserving food products.
Texture and chemical deterioration rates, as well as microbial growth, are greatly affected
by the water activity of foods. Moisture transfer through the packaging material limits the

shelf-life of most dehydrated products packaged in ﬂexible plastic materials.

Shelf-life models have been developed in the past for a single product: Heiss (1958), Karel
(1967), Labuza, Mizrahi and Karel (1972), Clifford et al. (1977), Peppas and Khanna
(1980), Kim (1992), Lee (1987), Kirloskar (1991), Cardoso and Labuza (1983). In
packages containing multicomponent food products, a transfer of moisture also occurs
from the component with higher aw to those at lower aw. At equilibrium, all components
will have the same aw and the ﬁnal moisture content of each component will inﬂuence the
quality and shelf-life of the mixed product (Hong et al., 1986; Gal, 1983; Labuza, 1984).
The prediction of equilibrium aw is therefore very important, when formulating a moisture

sensitive multicomponent food.

Studies on the prediction of water sorption behavior of mixed multicomponent foods from
the individual component's behavior have also been reported: Salwin and Slawson (1959),
Iglesias et al. (1980), Chinachoti and Steinberg (1985), Chinachoti and Steinberg (1988),
Leiras and Iglesias (1991), Lang and Steinberg (1980), Lang and Steinberg (1981), Nieto
and Toledo (1989) and Lang et al. (1981). All of these studies however, did not consider
the simultaneous moisture transfer across the packaging material. In studies for shelf-life
prediction, a linear sorption isotherm equation or equations with limited aw range of

applicability were used (Labuza, 1984; Iglesias er al., 1979).

22

The transfer of moisture in packages containing multicomponent moisture—sensitive
products, takes place through the packaging material and within the food components.
When the diffusion coefﬁcient of 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.

For multicomponent foods, it can be assumed that the amount of water transferred through
the package at any aw, is distributed proportionally to their respective sorption isotherms.
A weighed isotherm could be derived and combined with the shelf-life models previously
developed. This approach was followed by Iglesias et al. (1979), using the BET equation
to describe the mixture sorption isotherm. However, this equation is only applicable in the

aw range 0.05 - 0.40.

The objective of this work was to develop 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". A computer program was written and simulation runs were carried out.

23

Mathematical Model Development

The rate of water transport through a permeable ﬁlm is given by the following equation
(Labuza et al., 1972):

m—E - .

Where:
W is the weight of water uansported across the ﬁlm, in g
t is the time, in days .
P is the ﬁlm permeability coefﬁcient, in gum lm2 day mmHg
1 is the ﬁlm thickness, in um
p0, pi are the vapor pressure of water outside and inside of the package,

respectively, in mmHg.

Under the conditions of usage of a package (temperature and relative humidity) only the
internal pressure pi is unknown. However, it is assumed that product's moisture content is

in equilibrium with pi .

When the diffusion coefﬁcient of water through the packaging material is several order of
magnitude smaller than the diffusion coefﬁcient of water in the air and within the product,
we can assume that the packaging material controls the moisture ﬂow between the product
and the external environment. This is the case of most packaging applications of dried
foods. We also assume that there is a rapid equilibrium between water and the food. The
internal pressure pi is determined by the product equilibrium moisture content and the

storage temperature.

24

When two products A and B are packaged together, the amount of moisture dW
permeating through the package is equal to the moisture change in product A plus the
moisture change in product B:
dW = WA dMA + W]; dMB (6)
Where:
W A. WB are the dry weights of components A and B, respectively
dMA, dMB are the change in moisture content of component A and B

respectively, in g lg dry weight.
Substitution of equation (6) in equation (5) and rearrangement gives:

WAdMA+WB dMB=§Apslam-aw)dt (7)
Where:
p8 is the water vapor pressure at the storage temperature
awo, aw are the external and internal water activity, respectively

MA and M]; are products' equilibrium moisture content at aw
MA and MB are related to the aw through the sorption isotherm equations.

Equation (7) can be integrated to give a relationship between time and moisture content of

each component.

If the shelf-life of the mixture depends on the moisture content of the components, then the
integration of equation (7) will provide a mean to estimate the shelf-life of the packaged

mixture.

25

Two cases are analyzed depending on the type of sorption isotherms considered.

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 + bA aw (8-3)
M3 = a3 + bB aw (8.b)

Where aA, aB. b A and b3 are the coefﬁcients of the linear equation.

Then
bA
dM =d — 9.a
A MBbB ( )
b
dM =dM —B— (9.b)
B AbA

Combining equations (9) with equation (7) and integrating gives:

M}
=_[_ b3 dMA
tA PAp’ (VVA+W13E)IMl am -aw(MA) (10.a)

A

Mi
=—l—- .IZA —dMB—
t3 PAP; (WAbB +WB)L. aw-awma) (10.b)

26

Where:
MA1 and M31 are the initial moisture content of component A and B, respectively
to, and t3 represents the time required to achieve the moisture content MA2 and

M32, respectively.
The analytical integration of this equations gives:

tA = —L; (WAbA + VVBbB)1n
PAP

 

%] (11.a)

r3 = —J—s (WAbA + WBbB) ln
PAP

 

awo ' aw (Mﬁq (111))
am ' aw (ME)

Where:
aw (M A) 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

The shelf-life is considered as the lowest of tA and t3 needed to reach MA2 and M132

which are the critical values for product acceptance.
- n f n n- ' ’ them
When the linear equation is too simplistic to represent real problems, the whole isotherm

needs to be considered in the model and a numerical integration of equation (7) will be

necessary.

27

Let us assume that the sorption isotherms equations of components A and B are described

by,
MA = f (aw) (11%!)

MB = g (aw) (12.b)
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 = 1‘1 (MA) (13a)
aw = g'1 (MB) (131:)

We assume that there is equilibrium between the moisture content of the two products and
therefore:

MA=f[8“ (M3)] (14)
and

MB = g [f" (M4)] (15)
Therefore dMB can be expressed as a function of dMA:
dMB = D dMA (16)

Where the function D is deﬁned as:

= d _ dlglf-‘(Mnll
DNA) - d—Mﬁ - —dTA_ (17)

28

The expression of dM A as a function of dMB gives:

= dMA _ dltlg'l(MB)]H
D(MB) — —dMB — _—dMB (18)

The function D can be obtained analytically or numerically.

Equation (7) rearranged can then be integrated

Mi
= 1 WA + W]; D(MA) l
tA PAPS HM; awe ' aw (MA) dMA ( 9.a)
Mi
= [ WB + WA D(MB) d 19 b
tB PAP; [Mir awr)'aw(NIB) NIB ( O)

to calculate the shelf-life or to predict the moisture content over storage time.

A computer program was developed in MS-DOS QBasic language, to perform the above
calculations. The program is presented in Appendix B together with ﬂow charts describing
the sub—routines. A ﬂow chart of the sub-routine to calculate the shelf-life, is presented in

Figure 1.

The program calculates the coefﬁcients of the Henderson, Chen, Oswin, Halsey and GAB
moisture sorption isotherm equations for each component based on moisture sorption data
by linear regression (ﬁrst four equations) and by second order polynomial regression

(GAB equation). The form used for each equation is presented in Table 1. To evaluate the

29

goodness of the ﬁt, the relative percent root mean square of the difference between the
experimental and the calculated moisture content (R) was used as indicated by equation

(20):

M:

R=q/% Mi‘M-r x100 (20)

' l

.—

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

n is the number of experimental data points.

The equation presenting the best ﬁt of the moisture sorption data may be selected to
calculate the shelf-life or to calculate the moisture content of each component for different

storage periods of time.

 

30

Routine: SHELF

l
r Input packaging data (1, P, A) J

 

[ Input storage environment data (awo, ps) J

1

Input products dry weight, initial moisture content
and critical moisture content (W (I), M1(I), M2(I))

 

 

 

 

 

gET sorption isotherm coefﬁcients (from MODEL)|

 

Deﬁne functions for each component

according to the model chosen
FUNA#: aw(I) = f(M(I)) inverse isotherm

FUNM#: M(I) = g(aw) isotherm
I is the component

Deﬁne functions relating dM of

component 1 with dM of component 2,
FUNDM#

Calculate n° of interations. NIT
NIT = INT (ABS(M2(1)-Ml(l))/0.005)
Calculate dMl for integration
dMl = (M2(1)-Ml(l)) / NIT

H
(D

Figure l - Flow chart of the program sub-routine for shelf-life calculation

 

 

 

 

 

 

 

 

 

Figure 1 (cont'd)

v-1 @‘2
II
C

 

I FORJ=2TONIT+1 J

A
r

 

X
|
o

 

M(l,J) = Ml(1)+(J-l)dM1
aW(J) = f(M(lJ»
Re?“ I 2 = FUNDM(M(1,J), isotherm coefﬁcients)

 

 

X = (W(l) + W(2) dM2) dMl

awo - aw(J)

 

 

 

T=T+X

H T=Tl/(PAps)

The time for component 1 to achieve

 

l

 

the ﬁnal moisture content is T;

The ﬁnal moisture content of

 

 

component 2 is g(aw(N1T+l))

 

 

 

Y
@(NTT+1))>M2(2) H—> Do integration
N again, but in terms
v of component 2

 

I Tis the shelf-life I

32

Table I - Moisture Sorption Isotherrns Equations Used in the Computer Program

Henderson _ +

Oswin _ = A0 + A1 1n(M)

= +
=A°+Ajaa+Aga3

 

Materials and Methods

The operational characteristics of the computer program were tested with published data.
Moisture sorption data for cereal crackers and raisin were selected. A cereal cracker's
isotherm at 20°C was described by the Halsey equation as follows (Tubert and Iglesias,
1986):

an = exp (- ) (21)

5.2.5.
M191

and a raisin isotherm at 20°C was described by the GAB equation (Ayranci er al., 1990)

as:

_ 0.2906 aw
M (1- 0.94663...) (1 - 0.946655, + 2.91221") (22)

33

The program was run with four sets of data in order to predict the storage stability curves

for different conditions of (i) components' weight ratio, (ii) storage water activity, (iii)

packaging barrier properties and (iv) total weight to packaging area ratio. Three runs were

performed for each set. Table 2’summarizes the conditions used.

Table 2 - Conditions used in the computer simulation

 

 

 

 

 

 

 

 

 

 

 

 

Run cereal raisin total aW VP' 11;" Packaging
weight, g weight, g weight, g smug; area, m2
Set A: To evaluate the inﬂuence of components weight ratio
1 10 20 30 0.80 25 / 1.5 0.045
2 15 15 30 0.80 25 / 1.5 0.045
3 20 10 30 0.80 25 / 1.5 0.045
Set B: To evaluate the inﬂuence of storage water activity
1 15 15 30 0.80 25 / 1.5 0.045
2 15 15 30 0.75 25 / 1.5 0.045
3 15 15 30 0.70 25 / 1.5 0.045
Set C: To evaluate the inﬂuence of packaging barrier properties
1 15 15 30 0.80 25 / 2.5 0.045
2 15 15 30 0.80 25 / 1.5 0.045
3 15 15 30 0.80 30/ 1.5 0.045
Set D: To evaluate the inﬂuence of total weight to packaging area ratio
15 15 30 0.80 25 / 1.5 0.045
2 20 20 40 0.80 25 / 1.5 0.045
3 25 25 50 0.80 25 / 1.5 0.050

 

 

 

 

 

 

 

For all the runs the initial moisture content was considered to be 0.077 gig for the cereal

and 0.09 g/ g for the raisin.

34

Results and Discussion

Figures 2, 3, 4 and 5, present the results of the computer simulation using sets of data A,
B, C and D from Table 2. In each case the moisture content of both components packaged

are simulated for runs 1, 2 and 3. The calculated values are presented in Appendix C.

 

Raisin Run 3

Moisture Content, g/g

 

 

 

 

. . . I . I .
0 100 200 300 400

Figure 2 - Components moisture content as a function of time, for different components

weight ratio (runs 1, 2 and 3). Simulated results using set of data A from Table 2

35

‘ Figure 2 shows that increasing the ratio of the lower moisture product leads to an increased

moisture uptake. This illustrates the inﬂuence of the mixture formulation when shelf-er is

 

 

 

 

 

a concern.
0.30
(1st Raisin Run 1
on .
E) Run 2
._:- .
§ 0.20 - . - Ru“ 3
r: .
o
U .
g 0.15 - . ' Cereal Run 1
O
2 q ‘. “a r: Run 2
. / f r: ’ C R 3
' - , .. =4" 0 un
0.05 , - , . , .
0 1 0 O 2 O O 3 O O 4 O 0
time, days

Figure 3 - Components moisture content as a function of time, for different storage water

activities (runs 1, 2 and 3). Simulated results using set of data B from Table 2

The inﬂuence of storage relative humidity may be seen in Figure 3. As expected, the
simulated curves indicate that storing at higher relative humidity gives lower shelf-life
times. In most cases the storage environment conditions ﬂuctuate over a range of relative
humidity and temperature. The use of the program can bring signiﬁcant time and cost

savings when designing the packaging system. The assessment of the shelf life at different

36

storage conditions can lead to correct packaging speciﬁcations providing information on the

moisture barrier required and avoiding over-packagin g.

The inﬂuence of the packaging moisture barrier properties is presented in Figure 4. As
expected, the higher the packaging resistance to moisture transfer, i.e., the higher the UP
ratio, the longer the shelf-life. The use of different packaging materials or of different

material's thickness may be assessed.

 

 

 

 

0.30
Run 1
Raisin
0.25 4 Run 2
an , ' .
h . ' . Run 3
E - I .
g 0.20 . i
o .
U 1 i
g 0.15- - Cereal . Run 1
'g ” U 1 Run 2
2 ~.. 1 ...— d g
0.10- / /
u /*
0.05 r u - m + - u r
0 1 00 200 300 400
time, days

Figure 4 - Components moisture content as a function of time, for different packaging

banier pr0perties (runs 1, 2 and 3). Simulated results using set of data C from Table 2

37

The inﬂuence of the ratio - total components' weight to packaging area available for
moisture transfer - may be assessed from Figure 5. The simulated curves indicate that the

higher this ratio, the lower the moisture content of each component for the selected time, as

expected

 

 

 

 

 

 

0.30
0-25 " Raisin Run 1
g Run 2
E? h . ' Run 3
g 0.20 ' , -
6 . /.
2 . /-
:3 0-15' . ' Cereal Runl
'0 / I
2 /- ﬁ .0_____ _ Run 2
/. A - - Run 3
0.10- / ,au-‘W/
0.05 n r . r . 1 .
0 1 00 2 00 300 400
time, days

Figure 5 - Components moisture content as a function of time, for different total weight to

packaging area ratio (runs 1, 2 and 3). Simulated results using set of data D from Table 2

38

Conclusions

The simulation program is a useful tool for packaging design and optimization. Packaging
variables including the type of package, product composition, storage conditions, time and

cost can thus be analyzed.

The model developed assumes that the mixed products are in equilibrium in all periods of
time. This may not always be the case, depending on the relative resistance to moisture
transfer within the products itself to the packaging barrier. Additionally, it also assumes
that products do not interact and therefore that moisture is independently bonded to each

product. Experimental validation is presented in Chapter 111.

