SIMULATION OF NUTRIENT STABILITY _
IN DRY FOODS DURING STORAGE '

Thesis. for the Degree of M. S.
MICHIGAN STATE 'UNIVERSIIY
HADI KARIA‘ PU RWADARIA

1977 ‘ '

e
.- -..O-.—~—~m”g'.m ”m

 

III/IIIIIIIIIIIIIIIIII/II/IIIIII/III/II/I -

3 1293 10523 3273 .

NIICU Ig'uu elatc
Umvemty

 

ABSTRACT
SIMULATION OF NUIRIENT STABILITY

IN DRY KIDS DURING SIORAGE

By
Hadi Karia Purwadaria

Determination of the vitamin content of dry foods during storage
is essential for the processor to accorrplish label claims. The
objectives of this study were 1) to establish a mathemtical model
describing the rate of vitamin degradation (k) as a function of product
water activity (aw) and 2) to develop a canmter-aided predict ion of
vitamin degradation and moisture uptake in dry foods during storage.

A model food systen was used in this study with ascorbic acid
as the observed nutritional quality index. Shelf—life tests were
conducted at a temperature of 30°C, and at 10, 40, and 85% RH using

cardboard boxes with waxed—paper liners as the packaging material .

Hadi Karia Purwadaria

The results showed that the relationship between k for ascorbic
acid and aw is linear at 10, 20, and 30°C. The predicted results
provided good agreement with the experimental data. The similation

is applicable to predict the vitamin degradation for a one-year period.

Approved by:

DK-Aflss

 

Major Professor
and Department Chairman

SIMULATICN OF NUTRIENT STABILITY

IN DRY KIDS DURING STORAGE

By

Hadi Karia Purwadaria

A THESIS

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

MASTER OF SCIENCE

Agricultural Engineering Department

1977

AW

Thebauthor is deeply indebted to Dr. Dennis R. Heldman, Professor
and Chairman of the Agricultural Engineering Department, for suggesting
the thesis topic and his continuous support, interest and guidance
throughout the course of this work.

Sincere appreciation is extended to Dr. James R. Kirk, Professor
in the Department of Food Science and Human Nutrition, for his valuable
advice at various stages of the study. The author is also grateful to
Dr. Fred W; Bakker-Arkema (Professor in the Agricultural Engineering
Department) and Mr. Lloyd E. Lerew (Instructor in the Agricultural
Engineering Department) for their critical review and suggestions to
the manuscript.

Special thanks go to Mr. Daniel B. Dennison, fellow graduate
student, for his help in the laboratory experiments and conducting the
vitamin assays.

To the~Government of Indonesia which Opens the chance for the

author to continue his study, he expresses his gratitude.

ii

TABLE OF CDN'I‘ENTS

AW .

LIST OF TABLES

LIST OF FIGURES
IN'IRGDIIITIO‘I

REVIEW OF LITERATURE

The Influence of Water Activity, Moisture Content
and Temperature on Ascorbic Acid Degradation .

The Effect of Sorption Hysteresis on the Degradation
of Ascorbic Acid . .

The Influence of Oxygen on Ascorbic Acid Degradation

The Influence of the Packaging Film on Vitamin Degradation .

Canputer Simulations and Mathematical Models for
Food Quality . . . . . . .

WICAL GIVSIDERATICNS .

The Kinetics of Vitamin Degradation. .

The Role of Oxygen and Moisture Vapor Transfer into
the Package . . .

The Influence of Tenperature on the Rate Constant

'lhe Influence of Temperature and Relative Humidity
Fluctuation on the Rate Constant . .

EXPERIMENTAL CONSIDERATIONS .

Materials .
Procedures .

Measurenent of the moisture transfer coefficient
Measurement of the rate of ascorbic acid degradation
as a function of water activity. . .
Shelf-life test for the model food system .
Measurement of the product moisture content
Measurement of the ascorbic acid degradation

Descr ipt ion of Computer Pr0gram

iii

00 63630"! CO

15

15

15
16

18

22
23

23

24
25

25

RESULTS AND DISCUSSIONS .