References

Ayranci, E.; Ayranci, G.; Dogantan, Z. 1990.Moisture Sorption Isotherrns 0f Dried
Apricot, Fig and Raisin at 20°C and 36°C. Journal of Food Science. Vol. 55, No 6,
pp. 1591 - 1593,1625.

Cardoso, G.; Labuza,T.P. 1983. Prediction of Moisture Gain and Loss for Packaged Pasta
Subjected to a Sine Wave Temperature/Humidity Environment Journal of Food
Technology, Vol.18, pp. 587-606.

Clifford, W.H.; Gyeszly, S.W.; Manathunya,V. 1977. Packaging Development and
Systems. Sept/Oct, pp.29-32.

Chinachoti, P.; Steinberg, M. P. 1985. Interaction of Sodium Chloride with Raw Starch in
Freeze-Dried Mixtures as Shown by Water Sorption. Journal of Food Science.
Vol. 50. PP- 825-839.

39

Chinachoti, P.; Steinberg, M. P. 1988. Interaction of Sucrose with Gelatin, Egg Albumin
and Gluten in Freeze-Dried Mixtures as Shown by Water Sorption. Journal of
Food Science. Vol. 53, No 3, pp. 932-939.

Gal, 8.1983. The Need for, and Practical Applications of, Sorption Data. In W
W. R. Jowitt, F. E. Escher, B. Hallstrbm, H.F.T. Meffert,
W.E.L. Spiess and G. Vos (eds). Applied Science Publishers, Ltd, Essex.

Heiss, R. 1958. Shelf Life Determinations. Modern Packaging. Vol.31, pp.l 19, 125, 172-
175.

Hong, Y. C.; Bakshi, A. S.; Labuza, T. P. 1986. Finite Element Modeling of Moisture
Transfer During Storage of Mixed Multicomponent Dried Foods. Journal of Food
Science. Vol. 51, No 3, pp. 554-558.

Iglesias, H. A.; Chirife, J.; Boquet, R. 1980. Prediction of Water Sorption Isotherrns of
Food Models from Knowledge of Components Sorption Behavior. Journal of
Food Science. Vol. 45, pp. 450-457.

Iglesias, H. A.; Viollaz, P.;Chirife, J. 1979. Technical Note: A Technique for Predicting
Moisture Transfer in Mixtures of Packaged Dehydrated Foods. Journal of Food
Technology. Vol. 14, pp. 89-93.

Karel, M. 1967. Use-tests Only Real Way to Determine Effect of Package on Food
Quality. Food in Canada. Vol. 27, pp.43.

Kim, J.N. 1992. An Application of the Finite Difference Method to Estimate the Shelf Life
of a Packaged Moisture Sensitive Pharmaceutical Tablet. MS. Thesis. Michigan
State University.

40

Kirloskar, M. 1991. Shelf Life Predicrion of a Packaged Moisture Sensitive Solid Drug
Product Over a Range of Temperature and Relative Humidity Values. MS. Thesis.
Michigan State University.

Labuza, T.P.; Mizrahi, S.; Karel, M. 1972. Mathematical Models for Optimization of
Flexible Film Packaging of Foods for Storage. Transactions of the ASAE. V01. 15,
pp. 150-155.

Labuza, T. P. 1984. Moisture Sorption - Practical Aspects of Isotherrn Measurement and
Use. American Association of Cereal Chemistry, St. Paul, Minnesota.

Lang, K. W.; Whimey, McL.; Steinberg, M. P. 1981. Mass Balance Model for Enthalpy
of Water Binding by a Mixture. Journal of Food Science. Vol. 47, pp. 110-113.

Lang, K. W.; Steinberg, M. P. 1980. Calculation of Moisture Content of a Formulated
Food System to any Given Water Activity. Journal of Food Science. VoL 45, pp.
1228-1230.

Lang, K. W.; Steinberg, M. P. 1981. Predicting Water Activity from 0.30 to 0.95 of a
Multicomponent Food Formulation. Journal of Food Science. Vol. 46, pp. 670-
672.

Lee, CH. 1987. Temperature Dependence of the Equilibrium Sorption lsothenu and Its
Utility in Shelf Life Simulation of a Packaged Moisture Sensitive Pharmaceutical
Tablet. MS. Thesis. Michigan State University.

Leiras, M. C.; Iglesias, H. A. 1991. Water Vapour Sorption Isotherrns of Two Cake
Mixes and Their Components. International Journal of Food Science and
Technology. Vol. 26, pp. 91-97.

Nieto, M. 3.; Toledo, R. T. 1989. A Factorial Approach to Modeling aw of a
Multicomponent Food in the High Moisture Range (aw 0.90 - 1.00). Journal of
Food Science. Vol. 54, No 4, pp. 925-930.

41

Peppas, N. A.; Khanna, R. 1980. Mathematical Analysis of Transport Pr0perties of
Polymer Films for Food Packaging. H. Generalized Water Vapor Models. Polymer
Engineering and Science. Vol. 20, N0 17, pp. 1147-1156.

Salwin, H.; Slawson, V. 1959. Moisture Transfer in Combination of Dehydrated Foods.
Food Technology. Vol. 13, pp.715-718.

Tubert, A.H.; Iglesias, HA. 1986. Water Sorption Isotherrns and Prediction of Moisture
Gain During Storage of Packaged Cereal Crackers. Lebensmittel-Wissenschaft-
und-Technologie. Vol. 19, pp. 365 - 368.

CHAPTER III

MODELING THE MOISTURE CONTENT
OF TWO-COMPONENT FOOD PRODUCTS IN A FLEXIBLE PACKAGE
MODEL VALIDATION

42

43

Abstract

Shelf-life computer models are increasingly used as a means to save time and cost of shelf-
life determinations. In particular models for moisture-sensitive products have been
developed and successfully used in packaging design and optimization of single products

packaged in permeable packaging.

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, were developed
and presented in Chapter II. The objective of this work was to experimentally validate the
model and to assess the accuracy with which it estimates the moisture content change of

the packaged mixture components.

Mixtures of breakfast cereal and powder chocolate were used in the experiments. The food
components moisture isotherms and the packaging water vapor transmission rate were
determined and used in the model to predict the change in components moisture content
over storage time. The model predicted values were compared to those obtained
experimentally, for different components weight ratio and for two packaging materials

(OPP and PB).

The model tended to overestimate the components moisture content, in particular the
cereal's and for longer storage periods. Deviations seem to be dependent on the packaging
material barrier, which affected the relative tendency of the components to absorb moisture

simultaneously.

Introduction

Shelf-life prediction of food products is of great importance in packaging deve10pment and
packaging optimization. Computer modeling is a useful tool that provides rapid analysis
and design. The accuracy of the “model depends on how good the physical-chemical
characteristics of the product(s), package and environmental conditions are represented in

the model.

Many deterioration processes occurring in food products are associated with gain or loss of
moisture and with the product's ﬁnal water activity (aw). Dried products tending to absorb
moisture become soft and lose their desirable crispness or begin to develop off-ﬂavors.
Intermediate moisture products may either gain or lose moisture becoming either gummy,

sticky or hard.

Shelf-life modeling of moisture-sensitive single foods has been the focus of a considerable
attention (Cardoso and Labuza, 1983), but not multicomponent or mixed products
packaged together. A mathematical model. presented in Chapter II, was developed to
calculate the shelf-life of a two-component mixture packaged in a permeable package. The
model is based on the equation that describes the steady state transmission rate of moisture
through a permeable ﬁlm and on a moisture balance for the two components. The

following equation was obtained for the case of non-linear isotherms:

2

M
.=_1__ Wi-I-WB DCMi) . 2
t1 PADS IMI awo 'aw (Mi) dM ( 3)

 

45

where:
i is the component of interest and B the second component
p is the ﬁlm permeability coefﬁcient, in gum Im2 day mmHg
1 istheﬁlmthickness,inum
A is the package surface area available for moisture transfer, in m2
p8 is the water vapor pressure at the storage temperature, in mmHg
Wi, WE are reSpectively the dry weights of components i and B, in g
dMi is the change in moisture content of component i, in g lg dry weight
awo. is the external water activity
aw (Mi) represent the head-space water activity, in equilibrium with the moisture
content of component i
Mil , Mi2 are the initial and ﬁnal moisture content of component i, respectively
ti represents the time required to component i to achieve the moisture content M12
D(Mi) is deﬁned as a function of Mi relating the slopes of the components

isotherms at each aw

The model assumes that: (i) the shelf-life of the mixture depends on the moisture content
change of the components; (ii) the storage temperature and relative humidity are constant;
(iii) the amount of water vapor in the package head-space is negligible compared with the
products' moisture content; (iv) both components of the mixture reach fast equilibrium
with the package's head-space relative humidity; (v) the components do not show
hysteresis behavior on moisture sorption isorherms; (vi) the transfer of water through the
package is always at steady state; (vii) the packaging material controls the rate of water
transfer; and (viii) moisture is independently bonded to each components according to its

sorption isotherm.

46

The equilibration of the products' moisture content with the package head-space relative
humidity depends on the relative resistance to moisture transfer within the products to the
packaging barrier. A dimensionless number (L), similar to the Sherwood number, may be
useful to assess the applicability of assumption (vii) (Taoukis et al., 1988). The L number
was deﬁned as the ratio between the permeance of moisture in the food and the permeance
in the packaging material. For high values of L, control of moisture transfer by the
packaging material may be assumed, while for low values of L the moisture diffusion
within the food is the controlling mechanism and therefore assumption (vii) cannot be

applied.

Additionally to the above considerations on external and internal relative resistance, the
shelf-er model developed also assumes that moisture is independently bonded to each
product: the products behave as if packaged individually in what concerns the equilibrium
moisture content. However, interactions between the mixture components may result in
either a decreased or an increased water sorption by the mixture as compared to the
individual components. Hydrogen bonds between components that compete with hydrogen
bonds with water may result in a decreased water sorption, and solubilization of minor
constituents at high aw may result in an increased water sorption (Iglesias et al., 1990;
Chinachoti and Steinberg, 1988; Leiras and Iglesias, 1991; Chinachoti and Steinberg,
1985).

The objective of this work was to experimentally validate the model presented in Chapter
II. To achieve this goal, the food products isotherms and the packaging water vapor
transmission rate were determined. Different mixtures of two products were packaged and
stored. The change in products moisture content over time was monitored and compared to

the model predicted values.

47

Materials and Methods

W

Food products from a single lot were obtained through Portuguese companies. Breakfast
cereal (brand CREPITAS) and powder chocolate (brand SUCHARD EXPRESS) were
supplied by Nestle (Lisboa, Portugal). The ingredients of breakfast cereal included: corn,
sugar, wheat, honey, vegetable oil, malt extract, salt and non-fat dry milk. The powder
chocolate composition included: sugar, non-fat cacao, lecithin and salt. Raisin (brand
GLOBO) was supplied by A Colmeia do Minho (Seixal, Portugal). Raisin was chopped
into ca 3 mm thick slices in order to decrease equilibration time in isotherms

measurements.

Products were preconditioned before experiments: to get adsorption isotherms and for the
validation experiments, cereal and powder chocolate were pre-dried at 103°C overnight and
raisin at 60°C under vacuum for 48 hr; to get desorption isotherms, products were

equilibrated at 75% relative humidity for one week.

E l . I l . l
Oriented polypropylene (OPP) coextruded with a thermosealable layer at both faces, with
25 um thickness, was supplied by the converter Sociedade Portuguesa La Ce110phane
(Gaia, Portugal). Polyethylene coextruded with a barrier material (PE/barrier), of 65 um
total thickness, currently used for the breakfast cereal, was supplied by Nestle. Low density
polyethylene (30 um), was supplied by the producer Monteiro Ribas (Porto, Portugal). The
characterization of the packaging materials is presented in Appendix D.

48

For the validation experimentspouches of these materials were sealed using an impulse
sealer. The pouches integrity was checked by electrolytic testing (Axelson et al. 1990),

using a potential difference of 10V, 1% NaCl solution as electrolyte and steel electrodes.

WW
Moisture content of cereal and powder chocolate was determined by AOAC 925.09

method: 2 g of product were dried in vacuum oven (75°C, less than 20 mbar ) until

constant weight.

Raisin's samples were prepared according to the AOAC 934.06 method for moisture
content determination: 5 g of raisin were pulped and mixed with 2 g of pre-dried sand,
moistened with water and mixed thoroughly; the mixture was evaporated to dryness on a

steam bath and then dried in the oven at 103°C for 4 plus 1/2 hour.

I l . S . I 1
Products isotherms were determined at 25°C by equilibrating samples (3 replicates) at
different relative humidity values. The relative humidity was created inside closed
containers (20 cm height and 18 cm diameter) with saturated solutions of the following
salts: Lithium Bromide (6%), Lithium Chloride (11%), Potassium Acetate (23%),
Magnesium Chloride (33%), Potassium Carbonate (45%), Magnesium Nitrate (55%),
Sodium Nitrite (63%), Sodium Chloride (73%), Ammonium Sulfate (82%) and
Potassium Nitrate (93%). The relative humidity inside the containers was frequently

monitored with a calibrated hygrometer (Rotronic AG, Basserdorf, Switzerland).

The initial moisture content was determined as described above and samples were weighed

initially and after equilibration. A mass balance between the initial and ﬁnal stages gives

49

' that the initial amount of water plus the weight gain is equal to the ﬁnal amount of water.

This can be expressed as:

Yr + (Yr - Y1) = Yr (24)

_IMC_ _EMC_
IMC+1 EMC+1

where Yf is the ﬁnal weight, Yi is the initial weight, and IMC and EMC are the initial and
the equilibrium moisture content in g/g (dry basis), respectively. This expression can be
simpliﬁed to calculate the equilibrium moisture content as follows:

EMC, g/g anal—EMC - 1 (25)
1

E] E l .1.

Water vapor transmission rate of packaging ﬁlms was determined by an infrared sensor
method (ASTM F1249), using a PERMATRAN W200 (Mocon Inc., Minneapolis, USA)
The equipment was calibrated with polyester reference ﬁlms supplied by Mocon Inc. Three
replicates per material were tested at 25°C with 100% and with 75% of relative humidity as
driving force. The ﬁrst was obtained with water in the lower chamber of the cell, while the
second was obtained with a saturated solution of NaCl. After calibration with 100% of
relative humidity as driving force, the transmission rate of the reference ﬁlm was measured
with the saturated salt solution. The actual value of relative humidity in the lower chamber
of the cell was found by dividing the transmission rates of the material as indicated in

Appendix D.

Water vapor transmission rate of the pouches was also determined by the gravimetric
method (ASTM D3079). Three pouches of each material (15 cm x 15 cm) with silica gel

as desiccant, were stored in a chamber at 25 °C and 75 % relative humidity and weighed

50

daily, until constant increase of weight. Empty pouches were also stored to evaluate the

moisture sorption by the material itself.

11 lllll'l' E .

For model validation two experiments were carried out In the ﬁrst experiment mixtures of
cereal and powder chocolate were packaged in 20cm x 20cm pouches of OPP and stored in
a chamber (Aralab, Lisboa, Portugal) at 25 °C and 75% relative humidity. Mixtures of
different ratios of cereal to powder chocolate were prepared: 33/67, 50/50 and 67l33.
Pouches were weighed weekly and twice a month, two pouches of each mixture were
tested for moisture content determination of each product Five pouches of each product

itself were also prepared and weighed weekly.

In the second experiment mixtures of cereal and powder chocolate in a ratio of 50/50 were
packaged in PE pouches and stored as above. The sampling was done weekly. Three

pouches of each single product were also prepared.

Results and Discussion

1 l . S . I 1
Figures 6 - 8 present the experimental and the calculated GAB values of sorption isotherms
for cereal, powder chocolate and raisin at 25°C, respectively. Tables 3 - 7 show the ﬁtting
of the experimental sorption data with the Henderson, Chen, Oswin, Halsey and GAB
equations. Experimental values of sorption isotherms are presented in Tables E.l, E.2 and

E3 of Appendix E.

51

 

0.30
I Adsorption
0.25 " . Desorption
"" GAB Model (Adsorption) I

 

 

 

 

$3 020 - — GAB Model (Desorption)
a’
2
5 0.15 -
2 d
‘3,
'5 0.10 n
2

0.05 -

0.“) ' I ' l '7 j u I .

0.0 0.2 0.4 0.6 0.8 1.0

Water Activity

Figure 6 - Moisture adsorption and desorption isotherms of cereal at 25°C

As seen in Figures 6 and 7 both cereal and powder chocolate did not show signiﬁcant

hysteresis behavior. Both products appear to reach equilibrium within two days.

Raisin presented a sorption isotherm characteristic of the high sugar foods (Figure 8). At
low aw, high sugar products show low moisture contents since water is thought to be
adsorbed at the surface of crystalline sugar. At high aw, high sugar products show a

signiﬁcant increase of water content due to dissolution of crystalline sugar.

52

 

0.14

I Adsorption
0'12 ' . Desorption . l
' "" GAB Model (Adsorption)

 

 

 

 

$3 0-10 ‘ -- GAB Model (Desorption)
_, .
§ 0.08 ..
C
o 1
u
2 0.06 -
a .
.23
§ 0.04 -

0.02 -

4
0.00 . . t
0.0 0.2 0.4 0.6 0.8 1.0

Water Activity

Figure 7 - Moisture adsorption and desorption isotherms of powder chocolate, at 25 °C

This results in a phase conversion of the crystalline sugar into amorphous sugar, as
indicated by the presence of syrup exudation. Raisin adsorption-desorption isotherms
showed hysteresis behavior. As seen in Figure 8, this product presented a signiﬁcant
higher moisture content when equilibrated by desorption than by absorption. Similar

results were reported by Bolin (1980).

53

 

 

 

 

 

0.6
w I Adsorption,
0.5 - I Desorption
"" GAB Model (Adsorption)
$0 0.4 q — GAB Model (Desorption)
J
C
8
5 0.3 -
P.
3
g 0.2 -
2
0.1 "
0.0 . . . 1 . , . f .
0.0 0.2 0.4 0.6 0.8 1.0

Water Activity

Figure 8 - Moisture adsorption and desorption isotherms of raisin at 25 °C

Even when raisin was cut in small pieces of about 3 mm, the equilibration time was
around 15 days, much larger than for cereal or powder chocolate (ca. 2 days). This
indicates a very low diffusion coefﬁcient of water within the raisin. Lomauro and Bakshi
(1985) reported a value of 4.17x10'13 m2/s. Depending on the value of the packaging
ﬁlm permeance, the water diffusion through the packaging material may not be the

controlling step and therefore the model is not applicable.

54'

Since raisin showed sorption hysteresis and a very low water diffusion coefﬁcient, it could
not be used to validate the computer model. Therefore, validation experiments were carried

out with cereal and powder chocolate mixtures.

The GAB equation showed the best ﬁt for all the products. The goodness of ﬁt was
evaluated by calculating the relative percent root mean square of the difference between the
experimental and the calculated moisture content (R), presented in Tables 3 to 7. The
Halsey and the Oswin equations also represent well the experimental data, while the Chen
equation yields a poor ﬁt.

The amount of water tightly bound by the primary adsorption sites (monolayer value) was
calculated from the parameters of the GAB equation. The following values of moisture
content and equilibrium water activity were obtained: cereal - 0.0458 g/g (aw = 0.25),

powder chocolate - 0.0086 g/g (aw = 0.16), raisin - 0.1059 g/g (aw = 0.38).

55

Table 3 - Henderson equations ﬁtting experimental sorption data

      

AM... We

 
   
   

aw = 1 - exr) (47.322 M1342) 3 aw = 1 - exp (19.317 M1-411)

 
    

  

R=ll.5

  
   
   

' R = 11.4
Powder Chocolate

aw = 1 — exp (-13.518 M0327) aw = 1 - exp (-3337 M0481)

 
 

 
 
 

 

 

  

R: 11.4

 
 
 
  

R=34.4

 
    

   

I
i
l
1
|
l
l
|
l
|
I
1
I
l

aw = 1 - exp (-2.835 M0302)

 

aw = 1 - exp (-18.467 M2055)

   

R=l9.l

     

R=8.2

Table 4 - Chen equations ﬁtting experimental sorption data

,_ ___ _ ___.._—__———_—__—_.___—_—__ —____—___.—.____.___—_.__—_—____.___ ___ _.

Mﬁ_°n_

aw = exp ( -2.404 exp (-12.845 M ) ) aw = exp ( -2540 exp (-12.980 M ) )

 
   
         
 

  

     

   

R=37.5 _ ‘ _ _ __7_33- _ ,

Powder Chocolate

aw = exp ( -l.264 exp (-l7.997 M) ) aw = exp ( -l.098 exp (-10.445 M ))

 
        
   
 

  

R = 173.0 =510.0 -

 
 
    
   

aw = exp ( -l.422 exp (-3.726 M ) ) aw = exp ( ~4.l49 exp ( -8.592 M ) )

       
   

R=39.1

   

“3:225”

 

56

Table 5 - Oswin equations ﬁtting experimental sorption data

          
     
 

Adsorpnon 5...... _

aw I (l-aw) = 80.238 M1-774 , aw / (l-aw) = 83.680 M1330

   

  
 

    
     
 

R=5.7 f _ f R=7-0 to

. Powder Chocolate

aw / (l-aw) = 72.675 NII'I60

 

aw I (l-aw) = 9.488 M0658

 

  
 

      
     
  

R=25.4 _ R=99.

; aw / (l-aw) = 62.302 M2570

awl (l-aw) = 8.199 M1-154

 

 

  

  

R=3'1 - , _

Desorption Equation

 

aw = exp ( 0.034 m-l-m ) aw = exp ( 0036 MM”)
3:55 V? §R=63

aw = exp ( -0.030 M41325 )
3:163- ,

aw = exp ( 0.140 M41850)

 

R=3.4 __

57

Table 7 - GAB equations ﬁtting experimental sorption data.

Desorption Equation

aw / M = 2.351 + 17.289 aw - 18.836 aw2 . aw / M = 1.960 + 17.422 aw - 18.719 aw2

 

 

Powder Chocol

aw/M = 5.384 + 104.668 aw - 126.618aw2 aw/M = 9.489 + 85.221 aw - 110.133 aw2

; aw/M = -0.368 + 14.185 aw - 15.720 aw2

 

R=2-4 _ __ e

58

E} E l .1.
Values of the packaging materials permeance were experimentally determined. The results

are presented in Table 8. The detailed values are presented in Appendix D.

Table 8 - Materials permeance (g/m2 day mmHg) at 25 °c

 

 

 

 

 

As seen in Table 8, the permeance values of the packaging materials were within 8%,
which indicated good agreement between the different methods used. Table 8 also shows
that the permeance values of these materials were not affected by different driving forces.
The good agreement between the permeance values obtained by the gravimetric method
and the IR method additionally shows that the seals were efﬁcient in what concerns
moisture transfer and therefore they were appropriate for the validation experiments (this
was conﬁrmed by the electrolytic testing). The results obtained for the empty pouches in
the gravimetric method (Figure D2 in Appendix D) shows that the moisture absorption by
the packaging material itself can be neglected, as compared to the materials' water vapor

transmission rate.

Vl'l'E' 1

59

Experimental validation of the computer model was carried out by monitoring the change

in moisture content with time of each component of the packaged mixtures. The

experimental values of moisture content were then compared to the calculated values by the

computer model .

Experimental conditions:
Mixture components -
Pre-conditioning conditions -

Initial moisture content of components -

Average storage conditions -

Packaging ﬁlm -

Average pouches surface area -

cereal and powder chocolate

103 °C (i 1°C) air oven, overnight

cereal - 0.0038 g/g :1: 0.0003 g/g

powder chocolate - 0.0020 g/g i 0.0002 g/g
temperature - 25.5 °C i 0.9 °C

relative humidity - 73.6 % d: 2.3%

OPP

0.0748 m2 ($00023 m2)

Table 9 presents the average of cereal and powder chocolate dry weights in the pouches for

the validation experiment 1. Experimental values of moisture content as a function of

storage time are presented in Table 10. The individual pouches weight gain values are

presented in Appendix F. Table 11 shows the moisture content values for each component,

predicted by the computer model, using the GAB equation to describe the components

isotherms.

60

Table 9 -Va1idation 1. Cereal and powder chocolate dry weights *

' ; Cereal, g N Powder chocolate, g
Cereall Powder chocolate _ _ __ _ .f - f

9.588 :1: 0.837 1 19.874 :1: 0.992

14.092 $0.946 ‘ 13.340: 1.170
18.799 1 0.899 10.139 :1: 1.349

20.045¢0.903 . -
__ _ , ’ 20.366i1.12

 

* total weight ~ 30 g

Table 10 - Experimental moisture content* (g/g) of components as a function of storage

time (days). Validation l f

M“‘““

33/67

50l50

 

 

 

 

 

 

 

 

 

 

 

‘ Pow. chocolate ; 0.0020

"‘ each value is the average of two pouches

61

Table 11 - Values of components moisture content (g/g) as a function of storage time

(days), predicted by the computer model at experiment 1 conditions

M ___:28

33/67

    

 

 
   
 

Pow.chocolate
Cereal
Pow.chocolate
Cereal
Pow.chocolate
Cereal

 
  

 

  
    
 

 

  
   
 

 

 
 

 

 

 

 

 

 

 

 

In Figures 9 - 12 the experimental values are compared to the values predicted by the
model. Figure 9 refers to cereal and powder chocolate packaged individually, while Figures
10, 11 and 12 refer to mixtures with the following cereal to powder chocolate ratios: 33l67,

50/50 and 67/33, respectively.

62

 

 

 

 

 

0.15
I Experimental
. n
_ Calculated Cereal 100% area
70% area
£3 0.10 a
..r
c:
9
r:
o
O
2
g 005 4 POW.ChOC. __ 100% area
2 70% area
0cm ' I ' l ' | I ' u
0 20 40 60 80 100
time, days

Figure 9 - Validation 1. Experimental and calculated values of moisture content for the

single packaged components

From Figures 9 - 12 it appears that the experimental values are lower than what the model
predicted, including the case of the mixtures 100/0 and 0/100, corresponding to each
product packaged individually (Figure 9). Additionally, the moisture content of cereal,
when packaged together with powder chocolate, appears to stabilize at values lower than
the expected for longer storage periods (Figures 10, 11 and 12). This stabilization

however, is not seen when each component is individually packaged.

63

 

 

 

 

 

0.15
I Experimental
. n
J — Calculated Cereal 100% area
, 70% area
S: 0.10 -
..r . .
g I I I
G H
o
u r
2
g 05 "
g 0. ‘ POW.ChOC. 100% area
70% area
, O
0.00 ' I ‘ I l l
0 20 40 60 80 100
time, days

Figure 10 - Validation 1. Experimental and calculated values of moisture content for the

mixture 33/67

The percent error, calculated as the difference between the experimental and predicted
values of moisture content divided by the experimental values, presents values in the order
of 30% for the mixtures 33l67, 50/50 and 67/33. The components packaged individually
(mixtures 100/0 and 0/ 100) present values lower than 20%. The percent error for the
individually packaged components tends to decrease with time, while in the mixtures the

percent error tends to increase with time.

 

 

 

 

0.15 ,
. I Experimental
. n
_ Calculated Cereal 100% area
. 70% area
83 0.10 -
..r .
r: ' I
8 ~ - -
c
U
a I
§ 0
g .05 . POW.ChOC. 100% area
. 70% area
. I
-' O
0.“) b ' I ' I I T ' I I
0 20 40 60 80 100
time, days

Figure 11 - Validation 1. Experimental and calculated values of moisture content for the

mixture 50/50

The lower experimental values of components' moisture content may be caused by a lower
rate on the moisture transfer, either due to a lower storage relative humidity, or lower
pouches moisture transmission rate or lower pouches surface area available for moisture
transfer. Errors associated with model assumptions may also be responsible for the higher
values of moisture content predicted by the model as compared to the experimentally

determined.

65

 

 

 

 

0.15
I Experimental
. n
__ Calculated Cereal
+ 100% area
an 0.10 _ 70% area
.3 .
5 1 I
r: I I
o
O
2 .
‘2
E 0'05 Pow.Choc.
' 100% area
70% area
. I
, . _
01” I I . I I I I I I
0 20 40 60 80 100
time, days

Figure 12 - Validation 1. Experimental and calculated values of moisture content for the

mixture 67/33

The storage relative humidity was automatically monitored every hour and the average
value over the experiment period was used in the model (a standard deviation of 2.3% was
achieved over the testing period). A decrease of about 10% in the storage chamber relative
humidity was recorded around the 40th day. This lower value of relative humidity
remained for 3 days, which although contributing for lower values of moisture content
could not account by itself for the difference between the calculated and the measured

moisture content values.

66

The pouches' moisture transmission rate is not likely to be overestimated due to the results
obtained by the different methods (the results from the gravimetric method were used in

the model).

The inﬂuence of lower pouches surface area available for moisture transfer can be seen in
Figures 9 - 12. The moisture content values predicted by the model, assuming that all
pouches' surface was available for transfer and assuming that 30% was blocked, were
plotted together with the experimental values. The pouches were ﬂexible and not self-

supporting and therefore it is possible that their surface was not totally exposed.

The model assumed that each component reaches fast equilibrium with the package's head-
space relative humidity. As previously referred, the applicability of this assumption
depends on the relative resistance to moisture transfer within the food components to the
packaging material. For single packaged products, the higher the ﬁlm permeability, the
higher the deviations between the values of moisture content predicted by the model and
the experimental values - the assumption of fast equilibrium between the product's
moisture content and the package's head-space relative humidity is not met and the model
overestimates the experimental values. This could explain the lower values obtained in this
experiment. For packaged mixtures however, we have additionally assumed that moisture
is independently bonded by each component according to its isotherm. For higher storage
periods of time, corresponding to higher water activities, interactions between the packaged

components may lead to deviations in their sorption behavior.

Following the results obtained for validation experiment 2 are presented and discussed.

67

A second experiment for model validation was can-led out with a lower barrier packaging
material. Similarly to validation 1, the values of components' moisture content were

measured and compared to those calculated by the computer model.