Measurement of Moisture Transfer Coefficient.
Water Diffusion into the Product.

Influence of relative humidity .
Influence of tenperature
Influence of packaging film
Vitamin Retention During Storage
The relationship between the rate constant (k)
and water activity ( ) .
Verification of couputer prediction of vitamin

retention during storage .
Influence of tenperature

Computer Simulation of Vitamin mgradation
Influence of various input parameters
Influence of independent variables .
Influence of storage tenperature and relative

humidity fluctuation . . . . .
CXZNCIUSICNS .
SIEGESI‘ICNS FCR FURTHER STUDY
W

iv

Page
27

27
28

28
3O
32

37

37

43
44

49

49
57

57
63

65

70

Table

LIST OF TABLES

The rate of ascorbic acid degradation in some food
products .

Half-life for ascorbic acid degradation in desorption
(DJ) and adsorption (Ill) system (Lee and Labuza, 1975)

Ascorbic acid degradation in wheat flour and seaweed

Conposition of model food systen

Moisture transfer coefficient (K) for waxed paper with
and without cardboard box at various relative
humidities

Various input parameters for the canputer sinulation

Page

.28

Figure

10

11

12

13

LIST OF FIGURES

'Ihe carputer simulation flow sheet at a constant
temperature . . . . . . . .

The computer simulation flow sheet to establish the
relationship of k as a function of aw at any
temperature . . .

Computer simulation flow sheet at fluctuating
temperature and relative humidity

Computer predict ion and experimental data for the
product moisture content during storage at various
relat ive humidities . . . . .

Computer prediction of the model food systen moisture
content during storage at various texperatures

Energy constant (c) of BET equation as a function of
temerature . . . . . .

Monmolecular moisture content (Wm) of BET equation
as a function of temperature. . . .

szputer prediction of the model food systen moisture
content during storage at various packaging film
thicknesses . . . . . . .

Cerputer prediction of the model food systen moisture
content during storage at various moisture transfer
coefficients, K (gI-IZO-cm/m2 -hr-mmflg).

The rate constant of ascorbic acid degradation (k) as
a function of a.w at 10°C . . .

The rate constant of ascorbic acid degradation (k) as a
function of aw at 20°C .

The rate constant of ascorbic acid degradation (k)
as a function of aW at 30°C. . . .

The rate constant of ascorbic acid degradation (k) as
a function of aW in Lee and Labuza‘s model food systen

vi

.17

.19

.21

.29

.31

.38

.39

.41

Figure

14

15

16

17

18

19

20

21

22

23

25

26

27

Sorption isotherms of model food system I and model
food system II . . . . .

Computer prediction and experimental data for ascorbic
acid retention in the model food system during storage
at 10%RH . . . . . . .

Computer prediction and experimental data for ascorbic
acid retention in the model food system during
storage at 40%RH . . . .

Computer predict ion and experimental data for ascorbic
acid retention in the model food system during
storage at 85% RH . . . .

'Ihe Arrhenius curves for ascorbic acid degradation
in the model food system packed in large cans

Computer prediction of vitamin retention in a food
product during storage at various relative
humidities (see Table 6) .

Computer prediction of vitamin retention in a food
product during storage at various temperatures
(see Table 6) . . . .

Computer prediction of vitamin retention in a food
product during storage at various initial
moisture contents (see Table 6).

Computer predict ion of vitamin retention in a
food product during storage at various moisture
transfer coefficients (see Table 6).

Computer prediction of vitamin retention in a food
product during storage at various packaging
film thicknesses (see Table 6).

Computer prediction of vitamin retention in a food
product during storage at various product mass
per unit packaging surface area (see Table 6)

Computer predict ion using dt and a w as independent
variables corpared to experimental data for
ascorbic acid retention in a food product during
storage at 40% RH and 30°C . . .

Computer prediction of vitamin retention, ware—house
temperature and relative humidity during 1975
in Lansing, Michigan . . .