Experimental conditions:
Mixture components - cereal and powder chocolate
Pre-conditioning conditions - 103 °C air oven, overnight

Initial moisture content of components — cereal - 0.0050 g/ g i 0.0002 g/ g

powder chocolate == 0 g/g
Average storage conditions - temperature - 252°C :1: 0.7°C
relative humidity - 72.9% i 0.8%
Packaging ﬁlm - PE
Average pouches surface area - 0.0727m2 i 0.0023m2

Table 12 presents the average of cereal and powder chocolate dry weights in the pouches
used, for the mixture 50/50 and for the components packaged individually (mixtures 100/0
and 0/ 100). Tables 13 and 14 present the components' moisture content over storage time
determined experimentally and predicted by the model, respectively. These values are
plotted in Figures 13 and 14, respectively for cereal and powder chocolate packaged
individually and for the mixture 50/50.

68

Table 12 - Validation 2. Cereal and powder chocolate dry weights *

 

 

 

 

 

Ratio Cereal, g Powder chocolate, g
Cereal / Powder chocolate

50/50 I 14.357 1' 0.676 14.522 1 0.840 I

100/0 II 29.833 1- 0.067 - I

0/100 I - 28.926 i: 0.513 I

 

* total weight = 30 g

Table 13 - Experimental moisture content* (g/g) of components as a function of storage

time (days). Validation 2

Mixture 7 14 21 24 28 31 40 50
50/50 Cereal 0.0433 0.0638 0.0873 0.0905 0.0998 0.1046

Pow. chocolate
100/0 Cereal
0/ 100 Pow. chocolate 0.0168 0.0239 0.0283

 

* each value is the average of two pouches

Table 14 - Values of components moisture content (g/g) as a function of storage time

(days), predicted by the computer model at experiment 2 conditions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ 7 time, days
Mixture" Components 7 14 21 24 28 31 40 50
“ 50/50 Cereal 0.0565 0.0815 0.0965 0.1015 0.1065 0.1105 0.1185 0.1245
Pow.chocolate 0.0131 0.0199 0.025 1 0.0270 0.0290 0.0307 0.0343 0.0372
lmoml Cereal 0.0395 0.0625 0.0785 0.0835 0.0895 0.0935 0.1035 0.1 1 15
0/ 100 ll POW. chocolate 0.0219 0.0294 0.0338 0.0352 0.0372 0.0383 0.0410 0.0433

 

69

 

 

 

 

 

0.15
I Experimental
. n
— Calculated
Cereal 100% area
00
h 0.10 ‘ 70% area
.1
t:
8
8
U
2
3
g 005- Pow.Choc. 4_ 100% am
2 / 70% area
0.00 I I I I I I I 1 I I I
0 10 20 3O 40 50 60
time, days

Figure 13 - Validation 2. Experimental and calculated values of moisture content for the

single packaged components

Figures 13 and 14 show that the calculated and the experimental values of components'
moisture content differ in a similar form as seen in validation experiment 1. The percent
error between the calculated and the experimental values is 20% for the mixture SWSO and

15% for the single components. These values are lower than those obtained in validation

experiment 1.

70

 

 

 

 

 

0.15 .
. I Experimental
. n
— Calculated Cereal lm% area
. 70% area
I
82 0.10- I
a . '
8
r:
c
U
2 4
:7 0 05 7
g . q POW.ChOC. lm% area
. 70% area
4
0.00 7 ' I ' l ' l I l I l u
0 10 20 30 , 40 50 60
time, days

Figure 14 - Validation 2. Experimental and calculated values of moisture content for the

mixture 50150

Contrary to the results from validation experiment 1, results from validation experiment 2
presented in Figure 14, did not show a plateau of the cereal's moisture content after 35
days, at levels around 8%. Nevertheless, the difference between the calculated and the
experimental values appears to increase as storage time increases. Apparently, cereal do not
bind their full amount of moisture at higher water activities. Contributing to this deviation
is the fact that cereal carried some part of the powder chocolate during the moisture content

determination: it was very difﬁcult to avoid that some powder was carried by the cereal's

71

surface once the components have been mixed together. This problem was overcome by
increasing the amount of cereal for moisture determination. Since the powder chocolate had
a lower moisture content than the cereal, it contributed to a lower moisture content value of
the later. In spite of this, this effect is not likely to low the cereal moisture content in an

extent to justify the large deviation found particularly in experiment 1.

The values of cereal equilibrium moisture content were plotted against the values of
powder chocolate equilibrium moisture content. Moisture content values from validation
experiments 1 and 2 as well as the experimental values from the sorption isotherms are

plotted in Figure 15.

It can be seen in Figure 15 that the moisture content values of the mixtures from validation
experiments follow the same pattern as the moisture content values from the sorption
isotherms. However, it seems that the mixing of the two components have some effect on
the equilibrium moisture sorption behavior of the components. The cereal appears to
absorb less water when mixed with powder chocolate, above the 7 - 8% values of moisture
content. This effect seems to be larger with the pouches of OPP than with the pouches of

PE and therefore it seems to increase with the decrease of packaging materials permeance.

72

 

 

 

 

 

4
-‘3— lsotherm values OPP LDPE
1 “_9— Exp 2: mixture 50/50 . isotherm
3% I Exp 1: mixture 33/67
at a q A Exp 1: mixture 50/50
.3 0 Exp 1: mixture 67/33
0
U I
8
a
.2’.’
o 2 -
2
3
.9. 4
o
8
.c:
U 1 -
is
g A
o ‘ ‘
a.
o ‘ T I T ' l
2 4 6 8 1 O 1 2

Cereals Moisture Content, %

Figure 15 - Powder chocolate moisture content vs. cereal moisture content. Values from
isotherm (components individual sorption behavior) and values from validation

experiments (mixture sorption behavior)

In summary, several factors appear to contribute to the difference between the experimental
and calculated values of the components' moisture content. Firstly, there was a non—
controlled contact between the pouches during the validation experiments. This fact may
account for a lower area available for moisture transfer than the actual pouches' area.
Secondly, it seems that by packaging together these two products, the equilibrium moisture

content of each component may be affected by the presence of the other component.

73

Although this is merely an observation it would be worthwhile to carry out further
experiments to conﬁrm or reject this hypothesis. Finally, it may be possible that the
assumption of fast equilibrium between the head-space relative humidity and the moisture
content of each component is not completely valid. Using a higher barrier material will
make this assumption more valid since the diffusion time will be much larger than the

moisture equilibrium time in the product

Conclusions

The model tends to overestimate the moisture content of the components studied, in
particular for the cereal and for longer storage periods. Deviation appears to be dependent
on the packaging material barrier, which may affect the relative tendency of the
components to absorb moisture simultaneously. Further experiments with higher barrier
materials than OPP are required in order to verify how much the packaging material may
affect the moisture uptake or may change the equilibrium moisture sorption behavior of the

mixed components.

Further experiments are also required to verify the model assumption of components' fast
equilibrium with the package's head-space relative humidity and to deﬁne a criteria for

assumption's applicability.

Recommendations for future work:
- Experiments with higher as well as with lower moisture barrier packaging materials than
the ones used in the validation experiments 1 and 2;

- Improved separation of mixture's components prior to moisture determination;

74

- Usage of sugar-free and salt-free components;

- Controlled exposure area of the pouches in the storage chamber.

It is also suggested the deve10pment and set-up of an experiment where both the package's
head-space relative humidity and the components moisture content can be monitored over
time. This would allow for ultimate conclusions' draft on the component moisture sorption

behavior related to the moisture transfer through the packaging.

References

Axelson, L.;Soren, C.; Nordstrom, J. 1990. Aseptic Integrity and Microhole determination
of Packages by Electrolytic Conductance Measurement. Packaging Technology and
Science, Vol. 3, pp. 141 - 162.

Bolin, HR. 1980. Relation of Moisture to Water Activity in Prunes and Raisins. Journal
of Food Science, Vol. 45, pp. 1190 - 1192.

Cardoso, G.; Labuza, TR 1983. Prediction of Moisture Gain or Loss for Packaged Pasta
Subjected to a Sine Wave Temperature/Humidity Environment. Journal of Food
Technology, Vol 18, pp. 587 - 606.

Chinachoti, P.; Steinberg, MP. 1985. Interaction of Sodium Chloride with Raw Starch in
Freeze-Dried Mixtures as Shown by Water Sorption. Journal of Food Science,
Vol. 50, pp. 825 - 839.

Chinachoti, P.; Steinberg, MP. 1988. Interaction of Sucrose with Gelatin, Egg Albumin
and Gluten in Freeze-Dried Mixtures as Shown by Water Sorption. Journal of
Food Science, Vol. 50, pp. 932 - 939.

75

Greenspan, L. 1977. Humidity Fixed Points of Binary Saturated Aqueous Solutions.
Journal of Research, National Bureau of Standards (US), Series A, Vol. 81, pp. 89
- 06.

Iglesias, H.A.; Chirife, J .; Boquet, R 1980. Prediction of Water Sorption Isotherrns of
Food Models from Knowledge of Components Sorption Behavior. Journal of
Food Science, Vol. 45, pp. 450 - 457.

Leiras, M.C.; Iglesias, HA. 1991. Water Sorption Isothenns of Two Cake Mixtures and
Their Components. International Journal of Food Science and Technology. Vol.
26, pp. 91 - 97.

Lomauro, G.L.; Bakshi, AS. 1985. Finite Element Analysis of Moisture Diffusion in
Stored Foods. Journal of Food Science, Vol. 50, pp. 392 - 396.

Taoukis, P.S. El Meskine, A; Labuza, T.P. 1988. Moisture Transfer and Shelf Life of

Packaged Foods. In W J. Howhkiss (ed).
American Chemical Society, Washington DC.

APPENDIX A

EQUATIONS FOR MOISTURE SORPTION ISOTHERMS

76

The equations of the moisture sorption isotherms referred to on Chapter I, are presented

below. The bibliographic references cited are listed on References section of Chapter I.

i) BET equation (Brunauer et al., 1938 in Chirife and Iglesias, 1978)

__a.__=_t .MC-I)
(l-a.)M Mac Mac

Mm - isthe monolayer moisture content

C - constant related to the heat net of sorption

ii) BET modiﬁed equation (Brunauer, 1945 in Chirife and Iglom’as, 1978)

 

M- MmCaqu-(n+1)a.'.',-l-na.',',"l I
" 1-aw 1+(C-1)a..-Ca:+‘J

n - is the number of layers of water
iii) Bradley equation (Bradley, 1936 in Chirife and Iglesias, 1978)

In (Haw): K2K1M
K2 is a function of the sorptive polar groups

K1 is a function of the dipole moment of sorbed vapor
iv) Caurie equation (Caurie, 1970)

1nC=lnCo-raw

CgLOO-%H20
%H20

Co and r are constants

77

v) Chen equation (Chen, 1971 in Chirife and Iglesias, 1978)

aw = exp [K+a exp (- bM)]
K, a, b are constants

simpliﬁed version: aw = exp[-a exp (- bM)]

vi) Chen and Clayton equation (Chen and Clayton, 1971 in Chirife and Iglesias,
1978)

a-=exp[-K1T"“exp(- K2 TmM)]

K1, K2, m1, m2 are constants
vii) Chung and Pfost equation (Chung and Pfost, 1967 in Chirife and Iglesias, 1978)

=-_a_ -
lnaw RTexp( bM)

a and b are constants

viii) D'Arcy -Watt equation (Saravacos et al., 1986)

1+K1a..+K5”"’+ 1-K3a.

K1, K2, K3, K4, K5 are constants

78
ix) Day and Nelson equation (Day and Nelson, 1965 in Chirife and Iglesias, 1978)

1 -a. =exp (-er“ MW”)

51, h1.j2. h2 are constants
1:) Double Power Law equation (Peleg, 1993)

M = k1awnl + lrzaw112

k1, k2, n1, n2 are constants (n1 < 1 and n2 >1)

xi) Ferro Fontan equation (Ferro Fontan at al. 1982 in Chirife et al. 1983)

l) _
“Ia. — 01 M"
g is a parameter that accounts for the structure of sorbed water

a and r are constants

xii) GAB equation (Bizot, 1983)

.M.= CKa_..
Mo (l-Ka.)(1-Kaw+CKaw)
a.

or — = 0: a3 + a. +
M B 7
Mo - monolayer moisture content

C - Guggenheim constant

K - constant correlating pr0perlies of multilayer molecules with respect to bulk liquid

79

xiii) Hailwood and Horrobin equation (Hailwood and Horrobin, 1946 in Chirife and
Iglesias, 1978)

2;: - 2
M A+Ba. Can

A, B and C are constants
xiv) Halsey equation (Halsey, 1948 in Chirife and Iglesias, 1978)

a. =exp (- 11%)

K and r are constants

xv) Halsey's modiﬁed equation (Iglesias and Chirife, 1976 g in Chirife and Iglesias,
1978)

an = exp [- exp (bT + c)M"]

b. c and r are constants
xvi) Harkins-Jura equation (Harkins and Jura, 1944 in Chirife and Iglesias, 1978)

lnaw=B-A/M2

A and B are constants

80
xvii) Haynes equation (Haines, 1961 in Chirife and Igles‘as, 1978)
lnp=(a+bM)lnpo+(c+dM+gM7-)

a, b, c, d and g are constants

p0 is the vapor pressure of pure water at a given temperature

xviii) Henderson equation (Henderson, 1952 in Chirife and Iglesias, 1978)

1 - aw: exp (-an)

k and n are constants

xix) Iglesias and Chirife equation I (Iglesias and Chirife, 1976f in Chirife and
Igles’as, 1978)

ln(M+VW+M)5')=baw+p

M05 is the moisture content at aw = 0.5

b and p are constants

xx) Igloa’as and Chirife equation II (iglesias and Chirife, 1981)

 

M=A 3" +B AandBareconstants

xxi) Kuhn equation (Kuhn, 1967 in Chirife and Iglesias, 1978)

M=Ea—+b aandbareconstants
a.

81

xxii) Linear equation (Labuza et al., 1972 in Chirife and Iglesias, 1978)

M=a+baw aandbareconstants

xxiii) Mizrahi equation (Mizrahi et al., 1970 in Chirife and Iglem'as, 1978)

ac=3—+—M aandbareconstants
b+M

xxiii) Oswin equation (Oswin, 1946 in Chirife and Iglesias, 1978)

 

M=a[l‘_"’aw]n a,n areconstants

xxiv) Smith equation (Smith, 1947 in Chirife and Iglesias, 1978)

M=B-A1n(1-aw) A,Bareconstants

xxv) Strohman and Yoerger equation (Strohman and Yoerger, 1967 in Chirife and
Iglesias, 1978)

In aw=a 1n p0 exp (bM) + 0 exp (dM)
a, b, c, d are contants

P0 is the vapor pressure of pure water at a given temperature

82

xxvi) Young and Nelson equation (Young and Nelson, 1967 a in Chirife and
Iglesias, 1978)

MS=A(G+01)+B¢

Md=A(0+0t)+BOawmax

s,d refer to adsorption and desorption respectively

aw max is the water activity from which desorption commenced originally
0 = f (aw, E)

9 = aw q

a = f (aw, E)

APPENDIX B

DESCRIPTION OF THE COMPUTER PROGRAM

83

 

MENU OPTIONS:

1. Create Two Files With Experimental Sorption Data

2. Modify the Sorption Data Files

3. Modelling Experimental Sorption Data

4. Calculate Shelf-Life

5. Calculate Products Moisture Content at Different Storage Periods

6. Quit

 

 

 

————> CALL CREATE

————p PRINT Stored Data and Call MODIFY

—-—> GOSUB MODEL

—-> GOSUB SHELF
——> 008013 STABILITY

—> [Q GOTO FINAL

84

- CREATE

V

 

 

Create "isol. dat" ﬁle to store (relative humidity,
moisture content) sorption data points of

component 1
Create "i802. dat" ﬁle to store (relative humidity,
moisture content) sorption data points
of component 2

Print the stored data for both components

Return to main program

 

 

Want Y

 

 

 

to change I CALL MODIFY

 

 

 

any data

 

 

 

 

 

MENU

 

 

85

Print the modiﬁed stored data for both components

- MODIFY
.__’ Correct Data or
————> Add Data or
——> Delete Data
.__.>
.___.> Retum to main program

 

 

 

 

 

Want Y
to change ————>
any data
N
V

 

 

MENU

 

 

 

 

CALL MODIFY

 

86

———> CALL HENDERSON __.

 

 

 

—_—> CALL CHEN

 

 

 

——> CALL OSWIN

 

 

 

 

a CALL HALSEY

 

 

 

————> CALL GAB

 

 

+ Print coefﬁcients and goodness criterium of ﬁt

 

{—— Choose the model to be used

 

L_____> RetumtoMENU

87

.- SHELF

F— Input packaging data (1, P, A)
‘— Input storage environment data (awo, ps)

Input products dry weight, initial moisture content
and critical moisture content (W (I), M1(I), M2(I))

+—

{——— GET sorption isotherm coefﬁcients (from MODEL)

 

Deﬁne functions for each component

———>

 

according to the model chosen
FUNA#: aw(I) = f(M(I)) inverse is0therm
FUNM#: M(I) = g(aw) isotherm

I is the component

 

 

 

 

 

Deﬁne functions relating dM of
component 1 with dM of component 2,
FUNDM#

 

 

 

 

 

Calculate n° of interations, NIT
NIT = INT (ABS(M2(1)-Ml(1))/0.005)

 

 

 

 

 

Calculate dMl for integration
dMl = (MZ(l)-M1(l)) INIT

l
(D

 

 

 

88

 

 

 

 

 

 

 

 

FOR] =2 TO NIT+1

 

 

 

 

 

 

 

X=0

 

 

 

 

 

 

M(l,J) = M1(1) + (J-l) dMl
8180) = f(M(lJ»

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Next J dM2 = FUNDM(M(1,J), isotherm coefﬁcients)
A
X=(W(1) +W(2) dM2) dMl
awo - aw(J)
T=T+X
T = T l/ (P A ps)

 

 

 

 

 

The time for component 1 to achieve
the ﬁnal moisture content is T;
The ﬁnal moisture content of

component 2 is g(aw(N1T+l))

 

 

Y

 

 

 

 

 

” l

 

 

T is the shelf-er

 

 

v

MENU

 

 

 

 

g(aw(N1T+l)) > M2(2) ———> Do integration

again, but in terms

of component 2

89

@ - STABILITY
<———— Input packaging data (1, P, A)

{— Input storage environment data (awo, ps)

Input products dry weight and initial moisture content
(W (1). M10). M2(I))

<——

4——- GET sorption isotherm coefﬁcients (from MODEL)

‘— Input time period

 

 

—————-> Calculate dt for stability curve
dt = time period / 10

 

 

 

 

Initialize variables
aw(l) = FUNA(M1(1), isotherm coefﬁcients)

 

 

90

 

 

FOR N =1 TO 10

 

 

 

 

 

Next N

 

 

b
U(N) = N.dt

 

 

 

 

 

 

FORJ=2T050

 

 

 

 

 

 

 

 

 

M(1,N,J) =(J-1) 0.0005 + M1(l,N-1)
aw(J) = FUNA(M(1,N,J), isotherm coefﬁcients)
dMl = 0.0005
dMl = FUNDM(M(1,N,J), isotherm coefﬁcients)

 

 

 

Next J

 

 

 

X = W(l) dMl + W(2) dM2(J)

awo - aw(J)

 

 

 

 

 

U1(N,J) = U1(N, J-1)+ X l/ (PAps)

 

 

 

 

IF U1(N,J) > U(N) THEN EXIT FOR

 

 

 

 

 

M2(1.N) = (M(LNJ) + M(1,N,J-1)) / 2

 

 

 

 

PRINT U(N), M2(1,N), M2(2,N)

 

 

 

 

 

M1(1,N) = M(1,N,J)
aw(l) = FUNA( M(1,N,J), isotherm coefﬁcients)

Ul(N+l) = U1(N,J)

 

*

MENU

 

 

 

 

 

 

 

 

 

 

 

 

[[[IIIIII a.(((IIIIIIIlJlrlilrr.....
. rrrrIll (ll\.‘ ‘V

91

DECLARE FUNCTION FUNDM# (Q, NISOS, AW110, MC1, A010, A110, A210)
DECLARE SUB PRINTDATA O

DECLARE SUB HENDERSON (AOHE!0, AIHE10, CORRHE10)
DECLARE SUB CHEN (ACCH10, AICH10, CORRHE10)
DECLARE SUB OSWIN (A008 10, AIOS!O, CORR0810)
DECLARE SUB HALSEY (AOHA10, AIHA10, CORRHA10)
DECLARE SUB GAB (A0610, A1610, A2610, CORR610)
DECLARE SUB MODIFY (MOD5)

DECLARE SUB CREATE O

DECLARE FUNCTION FUNM# (NISOS. AWIl, A01, A11, A21)
DECLARE FUNCTION FUNA# (NISOS, MC1, A01, A11, A21)
DECLARE SUB PAUSA 0

%***#****¥*******t**************#**************************¥****************

CLS
QUADls = STRING$(78, "*")

QUADQS = m" + STRING$(74, " ") + "**"

PRINT : PRINT

PRINT QUADrs: PRINT QUADIs

PRINT QUADZS: PRINT QUAD2$

PRINT “*8“; TAB(15); ”Shelf-Life Modeling of"; TAB(77); "*I"

PRINT "I"; TAB(15); 'Twocomponent Packaged": TAB(77); "**"

PRINT "**"; TAB(15); ”Moisture-Sensitive Products”; TAB(77); "**"

PRINT "II"; TAB(15); "BY Maria FF. Poras and"; MW?» ”**"

PRINT "**"; TAB(15); " Ruben J. Hernandez"; TAB(77); ""1"

PRINT QUADQS: PRINT QUAD2$

PRINT nu»; TAB(40); "This program is capywrited by"; TAB(77); "**"

PRINT mm; TAB(40): "MFF.P0:|:as and R.J.Hernandez"; TAB(77); "**"

PRINT QUAD2s: PRINT QUADzs: PRINT QUADzs: PRINT QUAD28: PRINT QUADZS
FRUIT In"; TAB(34); "October 1995"; TAB(77); "**"

PRINT "**"; TAB(30); "School of Packaging”; TAB(77); "**"

m "it"; TAB(28); "Michigan State University"; TAB(77); "In"

PRINT QUADZS

PRINT QUADIS: PRINT QUADlS: CALL PAUSA

GOSUB MENU

ALLLAJ‘IL- LLL-JIILJ‘AAALJ-IAAJJ L. L14 L. .444 ‘_-L_A4 .ALJ
- -* ‘-
T . . . '— r-rv—rj—v . TTTTTT“ -r v- r v T r - -' TTTTTTT r1 . r "TTT‘V'T r v —' TTT-u-‘r-v-T'r rT—TTTTTT TT-gv—v—Tij j r .— '

T'YPEIso
RHAS SINGLE
MCAS SINGLE
ENDTYPE

DIM AIHE1(2), AOHE1(2), CORRHE1(2)
DIM AICH!(2), AGO-11(2), CORRCH1(2)
DIM AlOS1(2), AOOS1(2), CORROS1(2)
DIM AIHA1(2), AOHA1(2), CORRHA10)
DIM A261(2), A161(2), A061(2), CORRG!(2

I—LAALLJJAJ-AAALAJ LI.‘ LAIAAJILL‘

Tv-wu-r-jwrw—vw-vrr‘vT-Tr—vvww Tw—v-rw-Tw vr-ufrw'vvw-V'vvv—rv-vvuvv-ww—w-v-Tv‘v—TTVT-wv

CLEAR

MENU:

CLS

IDCA'I'E 6, 15: PRINT “ 12 f C i f I ‘. T I ;; L;;i;::: MAIN MENU *t***************$**"
LOCATE 8, 15: PRINT "1. Create Two Flies with Experimental Sorption Data“

LOCATE 10, 15: PRINT "2. Modify the Sorption Data Fries"

 

 

UUUUUUSI
IIIIIIIII

92

LOCATE 12, 15: PRINT "3. Modeling Experimental Sorption Data”
IDCATE 14, 15; PRINT "4. Calculate Shelf Life"
LOCATE 16, 15: PRINT ”5. Calculate Products Moisture Content at"
LOCATE 17, 18: PRINT "Different Storage Periods"
LOCATE 19, 15: PRINT "6. Quit"
LOCATE 23, 15: INPUT "Please enter the number of your choice"; CHOICE
SELECT CASE CHOICE
CASE 1
CALL CREATE
CASE 2
CALL PRINTDATA
INPUT "Do you want to (C)orrect. (A)dd or (D)elete any data ?", MODS
CALL MODIFY(MOD$)
CASE 3
GOSUB MODEL
CASE 4
GOSUB SHELF
CASE 5
GOSUB STABILITY
CASE 6
GOTO FINAL
CASE ELSE
PRINT "Please try again!!"
END SELECT

GOSUBMENU

WI***************#*****#********t*******************************************

MODEL:

CLS

PRINT ”1 am ﬁtting the experimental data points in the following equations:”

PRINT ”Henderson, Chen, Oswin, Halsey and GAB"

PRINT

FORMATS = "m.m Wﬁﬂ am.m Wﬁﬂ"

CALL HENDERSON(AOHE!O, AlI-IE10, CORRHE10)

CALL CHEN(AOCH10, AlCH10, CORRCH10)

CALL OSWIN(AOOS!(), AlOS!0, CORROS 10)

CALL HALSEY(AOHA10, AIHA10, CORRHA 10)

CALL GAB(AOG!0, A1610, A2610, CORR610)

CLS

PRINT TAB(15); ”HENDERSON EQUATION COEFFICIENTS"

PRINT TAB(19); ”A0" ,;TAB(31) "Al"; TAB(42); "RMS"

PRINT "Component 1", TAB(15); USING FORMATS; AOHE!(1); A1HE1(1); CORRHE1(1)
PRINT ”Component 2", TAB(15); USING FORMATS; AOHE!(2); A1I-IE1(2); CORRHE1(2)
PRINT TAB(15); ”CHEN EQUATION COEFFICIENTS"

PRINT TAB(19); "A0"; TAB(31); "A1";TAB(42); "RMS"

PRINT "Component 1", TAB(15); USING FORMATS; AOCH1(1); AlCl-I1(l); CORRCI-Il(l)
PRINT "Component 2", TAB(15); USING FORMATS; AOCH1(2); A1CI-I!(2); CORRCH1(2)
PRINT TAB(15); "OSWIN EQUATION COEFFICIENTS"

PRINT TAB(19); "A0"; TAB(31); ”Al"; TAB(42); "RMS"

PRINT ”Compment 1", TAB(15); USING FORMATS; A0081(1); AlOS!(l); CORROS1(1)

PRINT "Component 2", TAB(15); USING FORMATS; A0081(2); AlOS!(2); CORROS1(2)

PRINT TAB(15); ”HALSEY EQUATION COEFFICIENTS"

PRINT TAB(19); ”A0"; TAB(31); "A1";TAB(42); ”RMS"

 

I PPDIHHHGHH

EEERRDGI

S

93

PRINT "Component 1", TAB(15); USING FORMATS; AOHA1(1); AIHA1(1); CORRHA10)
PRINT "Component 2", TAB(15); USING FORMATS; AOHA1(2); A1HA1(2); CORRHA1(2)
PRINT TAB(15); ”GAB EQUATION COEFFICIENTS”

PRINT TAB(19); 'Ao"; TAB(31); "AI”; TAB(42); ”A2”; TAB(55); 'RMS"

PRINT ”Compoth 1", TAB(15); USING FORMATS; A0610); A161(1); A2610); CORRG!(I)
PRINT "Component 2", TAB(15); USING FORMATS; AOG!(2); A161(2); A261(2); CORRG!(2)
CALL PAUSA

PRINT

PRINT TAB(25); "Please input the isotherm equation to be used”;

PRINT TAB (30); "(I-IE)NDERSON"

PRINT TAB (30); ”(CIDEN "

PRINT TAB(30); "(OS)W1N"

PRINT TAB (30); ”(I-IA)LSEY "

PRINT TAB(30); "(GAB)”

INPUT NISOS

GOSUB MENU

WIII*#*********************************It**IkIt*IhhklkIklkti***********************

SHELF:

INPUT PACKAGING, STORAGE ENVIRONMENT AND PRODUCTS DATA
CLS

PRINT "Please input packaging data"

INPUT "THICKNESS in u =", L

INPUT ”PERMEABILITY COEFFICIENT in gu/m2 day mmHg =", P

INPUT "AREA in m2 =", A

PRINT : PRINT

PRINT "Please input storage environment data”

INPUT ”STORAGE WATER ACTIVITY =”, AWE

INPUT "VAPOR PRESSURE AT STORAGE TEMPERATURE in mmHg =", P8
PRINT : PRINT

PRINT "Pleme input products data"

INPUT ”DRY WEIGHT OF COMPONENT 1 in g =", W(l)

INPUT "DRY WEIGHT OF COMPONENT 2 in g =”, W(2)

INPUT "INITIAL MOISTURE CONTENT OF COMPONENT 1 in g/g =", MCO(I)
INPUT "INITIAL MOISTURE CONTENT OF COMPONENT 2 in glg =", MCO(2)
INPUT "FINAL MOISTURE CONTENT OF COMPONENT l in glg =", MCF(I)
INPUT "FINAL MOISTURE CONTENT OF COMPONENT 2 in g/g =", MCF(2)
PRINT : PRINT

IF UCASE$(NISOS) = "HE" THEN
FOR I = 1 TO 2
A010) = AOHE1(I)
A11(I) = A1HE1(I)
NEXT I
END IF .
IF UCASE$(NISO$) = "CH” THEN
FOR I = I TO 2
A01(I) = AOCH1(I)
Al 1(1) = AlCH1(I)
NEXT I
END IF
IF UCASESWSOS) = "03" THEN

94

FOR 1 = 1 TO 2
A010) = A00310)
A110) = AIOS10)
NEXT I
END IF
I? UCASEMNISO” = "HA" THEN
FOR I = 1 TO 2
A010) = AOHA10)
A110) = AIHA10)
NEXT 1
END IF
IF UCASWSO” = "GAB" THEN
FOR I = 1 TO 2
A010) = A0610)
A110) = A1610)
A210) = A2610)
NEXT 1