Computer prediction of product moisture content, and
ware—house temperature and relative humidity during
1975 in Lansing, Michigan .

vii

Page

42

45

46

47

48

51

52

53

55

61

62

A".

thl

MI

185

me:

ad

Get
II‘I‘C

35

fOr

INTRODUCTION

Dry foods can deteriorate during storage due to oxidative
mechanisms resulting in nutrient degradation, off-flavor development,
and color changes. Accurate determination of the vitamin content of
dry foods during storage is essential to provide the processor with
the assurance of meeting label claims.

Shelf—life tests for measurement of vitamin degradation are
time consuming and costly. Computer simulation of vitamin destruc—
tion in dry foods represents an alternative approach to shelf-life
testing which is worth considering. The development of acceptable
computer simulation requires the incorporation of experimental
kinetics data which describe the rate of vitamin degradation as a
function of water activity and temperature along with appropriate
moisture and.oxygen transport coefficients for the product packaging
material.

In this study. a computer simulation to predict the moisture
gain and the vitamin degradation in dry foods during storage was
developed. The simulation is useful for the manufacturer in selecting
product packaginglmaterial and product storage conditions as well
as meeting the labeled nutrition claim of the product.

Ascorbic acid was selected as the index of the nutrient quality
for the purpose of this research because of its labile natureicompared
to the other vitamins in foods. A model food system was used to provide

better control of the uniformity of initial food composition and

vitamin concentration. The mathematical model obtained in this study
is for ascorbic acid in the model food system. However, the proce-
dure described for establishing the mathematical model and for developing
the computer simulation can be applied to other vitamins in dry foods
with minor modifications.

The specific objectives of this research were:

1. To examine the rate of moisture adsorption as a function
of storage relative humidity and moisture transport coefficient of
the packaging film.

2. To develop a mathematical model to describe the rate of
vitamin degradation as a function of product water activity.

3. To develop a computer—aided prediction of ascorbic acid
degradation in the model food system during storage.

4. To examine the application of computer simulation to pre-
diction of ascorbic acid stability in dry foods during storage under
various storage conditions, various characteristics of the food

product and various packaging materials.

ad
the
01

111c:

I‘m

mug
of a

mis

Siam

REVIEW (F LITERATURE

The Influence of Water Activity, Moisture Content
and Temperature on Ascorbic Acid Degradation

Several researchers have recently conducted experiments on ascorbic
acid degradation in different kinds of food products. VOjnovitch and
IPfeifer (1970) carried out research on the stability of ascorbic acid
in wheat flour, corn-soya—milk (CSM), and mixed infant cereal. Lee
and Iabuza (1975) worked on a model food system composed of corn oil,
glycerol, cellulose, ascorbic acid, and water (model food system I).
Kirk _e_t_a_1_. (1976) used a different model food system containing pro-
tein, fat, carbohydrate, reducing sugar, sucrose, and salt (model food
system II) into which ascorbic acid was added.

All of the above studies showed that the degradation of ascorbic
acid at various water activities and storage temperatures follows
the first order kinetic reaction. Table 1 illustrates that the rate
of ascorbic acid degradation increases (half-life decreases) with
increasing water activity (and thus moisture content), and with
temperature.

Based.on the activation energy (E) data, Lee and Labuza (1975)
concluded that there was no change in the mechanism of the oxidation
of ascorbic acid as a function of water activity in intemediate
unnaturetfoods.

Kirk g§_§1, (1976) observed that the total ascorbic acid.(TAA)

stability is a function of storage temperature as well as aw.

4

T'able 1. The rate of ascorbic acid degradation in sole food products.