 

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PRINT "Please wait a moment ...............
PRINT
DIM MC1(2, 3000), AW11(3000), DMC1#(3000), DMC2#(3000)
NIT = INT(ABS(MCF(1) - MCO(1)) I .00005)
IF NIT > 2999 THEN
NIT = 2999
END IF
PRINT NISOS
PRINT ”nits”, NIT
DMC1# = (MCF(1)- MCO(1)) l NIT
MC1(1, l) = MCO(I)
MC1(1, NIT + I) = MCF(I)
MC1(2, l) = MCO(2)
AW11(1) = FUNA#(NISOS, MC1(1, l), A01(1), A1 1(1), A21(1))
T = 0
FOR J = 2 TO NIT + 1
X = 0
MC1(1, J) = MC1(1, 1) + (J - 1) * DMC1#
AW11(J) = FUNA#(NISOS, MC1(I, J), A010), A110), A210))
IF UCASES(NISOS) = "GAB" THEN
DMC2#(J) = FUNM#(NISOS, AW11(J), A01(2), A1 1(2), A21(2)) - FUNM#(NTSOS, AW11(J - 1),
A01(2), All(2), A21(2)) -
ELSE
DMC2#(J) = DMC1# * FUNDM#(I, NISOS, AW110, MC1(1, J), A010, A110, A210)
END IF
X = (W(l) * DMC1# + W(2) * DMC2#(J)) / (AWE - AW11(J))
T=T+X
NEXT J
TEMPOS = "W days"
MOISTS = ”AW g/g"
T=T*LI(P*A*PS)
PRINT "The time for component 1 to achieve ﬁnal moisture content is"; USING TEMPOS; T

«n+CnLH‘-

95

PRINT ”The ﬁnal moisture content of component 2 is =”; USING MOIST$; FUNM#(NISOS, AW11(NIT
+ l), A01(2), A11(2), A21(2))
CALL PAUSA
INPUT "The ﬁnal moisture content of component 2 is higher than the critical (Y/N)", zxcs
IF UCASE$(zxc$) = ”Y” THEN
NIT = INT(ABS(MCF(2) - MCO(2)) I .00005)
IF NIT > 2999 THEN
NIT = 2999
END IF
PRINT 'nit=", NIT
DMC2# = (MCF(2) - MCO(2)) / NIT
MC1(2, l) = MCO(2)
MC1(2, NIT + l) = MCF(2)
MC1(1, 1) = MCO(l)
AW11(1) = FUNA#(NISO3, MC 1(2, 1), A01(2), A11(2), A21(2))
T2 = 0
FOR J = 2 TO NIT + l
X = 0
MC1(2, J) = MC1(2, l) + (J - 1) * DMC2#
AW11(J) = FUNA#(NISOS, MC1(2, J), A01(2), A11(2), A21(2))
IF UCASE$(NISO$) = "GAB” THEN
DMC1#(J) = FUNM#(NISOS, AW11(J), A010), A110), A21(1)) - FUNM#(NISOS, AW11(J - 1),
A01(l), A11(l), A21(1))
ELSE
DMCI#(I) = DMC2# * FUNDM#(Z, NISOS, AW110, MC1(2, J), A010, A110, A210)
END IF
X = (W(2) '1‘ DMC2# + W(I) * DMC1#(J))/ (AWE - AW11(J))
T2 = T2 + X
NEXT I
T2=T2*LI(P*A*PS)
PRINT "The shelf life is"; USING TEMPO$; T2
PRINT "The ﬁnal moisture content of component 1 is ="; USING MOISTS; FUNM#(NISOS, AW11(N1T
+ l), A010), A110), A21(1))
CALL PAUSA
ELSE
PRINT "The shelf life is"; USING TEMPOS; T
PRINT "The ﬁnal moisture content of component 2 is ="; USING MOISTS; FUNM#(NISOS, AW11(NIT
+ I), A01(2), A11(2), A21(2))
CALL PAUSA
END IF
GOSUB MENU

STABILITY:

'INPUT PACKAGING, STORAGE ENVIRONMENT AND PRODUCTS DATA
CLS

DIM M0!(2, 10)

PRINT ”Please input packaging data"

INPUT "THICKNESS in u =", L

INPUT "PERMEABILITY COEFFICIENT in gu/m2 day mmHg =", P

INPUT "AREA in m2 =", A

PRINT : PRINT

PRINT "Please input storage environment data”

INPUT ”STORAGE WATER ACTIVITY =", AWE

INPUT "VAPOR PRESSURE AT STORAGE TEMPERATURE in mmHg =", PS

”KEEPER! (nu.

96

PRINT: PRINT

PRINT “Please input products data"

INPUT ”DRY WEIGHT OF COMPONENT l in g =”, W(l)

INPUT "DRY WEIGHT OF COMPONENT 2 in g =”, W(2)

INPUT "INTTIAL MOISTURE CONTENT OF COMPONENT 1 in g/g =”, M010, 0)
INPUT "INITIAL MOISTURE CONTENT OF COMPONENT 2 in g/g =", M0!(2, O)
PRINT : PRINT

LAAJ - _LA LLA_A__LA

rTv—v—vTTrTTv t-

'GET SORPTION ISOTHERM COEFFICIENTS
IF UCASE$(NISO$) = "HE" THEN
FOR I = 1 TO 2
A010) = AOHE1(I)
A110) = All-I510)
NEXT I
END IF
IF UCASE$(NISO$) = "CH" THEN
FOR I = 1 TO 2
A010) = AOCH10)
A110) = AlCH10)
NEXT I
END IF
IF UCASE$(NISO$) = "08" THEN
FOR I = 1 TO 2
A010) 8 AOOS10)
A110) = AlOS10)
NEXT I
END IF
IF UCASE$CNISO$) = "HA” THEN
FOR I a: 1 TO 2
A010) = AOHA10)
A110) = AIHA10)
NEXT I
END IF
IF UCASE$(NISO$) = "GAB” THEN
FOR I = 1 TO 2
A010) = A0610)
A110) = A1010)
A210) :3 A2610)
NEXT I
END IF

'*************

CALCULATE STORAGE STABILITY
'ttttttttttttttttttttttt*********ttttIt*tttttttttttilt*ttttttttttttttttttttttt
DIM M1(l TO 2, 0 TO 10, 1 TO 100), AW1(1 TO 100), DM1#(1TO 100), DM2#(1 TO 100)
DIM U(O TO 10), U1(0 TO 11, 1 TO 100), MF1(1, 0 TO 10)

INPUT “Time interval (days)=", T‘F

DT = TE] 10

U(O) = 0

U10, 1) = 0

M1(l, 0, 1) = M010, 0)

AW1(1) = FUNA#(NISOS, M010, 0), A01(1), A11(1), A21(1))

CLS

PRINT NISOS: CALL PAUSA
PRINT

97

 

TOMATOS = " ##1## 1W ##4##"
PRINT TAB(20); "Storage Stability Data"
PRINT TAB(20);" "
PRINT TAB(IO); "Time, days"; TAB(25); "MC of Component 1"; TAB(45); ”MC of Component 2"
PRINT TAB(IO);" --------" ;TAB(25);" -------- --" ;;TAB(45) "------ ------
FOR N=1 TO 10
U(N) = N * DT

FOR J = 2 TO 100
M10, N, J) = (J - 1) '1‘ .001 + M010, N - I)
AW1(J) = FUNA#(NISOS, M10, N, J), A010), A110), A21(1))
DM1# = .001
IF UCASB$(NISOS) = "GAB" THEN
DM2#(J) = FUNM#(NISOS, AW1(J), A01(2), A11(2), A21(2)) - FUNM#(NISOS, AW1(J - 1), A01(2),
A11(2), A21(2))
ELSE
DM2#(J) = DM1# '1' FUNDM#(I, NISOS, AW10, M10, N, J), A010, A110, A210)
END IF
X = (W(l) '1' DM1# + W(2) '1' DM2#(J)) I (AWE - AW1(J))
U1(N,J)=U1(N,J-1)+X*LI(P*A*PS)
IFU1(N, D) U(hDTIIENEXTTFOR
NEXT J
MF10, N): M10, N, J)
PRINT TAB(IO); USING TOMATOS; U(N); MF1(1, N); FUNM#(NISOS, AW1(J), A01(2), A11(2),
A21(2))
M010, N) = M10, N, J)
AW1(I) = FUNA#(NISOS, M10, N, J), A010), A110), A210))
U1(N + l, 1) = U1(N, J)
NEXT N
CALL PAUSA
GOSUB MENU

FINAL:

CLS

PRINT "BYE11111": CALL PAUSA
END

SUB CHEN (AOCH10, AICH10, CORRCH10)
DIN! expdt AS 180
DIM RH!(2, 20). MC1(2, 20), X1(2, 20), Y1(2, 20), SX1(2), SY1(2), SX21(2), SXY 1(2)
DINI XM1(2), YM1(2), CCCH1(2), N(2)
OPEN ”1501.08!" FOR RANDOM AS #1 LEN = LEN(expdt)
N(l) = 0
FOR K = 1 TO LOF(1) I LEN(expdt)
GET #1, K, expdt
RHKI, K) I: expdtRH
MC 1(1, K) = exdeMC
N(l) =.- N0) + 1
NEXT K
CLOSE #1

OPEN "1802.08!" FOR RANDOM AS #1 LEN = LEN(cxpdt)
FOR K = I TO LOF(1) / LEN(expdt)
GET #1, K, expdt

98

RH1(2, K) = expdtRH
MC1(2, K) = exdeMC
N(2) .-. N(2) + 1

NEXT K

CLOSE #1

%**¥************************************************************************

CALCULATE LINEAR REGRESSION

'***#************#*******¥***************************************************

5X10) = 0: SY10) = 0: SX210) = 0: SXY10) = 0
FORI = 1 TO 2
FOR K = 1 TO N(I)
X10, K) = MC10, K)
Y10, K) = LOG(-LOG(RH10, K) I 100))
3X10) = 8X10) + X10, K)
SY10) = SY10) + Y1(I, K)
SX210) = SX210) + X10, K) * X10, K)
SXY10) = SXY10) + X10, K) ’1‘ Y10, K)
NEXTK
XM10) = 8X10) I N0): YM10) = SY10) I N0)
AlCH10) = (N0) ‘1' SXY10) - 8X10) * SY10)) / (N0) '1‘ SX210) - 8X10) * SX1(I))
AOCH10) = YM10) - AICH10) ‘1‘ XM10)

CCCH10) = 0
FOR K = 1 TO N(I)
CCCH1(I) = CCCH1(I) + ((MC1(I, K) - ((Y1(I, K) - AOCH1(I)) /A1CH1(I))) I MC 10, K)) " 2
NEXT K
CORRCH10) = SQR(CCCH1(I) I N0» '1‘ 100
NEXT I

Wtittttﬁtt¥t¥$t¥t¥¥t$t¥t****tit********************************************

'PRINT RESULTS OUTPUT
'***************************************************************************
FMAT$ = " #1? ##3##!” ##W”
INPUT "Do you want to see the calculated moisture content with the Chen Equation (y/n) ? ", MNB$
PRINT
IF UCASE$(MNB$) = "Y” THEN
FOR I = 1 TO 2
CLS
PRINT ”Chen Equation”
PRINT "------"
PRINT ”COMPONENT ", I
PRINT ”Ace", AOCH1(I)
PRINT 'Al=", AICH10)
PRINT
PRINT TAB(15); "DATA POINT N.", "EXP MC", "CAL MC"
PRINT TAB(15); " ", " ", " "
FOR K = 1 T0 N0)
PRINT TAB(15); USING FMATS; K; MC10, K); (Y!(I, K) - AOCH1(I)) I A1CH10)
NEXT K
PRINT
PRINT "RMS% =", CORRCH10)
PRINT : PRINT

 

CALL PAUSA
NEXT I
END IF
END SUB

SUB CREATE
CLS
DIM expdt AS 150
OPEN "isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
INPUT “Ntnnber of experimental points for component 1 ?", N1
FOR I = 1 TO N1

INPUT "Relative humidity =”; expdtRH

INPUT ”Moisture Content ="; exdeMC

PUT #l, I, expdt
NEXT I
CLOSE #1
OPEN ”is02.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
INPUT "Number of experimental points for component 2 ?", N2
FOR I = 1 TO N2

INPUT "Relative humidity ="; expdtRH

INPUT ”Moisture Content ="; exdeMC

PUT #1, I, expdt
NEXT I
CLOSE #1

CALL PRINTDATA
END SUB

FUNCTION FUNA# (NISOS, MC1, A01, A11, A21)
IF UCASE$(NISO$) = ”HE" THEN
FUNA# = 1 - EXP(-EXP(AO1 + A11 ’1‘ LOG(MC1)))
END IF
IF UCASE$(NISO$) = "CH" THEN
FUNA# = EXP(-EXP(A01 + A11 '1‘ MC!))
END IF
IF UCASE$(NISO$) = ”08" THEN
FUNA# = (EXP(A11 ’1' LOG(MC1) + A0!» I (1 + EXP(A11 '1' LOG(MC1) + A01))
END IF
IF UCASE$(NISO$) = "HA" THEN
FUNA# = EXP(-EXP(AO1 + A11 ’1‘ LOG(MC1)))
END IF
IF UCASE$(NISO$) = ”GAB” THEN
A=A21*MC1:b=AI1*MC1-1:c=AO1* MC!
FUNA#=(-b-SQR(b"2-4* A*c))I(2 *A)
END IF

END FUNCTION

FUNCTION FUNDM# (Q, M305, AW110, MC1, A010, A110, A210)
IF Q = 1 THEN
IF UCASBNSOS) = "HE" OR UCASEMNISOS = "03" OR UCASBMNISO” = "HA" THEN
FUNDM# = EXP((A01(1) - A010)) I A11(2)) * (A11(1)/ A11(2)) '1‘ MC1 A (A110) I A11(2) - 1)
ELSEIF UCASE$(NISO$) = "CH" THEN

100

FUNDM# = A11(1) / A11(2)
END IF
ELSEIF Q = 2 THEN
IF UCASE$(NISO$) = "HE" OR UCASE$(NISO$) = "03" OR UCASE$(NISO$) = "HA" THEN
FUNDM# = EXP((A01(2) - A01(1)) / A11(1)) =1 (A11(2) / A11(1)) =1 MC1"(A11(2)/A11(1)- 1)
ELSEIF UCASE$(NISO$) = "CH” THEN
FUNDM# = A11(2) I A11(1)
END IF
END IF
END FUNCTION

FUNCTION FUNM# (NISOS, AW11, A01, A11, A21)
IF UCASESO‘HSOS) = “HE" THEN
FUNM# = EXP((LOG(-LOG(1 - AWI1)) — A01) / A1!)
END IF
IF UCASE$(NISO$) = "CH" THEN
FUNM# = (LOG(-LOG(AWI1)) - A0!) I A]!
END IF
IF UCASE$(NISO$) = "OS" THEN
FUNM# = (EXP(-AO1 I A11)) '1‘ (AWI1 I (1 - AWI1)) " (1 /A11)
END IF
IF UCASE$(NISO$) = "HA" THEN
FUNM# = EXP((LOG(-LOG(AWI1)) - A0!) I A11)
END IF
IF UCASE$(NISO$) = "GAB” THEN
FUNM#: AWI1/(A21’1‘ AWI1‘1‘ AWI1+ A11 '1' AWI1+ A0!)
END IF

END FUNCTION

SUB GAB (A0610, A1G10, A2610, CORRG10)
DIM expdt AS Iso
DIM RH!(2, 20), MC1(2, 20), X1(2, 20), Y1(2, 20), SX1(2), SY1(2), SX21(2), SXY 1(2)
DIM SX31(2), SX41(2), SX2Y1(2), Fl1(2), F21(2), F31(2), F41(2)
DIM XM1(2), YM1(2), CCG1(2), N(2)
OPEN ”isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(l) = 0
FOR K = 1 TO LOF(1) [LEN(expdt)
GET #1, K, expdt
RH1(1, K) = exdeRH
MC10, K) = exdeMC
N0) =2 N(l) + 1
NEXT K
CLOSE #1

OPEN "is02.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(2) = 0
FOR K = 1 TO LOF(1) I LEN(expdt)
GET #1, K. expdt
RH1(2, K) = expdtRI-I
MC1(2, K) = exdeMC
N(2) = N(2) + 1
NEXT K

101

CLOSE #1

uLALLLALL-l-AJJ-‘Ll.AAA-LIL‘l-l :**; AL-Ll-A-Lﬁjllll-A-llll IA-LA._Ln

trrvfwr-rv—jrf—r—rj.ery—v‘f-rv—u vyj..—..'—..r1rvrrv

CALCULATE QUADRATIC REGRESSION

:7 5 ‘ ‘ . ‘ 1 fi;' 1 if :1”. 2‘. f l:$$* r . . “I!!! ********************************************

 

T1 v11

3X10) = 0: SX210) = O: SX310) = 0: SX41(I) = O
SY10) = 0: SXY10) = 0: SX2Y10) = 0
FOR I = I TO 2
FOR K = 1 TO N(I)
X10, K) = RH10, K) I 100
Y10, K) = (RH10, K) I 100) / MC10, K)
8X10) = 8X10) + X 1(1, K)
SX210) = SX210) + X10, K) * X10, K)
SX310) = SX310) + X10, K) '1‘ X10, K) '1‘ X10, K)
SX410) = SX410) + X10, K) * X10, K) '1‘ X10, K) '1‘ X10, K)
SY!0) = SY10) + Y1(I, K)
SXY10) = SXY10) + X10, K) * Y!(I, K)
SX2Y1(I) = SX2Y10) + X10, K) * X10, K) * Y1(I, K)
NEXTK
F110) = N0) '1‘ SX210) - 8X10) '1‘ 8X10)
F210) 2 N(I) ’1‘ SX310) - 8X10) ‘1‘ SX210)
F310) = F110) '1' (N0) * SX2Y1(I) - SY10) '1' SX210))
F410) = F210) '1' (N0) ‘1‘ SXY10) - SY10) '1' 8X10))
A2610) = (F310) - F410» I (Fl10) * (N0) * SX41(I) - SX210) ’1‘ SX210)) - F210) '1‘ F210»
A1610) = (N(I) ‘1‘ SXY10) - 8X10) '1‘ SY10) - A2610) '1‘ F210)) IF110)
A0610) = (SY10) - A1610) '1‘ 8X10) - A2610) '1‘ SX210)) I N(I)

CCG10) = 0
FOR K = 1 T0 N(I)
CCG10) = CCG10) + ((MC10, K) - X10, K) I (A2610) * X10, K) ’1‘ X10, K) + A1610) '1‘ X10,
K) + A0610)» I MC10, K)) " 2
NEXT K
CORRG10) a SQR(CC61(I) / N0)) '1‘ 100
NEXT I

L:.;.:_A.::_::LAAAAALAAAALAAAAAAAAALAA AALLLLALLA.A.AAA_AA. AJAl‘ll‘llkJLJ‘AA-IIAJ
‘-
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'PRINT RESULTS OUTPUT

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n.A__A_A_4_A ALLJA-LL- :L::::.AL:::A.A_LA*" JJAIAILAL‘ JATA‘
-
1

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Ti-‘i‘Vf’v-‘r- u—rr-wvrw—vwvrr—v-ur-rw-ujuwvrv—TT

FMATS c" ## ##. ##1## #111. ##1##"
INPUT ”Do you want to see the calculated moisture content with the GAB Equation (y/n) ? ", MNBS
PRINT
IF UCASESMNBS) = "Y” THEN
FOR I = 1 TO 2
CLS
PRINT"GAB Equation”
PRINT" .........~
PRINT "COMPONENT" , I
PRINT "Ao=", A0610)
PRINT "A1=", A1610)
PRINT ”A2=", A2610)
PRINT
PRINT TAB(15); ”DATA POINT N. " ,"EXP MC", "CAL MC"
PRINT TAB(15);” , ", "

 

102

FOR K a 1 TO N0)
PRINT TAB(15); USING FMATS; K; MC10, K); X10, K) / (A0610) + A1610) '1‘ X0, K) + A2610)
* X0. K) '1' X0. 10)
NEXT K
PRINT
PRINT "RMS% =", CORRG10)
PRINT : PRINT
CALL PAUSA
NEXT I
END IF

ENDSUB

SUB HALSEY (AOHA10, AIHA10, CORRHA10)
DIM expdt AS 150
DIM RH1(2, 20), MC1(2, 20), X1(2, 20), Y1(2, 20), SX1(2), SY1(2), SX21(2), SXY 1(2)
DIM XM1(2), YM!(2), CCHA1(2), N(2)
OPEN ”isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(I) = 0
FOR K = 1 TO LOF(1) /LEN(expdt)
GET #1, K, expdt
R1110, K) = expdtRH
MC1(1, K) = exdeMC
N0) = N(l) + 1
NEXT K
CLOSE #1

OPEN "is02.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(2) = 0
FOR K = 1 TO LOF(1) [LEN(expdt)
GET #1, K, expdt
RH1(2, K) = exdeRH
MC1(2, K) = exdeMC
N(2) = N(2) + 1
NEXT K
CLOSE #1

 

‘C:::: C i :1: C ilééiiiii ll L T“. Tffiii:-**#*************************#***************

CALCULATE LINEAR REGRESSION

- T72 C : :ﬁfii 1: T i T: I C iii::ifé*!$’1!********************************************

 

8X10) = O: SY10) = 0: SX210) = O: SXY10) = O
FORI = 1 TO 2
FOR K = I TO N(I)
X10, K) = LOG(MC10, K))
Y10, K) = LOG(-LOG(RH10, K) I 100))
8X10) = 8X10) + X10, K)
SY10) = SY10) + Y1(I, K)
SX210) = SX210) + X10, K) ’1‘ X10, K)
SXY10) = SXY10) + X10, K) * Y1(I, K)
NEXT K
XM10) 3 8X10) I N0): YM10) 8 SY10) I N0)
AIHA10) = (N0) '1‘ SXY10) - 8X10) * SY10)) / (N(I) * SX210) - 8X10) * SX1(I))

103

PAOHA10) = YM10) - A1HA10) '1' XM10)

CCHA10) = 0
FOR K = 1 TO N(I)
CCHA10) = CCHA10) + ((MC10, K) - EXP((Y10, K) - AOHA10)) I A1HA10))) IMC10, K)) "
2
NEXT K
CORRHA10) = SQR(CCHA10) I N(I)) * 100
NEXTI

‘**#*¥**************************************It**t8***************************

'PRINT RESULTS OUTPUT

A LIA-LLJ_L4_LA_LJ‘J.LLJJ.I A Lil... A._A_A_.A__A_A AA_A.A_A_A.A_A..A_,AL_A_A__AJ_A_A A.A_A__A_A_A.A_A_A__A. LL.‘ A.A A AAA

1I1

rTwwwwwvrrTer-r—rvr vaTTr-r-v—r—r-v- u-v—wwwwa—rvvuuwwvvw—r-vvw'w'vv-r- urr

FMATS = " ## ##1## ##1##”
INPUT "Do you want to see the calculated moisture content with the Halsey Equation (y/n) ? ", MNBS
PRINT
IF UCASE$(MNBS) = "Y" THEN

FOR I = 1 TO 2

PRINT ”COMPONENT ", 1
PRINT ”Ao=", AOHA1(I)
PRINT "Al=", A1HA10)
PRINT
PRINT TAB(15); ”DATA POINT N.", ”EXP MC", "CAL MC"
PRINTTAB(15);" ", ~ 1, ~ ..... «
FOR K = 1 To N(I)
PRINT TAB(15); USING FMATS; K; MC1(I, K); EXP((Y1(I, K) - AOHA1(1)) I A1HA1(I))
NEXT K
PRINT
PRINT 'RMS% =", CORRHA10)
PRINT : PRINT
CALL PAUSA
NEXT I
END IF
END SUB

 

SUB HENDERSON (AOHE10, AlHE!0, CORRI-IE10)
DIM expdt AS Iso
DIM RH!(2, 20), MC1(2, 20), X1(2, 20), Y1(2, 20), SX1(2), SY1(2), SX21(2), SXY1(2)
DIM XM1(2), YM!(2), CCHE1(2), N(2)
OPEN "isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(l) = 0
FOR K = 1 TO LOF(1) I LEN(expdt)
GET #1, K, expdt
RH1(1, K) = exdeRl-I
MC1(1, K) = exdeMC
N0) = N0) + 1
NEXT K
CLOSE #1

OPEN "isoldat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(2) a O

104

FOR K = 1 TO LOF(1) I LEN(expdt)
GET #1, K, expdt
RH1(2, K) = exdeRH
MC1(2, K) = exdeMC
N(2) = N(2) + 1
NEXT K
CLOSE #1

 

'Jlllilfi;:::i:llli;iil;;$+-¥L;.i ********************************************

'CALCULATE LINEAR REGRESSION

'************************************************************#***************

3X10) = 02 SY10) = 0: SX210) = 0: SXY10) = 0
FOR I = 1 TO 2
FOR K = 1 TO N0)
X10, K) = LOG(MC10, K))
Y10, K) = LOG(-LOG(1 - RH10, K) I 100))
3X10) = 3X10) + X10, K)
SY10) = SY10) + Y10, K)
SX210) = SX210) + X10, K) * X10, K)
SXY10) = SXY10) + X10, K) * Y1(I, K)
NEXTK

XM10) - sx1(1) I N(I): YM!(I) = 3111(1) / N(I)
A1HE1(I) = (N0) =1 SXY10) - sx1(1) * SY10)) / (N(I) * SX210) - sx1a) * sx1(1))
AOHE1(I) .-. YM!(I) - A1HE1(I) * XM1(I)
CCHE1(I) = 0

FOR K = 1 To N(I)

CCHE1(1)= CCHE1(I) + ((MC1(I, K) - EXP((Y1(I, K) - AOHE1(I)) / A1HE1(I))) I MC1(I. K» A

2

NEXT K
CORRI-IE1(I) = 100 * SQR(CCHE!(I) IN(1))

NEXTI

IL-JILLLIIAI.tIlJILIIIIII.LLLIIJ‘IIJIIIIJ-IllllI-A-Ill-Al-ll-IIIIJQIIIIL AAAAA

FMATS = " #11 ##W ##1##”
INPUT "Do you want to see the calculated moisture content with the Henderson Equation (yIn) ? ”, MNBS
PRINT
IF UCASESWBS) = ”Y” THEN
FOR I = 1 TO 2
CLS -
PRINT ”Henderson Equation"
PRINT "-----------”
PRINT "COMPONENT ", I
PRINT ”Aor=", AOHE10)
PRINT "Al=", All-11310)
PRINT
PRINT TAB(15); "DATA POINT N. " ,"EXP MC", "CAL MC"
PRINT TAB(15); .....-...--..-, .«......~, 1-..-..»
FOR K=1 T0 N0)
PRINT TAB(15); USING FMATS; K; MC10, K); EXP((Y 1(1, K) - AOHE1(I)) I A1HE10))

105

NEXT K
PRINT
PRINT "RMS% =", CORRHE10)
PRINT : PRINT
CALL PAUSA
NEXT 1
END IF

ENDSUB

SUBMODIFYCMODS)
DIMexpthSIso
”“**‘ “ ‘ “ ““T' ‘ ‘4***““ ‘ ‘$é*“ L”‘*‘**‘*‘ ‘ ' “ ‘Siiéffi f$#***$$*$2 Z 22 “““

‘
TTTTTVVITT-TT-r—rww- ru-r-

FORMATOS = "# ##.# ##1##"
IF UCASE$(MOD$) = ”C" THEN
INPUT "Do you want to correct data of component 1 ? (Y IN)", qw$
IF UCASE$(qw$) = "Y“ THEN
OPEN "isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
D0
INPUT "Input the data point you want to correct", x1
GET #1, x1, expdt
INPUT "Relative humidity ="; exdeRH
INPUT ”Moisture Content ="; expdt.MC
PUT #1, x1, expdt
INPUT ”Do you wish to correct more data points ? (YIN)"; ans$
LOOP UNTIL UCASE$(ans$) = ”N”
CLOSE #1
ELSEIF UCASE$(qw$) = "N" THEN
PRINT "You'll ccnect data of component 2"
OPEN "iso2.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
DO
INPUT "Input the data point you want to correct", :12
GET #1, x2, expdt
INPUT "Relative humidity =”; exdeRI-I
INPUT ”Moisture Content ="; exdeMC
PUT #1, x2, expdt
INPUT "Do you wish to correct more data points ? (YIN)"; ansS
LOOP UNTIL UCASE$(ans$) = ”N"
CLOSE #1
END IF
END IF

IF UCASE$(MOD$) = "A" THEN
MUT "Do you want to add data to component 1 ? (YIN) ", Y$
IF UCASE$(Y$) = "Y" THEN

OPEN "isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)

I = LOF(1) I LEN(expdt)

DO
INPUT "Relative humidity ="; exdeRH
INPUT "Moisture Content ="; exdeMC
I=I+l

106

PUT #1, I, expdt
INPUT ”Do you wish to add more data points ? (YIN)"; ansS
LOOP UNTIL UCASES(ans$) = ”N”
CLOSE #1
ELSEIF UCASE$(Y$) = 'N" THEN
PRINT "You'll add data to component 2"
OPEN ”is02.dat” FOR RANDOM AS #1 LEN = LEN(expdt)
I = LOF(1) I LEN (expdt)
DO
INPUT ”Relative humidity ="; exdeRH
INPUT “Moisture Content ="; exdeMC
I=I+1
PUT #1, I, expdt
INPUT "Do you wish to add more data points ? (YIN)”; ans$
LOOP UNTIL UCASE$(ans$) = "N"
CLOSE #1
END IF
END IF