 

 

Product Meisture a T, Half-life, E,
Content W 0C days Keal/mole
g HZO/lOO
g solids
Mixed inf t 5.0 - 45 23.8 14.8
cereal a 37 45.3
26 103.2
7.0 - 45 14.3 12.5
37 25.0
26 47.5
10.7 - 45 10.2 4.9
37 15.0
26 19.4
Model food - 0.32 45 4.2 21.7
system I b) 40 6.9
35 12.2
23 52.5
- 0.51 45 1.7 20.8
40 3.8
35 5.9
23 23.3
- 0.67 45 1.2 17.9
40 2.0
35 3.5
23 10.6
- 0.75 45 0.6 17.1
40 1.0
35 1.4
23 4.4
- 0.84 45 0.2 18.3
40 0.3
35 0.6
23 1.9
Model food — 0.24 30 39 15-9
systen II C) 20 73
10 187
.. 0.40 30 22 17.6
20 54
10 165
_ 0.65 30 6 24.0
20 48
10 139

 

a>Vanovitch and Pfeifer (1970)
ID)nee and Labuza (1975)
C)Kirk et a1. (1976)

None of the researchers, previously mentioned, established the

relationship between the rate of ascorbic acid destruction and aW

The Effect of Sorption Hysteresis
on the Degradation of Ascorbic Acid

Bach (1974) and Lee and Labuza (1975) found a hysteresis effect
on the sorption isotherm of model food system II and model food
system I, respectively.

A greater loss of ascorbic acid was reported on the desorption (DI/I)
loop than on the adsorption (DH) loop of the model system. Table 2
shows the half-lives for the adsorption system are larger than those
for the desorption system (Lee and Labuza, 1975) . The possible reason
for this phenomena is that the desorption system has a higher moisture
content, and the degradation occurs rapidly due to lower viscosity

and possible dilution in the aqueous phase.

Table 2. Half—life for ascorbic acid degradation in desorption (DVI)
and adsorption (DH) systems (Lee and Labuza, 1975).

 

 

 

 

 

 

aW Half—life , days
23 CC 35 0c 40 0C 45 OC
DM DH DM DH DM DH DM DH
0.32 37.7 52.5 10.1 12.2 5.9 6.9 3.5 4.2
0.51 20.3 23.3 5.7 5.9 2.8 3.8 1.5 1.7
0.67 7.2 10.6 2.5 3.5 1.2 2.0 0.9 1.2
0.75 2.8 4.4 0.8 1.0 0.5 1.0 0.2 0.6

0.84 1.0 1.9 0.3 0.6 0.18 0.3 0.1 0.2

 

6

The Influence of Oxygen on Ascorbic Acid Degradation

It is generally known that the presence of oxygen increases the
rate of ascorbic acid degradation, but no specific information of the
role of oxygen on the kinetics or mechanism of ascorbic acid oxidation
is available.

Labuza and 'I‘annenbaum (1972) discussed the results of Jensen (1967)
and Vojnovitch and Pfeifer (1970) as shown on Table 3. It was suggested
that the mechanism predominating at high aW might be nonenzymatic
browning, while the low activation energy at low aW and the loss of
ascorbic acid below the monolayer moisture content might possibly be

due to other oxidation mechanisms.

The Influence of the Packaging Film
on Vitamin Degradation

A packaging film separates an internal environment wherein a
food product containing vitamins is stored, from an external environ-
ment . Differences in oxygen partial pressure and water activity between
the internal and external environment result in the potential transfer
of oxygen and moisture through the packaging film.

The outside environment, the barrier properties of the packaging
material, and the inside environment all influence the vitamin
stability of the product (Karel, 1972a; Heldnan. 1974).

Karel gt__a_1_. (1959) studied the transfer rate of moisture vapor
through several types of packaging film at various conditions of relative
humidity and temperature. The results showed a linear relationship for

both transfer rate versus relative humidity and transfer rate versus

7
temperature. An in-depth investigation resulted in a polynomial
relationship between water vapor transfer and water activity (Karel

et a1. , 1971).

Table 3. Ascorbic acid degradation in wheat flour and seaweed.

 

 

Product Moisture aw T, k, days‘1 E,
Content , OC Kcal / mole
g 1120/ 100
g solids
Seaweed a) 11.1 — 25 6.6 x 10‘3 8 8
10 3.8
4 2.3 2
17.6 — 25 1.54 x 10:3 10.5
10 5.78 x 10
4 2.89 2
33.3 — 25 7.21 x 10‘ 22.0
10 6.93
4 4.6
.4
Wheat b) — 0.25 45 4.28 x 10 11.0
flour 37 2.86
26 1.43 _3
— 0.55 45 1.86 x 10 16.0
37 1.29 _4
26 5.7 x 10_2
— 0.65 45 1.97 x 10_3 22.3
37 7.0 x 10
26 2.1

 

a)Jensen (1967)
b)Vojnovitch and Pfeifer (1970)

Qiast and Karel (1973) pointed out that the quality degradation of
food products is not only affected by moisture transfer into the
package but by oxygen transfer as well. The moisture and oxygen
transfer expressed as optimal permeability of packaging film, which is
the ratio of oxygen permeability to moisture permeability (KOZ/KW),
were found as a function of the bulk density of the food product and

the outside relative humidity.

8
The barrier properties of packaging films are usually expressed
as the moisture transport coefficient and oxygen transport coefficient,
which are moisture and oxygen permeability per unit film thickness per

unit area of the package, respectively (Heldman, 1974).

Computer Simulations and Matheratical
Models for Food Qlality

Kwolek and Bookwalter (1971) developed a mathematical model to

predict storage stability of food as follows:

Y=a+tf(Ti)+u (l)
where:

Y: a measure of product quality

a: initial product quality measurerent

t: time

f(Ti): the time rate change in Y
associated with the temperature

u: random error because of the deviation of
observed Y

The functions f(Ti) considered are:

f(Ti) = m + KTi (2)
f(Ti) = m TiK (3)
mi) = m/(K—Ti) (4)
mi) = m exp(-K/Ti> (5)
f(Ti) = m KT1 (6)

where:

m, K: constants

9

The functions applied to the mathematical model were equation (4)
and (5). Equation (5) which is the Arrhenius model predicted flavor
and peroxide value of the food product satisfactorily.

Karel (1972b) predicted the storage life of foods based on infor-
mation gained by experimentally determining the properties of the food,
the kinetics of food deterioration , and the package properties . The
deterioration mechanism limiting shelf life of a food product and its
dependence on the environmental parameters can be described by the
following mathematical function:

dD/dt = f (RH, P02, T) (7)
where:

D: deteriorat ive index

t: time

RH: equilibrium relative humidity

P02: oxygen pressure

T: temperature
Changes in water activity can be related to the environmental parameters

and the food and package properties:

a=f(a0,t,RH,k1...kn,T...) (8)
where:

a: water activity in the food at any time

a0: 1n1t1al a

k1 . . .k : constants characterizing sorptive and diffusional

properties of the food and the package

Mizrahi et a1. (1970) developed a simulation of browning in freeze-—
dehydrated cabbage stored in packages with film having different

permeabilities to water vapor. The corputer program was based on the

line

of p
(1819

rem.

10

browning reaction kinetics, the moisture transfer characteristics of the
packaging films, and the product moisture contents.

Simon _e_1_;_a_1_. ( 1971) presented a computer prediction describing
the oxidative deteriorat ion of freeze-dried shrimp. Organoleptic
deterioration was correlated with absorption of oxygen and with loss of
carotenoid pigment .

Labuza fl. ( 1972) established a matheratical model to calculate

moisture gain by a dehydrated food in a package:

ln(me-mi)/(me-mc) = (HBO/xxA/wSxpO/mt (9)
where:
me: moisture content of food as predicted by the

isotherm equation if exposed to the external

package relative humidity

mi: initial moisture content of the food
mc: final moisture content

kHZO: permeability of the film

x: film thickness

A: area of the film

wS: weight of dry solids enclosed

p0: saturation vapor pressure of water at a given
constant temperature, T

b: barometric pressure

The equation was derived by assuming the sorpt ion isotherm to be a
linear function of relative humidity.