W***‘************************************$***##3##**************************

IF UCASESMODS) = 'D" THEN
INPUT "Do you want to delete data from component 1 ? (YIN) ", YS
IF UCASE$(Y$) = ”Y” THEN ’
OPEN "isol.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
OPEN "temp.dat" FOR RANDOM AS #2 LEN = LEN(expdt)
DO
INPUT ”Input the data point you want to delete", ND
FORI = 1 TO ND - 1
GET #1, I, expdt
PUT #2, I, expdt
NEXT I
FOR I = ND + ITO LOF(1) / LEN(expdt)
GET #1, I, expdt
IX = I - l
PUT #2, IX, expdt
NEXT I
INPUT "Do you wish to delete more data points ? (YIN)"; ansS
LOOP UNTIL UCASE$(ans$) = ”N"
CLOSE #1
CLOSE #2
SHELL "DEL isol.dat”
SHELL 'REN temp.dat isol.dat"
ELSEIF UCASE$(Y$) = "N" THEN
PRINT ”You'll delete data from component 2"
OPEN "iso2.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
OPEN "temp.dat" FOR RANDOM AS #2 LEN = LEN(expdt)
DO
INPUT ”Input the data point you want to delete". ND
FOR I = 1 TO ND - 1
GET #1, I, expdt
PUT #2, I, expdt
NEXT I
FOR I = ND + 1 TO LOF(1) / LEN(expdt)
GET #1, I, expdt

107

IX =1 - 1
PUT #2, IX, expdt
NEXT I
INPUT "Do you wish to delete more data points ? (YIN)"; ansS
LOOP UNTIL UCASE$(ans$) = ”N”
CLOSE #1
CLOSE #2
SHELL “DEL is02.dat"
SHELL ”REN temp.dat iso2.dat"
END IF
END IF

W*¥*******¥*********************iklk13************IHIIit*************************

CALL PRINTDATA
END SUB

SUB OSWIN (AOOS10, AlOS!0, CORROS10)
DIM expdt AS Iso
DIM RH1(2, 20), MC1(2, 20), X1(2, 20), Y1(2, 20), SX1(2), SY1(2), SX21(2), SXY1(2)
DIM XM1(2), YM!(2), CCOS1(2), N(2)
OPEN "isol.dat” FOR RANDOM AS #1 LEN = LEN(expdt)
N(l) = 0
EUR K = 1 TO LOF(1) [LEN(expdt)
GET #1, K, expdt
RH1(1, K) = expdtRH
MC1(l, K) a exdeMC
N(l) = N(l) + 1
NEXT K
CLOSE #1

OPEN "isoldat" FOR RANDOM AS #1 LEN = LEN(expdt)
N(2) = 0 '
FOR K = 1 TO LOF(1) I LEN(expdt)
GET #1, K, expdt
RH1(2, K) = expdtRH
MC1(2, K) = exdeMC
N(2) = N(2) + 1
NEXT K
CLOSE #1

A4;AA4.AA.A__A.A_A.A.AAAALAAAAAAAJALALLLLJALAALLLAJLLLLLAALJ A__A LJA-‘ACAJJJ-lL-L-LJ‘DLLL

vt-wj—vrvrr—rirvwvr-rrI—r-r-vvrr-rrwv v‘v I‘vv-fr uTrTv rv-rIVTT-vw-uur1vvvvvwvv‘v‘

CALCULATE LINEAR REGRESSION

”AALAJJAJAALA IJALL-LALALLAALAJAJ‘JAI A AJA AAA_LAAA._A.4..A__AA.AL_AA A AAALJAAALAALLAAAJ

Tw—ruvrvr-w—v—w r—wvrvar—va—vw'vwr—v—v—w-vw-v—Vr'v rku—r-r. ITTT‘ 'TT'I-‘y .- u—vwa—r—ry—r—vauw—r—v

8X10) = 0: SY10) = 0: SX210) = 0: SXY10) = 0
FOR I = 1 TO 2
FOR K = 1 TO N(I)

X10, K) = LOG(MC10, K))
Y10, K) = LOG(RH10, K) I 100 I (1 - RH10, K) / 100))
8X10) = 8X10) + X10, K)
SY10) = SY10) + Y10, K)
SX210) = SX210) + X10, K) '1‘ X10, K)

108

SXY10) = SXY10) + X10, K) * Y10, K)
NEXTK

XM10) = 8X10) I N0): YM10) = SY10) I N0)
AIOS10) = (N(I) '1‘ SXY10) - 8X10) * SY10)) I (N0) * SX210) - 8X10) '1‘ SX!0))
AOOS10) = YM10) - AIOS10) * XM10)
CCOS10) = 0
FOR K = 1 TO N(I)
CCOS10) = CCOS10) + ((MC10, K) - EXP((Y 10, K) - AOOS10)) I AIOS10)» I MC10, K)) A 2
NEXT K
CORROS10) = 100 ‘1' SQR(CCOS10) / N0))
NEXTI

'***************************************************************************

'PRINT RESULTS OUTPUT
'*************************************$*************************************
FMATS = " #111 ##W ##1##?"
INPUT "Do you want to see the calculated moisture content with the Oswin Equation (y/n) ? ", MN’BS
PRINT
IF UCASESCMNBS) = "Y" THEN
FOR I = 1 TO 2

CLS

PRINT ”Oswin Equation”

PRINT" ..........-"

PRINT"COMPONENT ", I
PRINT "Ao=", AOOS10)
PRINT "Al=", AIOS10)

PRINT
PRINT TAB(15); "DATA POINT N. " ,"EXP MC", ”CAL MC"
PRINT TAB(15);" ", " ", "

 

FOR K=1 TO N(I)
PRINT TAB(15); USING FMATS; K; MC10, K); EXP((Y 10, K) - AOOS10)) I AIOS10))
NEXT K
PRINT
PRINT 'RMS% =", CORROS10)
PRINT : PRINT
CALL PAUSA
NEXT I
END IF

ENDSUB

SUB PAUSA

DO

LOOP UNTIL (INICEYS <> "")
END SUB

SUB PRINTDATA
CLS

DIM expdt AS 150
FORMATOS = "#13 ##.# ##.W”

OPEN ”isol .dat" FOR RANDOM AS #1 LEN: LEN(expdt)
LOCATE 5, 15: PRINT "Sorption data of component 1"
LOCATE 6,15:PRINT"

 

109

PRINT TAB(15); "n§"; TAB(25); "Rel.Humidity"; TAB(40); "MoistContent"
FOR I = 1 TO LOF(1) /LEN(expdt)

GET #1, I, expdt

PRINT TAB(15); USING FORMATOS; I; exdeRH; exdeMC

NEXT I

CLOSE #1

CALL PAUSA

OPEN "isoZ.dat" FOR RANDOM AS #1 LEN = LEN(expdt)
CLS

LOCATE 5, 15: PRINT "Sorption data of component 2"
LOCATE 6, 15: PRINT " "

PRINT TAB(15); "n§"; TAB(25); 'Rel.Humidity"; TAB(40); "MoistContent"
FOR I = 1 TO LOF(1) / LEN(expdt)

GET #1, I, expdt

PRINT TAB(15); USING FORMATOS; I; exdeRH; exdeMC
NEXT I

CLOSE #1

CALL PAUSA

 

ENDSUB

APPENDIX C

COMPUTER SIMULATED RESULTS

110

Table C.1 - Components moisture content as a function of time for different components

weight ratio. Simulated results using set of data A from Table 2

Components Moisture Content, g/g
Run 1 Run 2

 

 

Cereal

Raisin

Cereal

Raisin

 

0.0900

0.0770

0.0900

 

0.1153

0.0875

0.1179

 

0.1362

0.0965

0.1414

 

0.1520

0.1035

0.1600

 

0. 1680

0.1095

0.1761

 

0.1816

0.1145

0.1898

 

0. 1926

0.1185

0.2009

 

0.2037

0.1225

0.2122

 

0.2122

0. 1265

0.2237

 

0.2208

0.1295

0.2324

 

 

 

0.2295 _ ._

 

04235 _

 

f 720.412

 

 

 

Table C.2 - Components moisture content as a function of time for different storage water

111

activities. Simulated results using set of data B from Table 2

Components Moisture Content, g/g

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Run 1 Run 2 Run 3

Time, days Cereal Raisin Cereal Raisin Cereal Raisin
0 0.0770 0.0900 0.0770 0.0900 0.0770 0.0900
30 0.0875 0.1179 0.0865 0.1 153 0.0855 0.1 127
60 0.0965 0.1414 0.0935 0.1335 0.0915 0.1283
90 0.1035 0.1600 0.1005 0.1520 0.0975 0.1440
120 0.1095 0.1761 0.1055 0.1653 0.1015 0.1546
150 0.1145 0.1898 0.1095 0.1761 0.1055 0.1653
180 0.1 185 0.2009 0.1135 0.1870 0.1085 0.1734
210 0.1225 0.2122 0.1175 0.1981 0.1115 0.1816
240 0.1265 0.2237 0.1205 0.2065 0.1145 0.1898
270 0.1295 0.2324 0.1235 0.2150 0.1165 0.1953
300 0.1325 0.2412 _ 0.1255 00.228 0.85 0.2009

 

 

 

112

Table C.3 - Components moisture content as a function of time for different packaging

banier properties. Simulated results using set of data C from Table 2

Components Moisture Content, g/g
Run 2

 

 

Raisin

Cereal

Raisin

Cereal

 

0.0900

0.0770

0.0900

 

0.1335

0.0875

0.1179

 

0.1653

0.0965

0.1414

 

0. 1898

0.1035

0.1600

 

0.2094

0.1095

0.1761

 

0.2266

0.1145

0.1898

 

0.2412

0.1185

0.2009

 

0.2532

0. 1225

0.2122

 

0.2654

0. 1265

0.2237

 

0.2747

0. 1295

0.2324

 

 

 

0.2841

 

.1325

 

0.2412

 

 

 

Table C.4 - Components moisture content as a function of time for different total weight to

113

packaging area ratio. Simulated results using set of data D from Table 2

 

 

Components Moisture Content, gﬁ

 

 

 

 

 

 

 

 

 

 

 

 

 

Run 1 Run 2 Run 3
Time, days Cereal Raisin Cereal Raisin Cereal Raisin
0 0.0770 0.0900 0.0770 0.0900 0.0770 0.0900
30 0.0875 0.1 179 0.0855 0.1 127 0.0845 0.1101
60 0.0965 0.1414 0.0925 0.1309 0.0905 0.1257
90 0.1035 0.1600 0.0975 0.1440 0.0965 0.1414
120 0.1095 0.1761 0.1035 0.1600 0.1005 0.1520
150 0.1145 0.1898 0.1075 0.1707 0.1055 0.1653
180 0.1185 0.2009 0.1115 0.1816 0.1095 0.1761
‘ 210 0.1225 0.2122 0.1155 0.1926 0.1125 0.1843
240 0.1265 0.2237 0.1 185 0.2009 0.1 155 0.1926
270 0.1295 0.2324 0.1225 0.2122 0.1185 0.2009
300 0.13 __ 0.2412 _ 0.245 _ 0217___ ~_- 0.1215 __ 0.2094

 

 

 

 

 

 

APPENDIX D

PACKAGING MATERIALS CHARACTERIZATION

114

1. Film Permeability

Table D.1 - Materials water vapor transmission rate (g/m2 day) at 25 °C. Infrared sensor

method

0") _

1.304
1.304
1.296
1.301

  
  
   

    

 

 

 

 

(*)

polyester water vapor transmission rate with water = 2.088 g/m2 day
polyester water vapor transmission rate salt solution = 1.552 g/m2 day
then ARH = 1.552 / 2.088 = .743

115

 

 

 

 

2.0
‘ —-— OPP]
‘ —*— 0992 ‘
j —o— OPP3 _
w 1.5- —O— PEI ‘
. a —D— PEZ I .
'5 1 —A— PE3 A
3.? 1 O
'51; . + PFJbarrierl '
'g 1.0- —+— PEIbarrierZ o
3 ' + PFJbam’er3 .
A: " I
o I
3 . ' /
an /
0.5' : /
. /.
‘ / r 7 /
d " - —— '/
. 5”
00 4 . . . . . ﬁ, . . f .
o 5 1o 15
time,days

Figure D.1 - Pouches with desiccant weight gain over time for packaging permeance

determination by the gravimetric method

116

Table D.2 - Experimental data for packaging permeance determination by the gravimetric

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pouch Sample Pouch Dimensions, 810pe, g/day Correlation Coef.
. cm i .
.- .- j - 2--.-.. 23---. ,
OPPl 14.5 x 15.5 0.0540 9 0.9999
OPP2 15.0 x 14.0 . 0.0482
OPP3 { 15.0 x 14.5 ; 0.0510
PEl ' 15.5 x 14.0 : 0.1004
PE2 15.0 x 16.0 0.1144
PE3 18.0 x 15.5 , 0.1284
PE/barrierl 14.5 x 16.5 9 0.0236
PEbarrierZ 15.0 x 14.5 ; 0,0214
PE/barrier3 15.0 15.5 f 0,0232
0.010
. —""" OPP4
. —:-— 0905
+ P134
‘ —0— PBS
no .
5* —ﬂ— PElbam'er4
on 0'005' —A'— PE/bam’erS
E I
.30
0
3
§
0
8
0..
-0.005 1 1 r ﬁ I v u r v
0 5 10 15

time, days

Figure D.2 - Empty pouches weight gain over time for packaging permeance

determination by the gravimetric method

117

Table D3 - Materials water vapor transmission rate (g/m2 day) at 25 °C. Gravimetric
method

,__—,_ _ . .______ _. _—

—

 

 

 

 

118

2. Materials Identiﬁcation

 

Figure D.3 - OPP ﬁlm observed at microscope with phase contrast (x 560)

The outer layers were tentatively identiﬁed as PP-PE copolymers.

Total thickness: 25 um

119

"

,_.._,_, .,... aw." nWW—nww Wm
M “.0023“th 0 *‘ ’"' WmMuah . -.

MkW-m

 

Figure D.4 - PE] barrier ﬁlm observed at microscope with phase contrast (x 560)

This material was found to be composed by two layers of PE, being one white pigmented,
and one layer of a third material, possibly EVOH.

Total thickness: 65um

First PE layer thickness: 30pm
Interior PE layer thickness: 250m
Third layer thickness: 10pm

APPENDIX E

MOISTURE SORPTION ISOTHERM DATA

120

Table E.l - Experimental Moisture Sorption Isotherrn of Cereal, at 25 °C

       

— 1 _f I; "
___—.-Sv-

 

 

 

 

 

 

 

 

 

 

 

 

Table E.2 - Experimental Moisture Sorption Isotherrn of Powder Chocolate, at 25 °C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

121

Table E.3 - Experimental Moisture Sorption Isotherm of Raisin, at 25 °C

 

- 9.5

0.064
0.207
0. 109
0.044
0.120
0. 102

 

 

 

 

 

 

 

 

 

 

 

 

 

 

APPENDIX F

DETAILED DATA OF VALIDATION EXPERIMENTS

 

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mmmam $38 $98 ogdm 03.3 woﬁmm mmodm Evdm emf; 25.2 Bod mm
90va 59.3 camm 95m 353 maxim mmzm 82m 368 mwudm 2.3L 8
mmmdw 30mm 08.9.. 80? 39mm 58.8 25mm 33.; 25.2 52: 8

85mm Seam 20mm 2.4.? :m.mm dem coadn omadm $21.8 mvvd mm

18.9 ommdm mgdm 89S www.mm ocmdm 22m mamdm End cm

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