Qlast M. ( 1972) developed a mathematical model for oxidation
of potato chips. The rate of oxygen uptake for potato chips was
determined as a ftmct ion of oxygen partial pressure, equilibrium

relative humidity, and extent of oxidation. Qiast and Karel ( 1972)

“DEN

oxygen and by textural changes due to moisture adsorption.

where :

11

developed a computer simulation for potato chips which deteriorate by

two mechanisms simultaneously, i.e. , by oxidation due to atmospheric

The rate of

accumulation of oxygen in the package, the rate of oxidation and the rate

of change of moisture content were expressed as dimensionless variables:

 

 

 

 

 

if}? = W (1 ‘ Y1) ‘ 15395301000 (dd?) (10)

gig: [m'm + 7134:7131sz ' W] [$133052 . Yl.P020] (11)
EMAX

d—a‘? = Li?“ - m. LANA"? ATE“ [Rte - Y3] <12)

Y1 = P02/P020

Y2 = EXT/FMAX

Y3 = RH/RHMAX

P02: oxygen partial pressure inside package

P020: outside oxygen partial pressure

EXT: extent of oxidation

EMAX: maximum allowable extelt of oxidation

RHMAX: maximum allowable equilibrium relative humidity of

the product

K02: oxygen permeability

T0: reference temperature

V: total headspace volume

w: weight of product

KW: water vapor permeability

PWS: pressure of saturated water vapor

P1,2,3,4,5:

constants

12
The rate of change of moisture was found using the Kuhn isotherm for
the moisture-aW relationship which was considered as the best fit for
potato chips (Quast and Karel, 1972).

Later, Quast and Karel ( 1973) used this computer simulation to
calculate optimal permeabilities for minimizing the deterioration due
to these two interacting mechanisrs. The influence of packaging film
size, bulk density of the product, and initial condition of oxygen
concentration and relative humidity were studied.

Further developments have been concerned with nutritional
stability in foods. Based on data published by Vojnovich and Pfeifer
(1970), Wanninger (1972) established a matheratical model to predict

the ascorbic acid stability during storage:

1nk=-E/RT+a1nH20+b (13)
where:

k: rate constant of ascorbic acid degradation

E: activation energy

R: gas law constant

T: absolute temperature

H20: moisture content

a,b: constants
The model assumes that moisture content will modify the rate constant
(k), but does not have a significant influence on the activation energy
E while the oxygen content is constant. It was stated that the storage
humidity might affect the rate of degradation.

Heldman (1974) proposed a basic computer simulation for storage
conditions which influence vitamin stability. The mathematical model

for the rate constant k as a function of oxygen and water activity is

as follows:

The ma
transp

descri

Tiere-

13

k = f(pi.ai) (14)
where: h

pi: oxygen partial pressure inside the package

ai: water activity inside the package

The oxygen uptake by the reaction, which results in vitamin loss,

affects the oxygen partial pressure inside the package:

i i ,
p = p0 exp(-k t) (15)
where:
pg: initial oxygen partial pressure inside the package

k': oxygen uptake rate constant

t: time
The water activity inside the package is influenced by the moisture
transport through the packaging film. The moisture transport can be
described as:

dM/dt = <K/x><A/wsnps<a°-ain (16)
where:

dM/dt: the rate of moisture transport through the packaging

film
K: film transfer coefficient
A: packaging surface area
a0: water activity outside the package
x: film thickness
wS: mass of food product inside the package
pS: absolute pressure of air in the storage

The water activity inside the package can be calculated by the

Brunauer, Emmett, and Teller (BEI‘) equation (Bach, 1974):

14

ai/M (l-ai) = 1/wmc + (c-l) ai/wmc (17)

M: equilibrium moisture content of the food product

wm and c: BET constants of food product

Singh and Heldman (1975) presented a simulation of ascorbic acid
degradation in a liquid infant food formula. The oxygen uptake by the
liquid food was studied at different light intensities and effective
depths of light penetration into the food product .

lee ( 1976) established a computer simulation to predict ascorbic
acid degradation in canned torato juice during storage. The effect
of pH, copper ion, and storage terperature were the parameters in

the mathemtical model .

THEORETICAL ONSIDERATIO‘IS

The Kinetics of Vitamin Degradation

For the purpose of this study, model food system II was prepared

using ascorbic acid destruction as the quality index. In the presence

of oxygen, the reaction scheme is as follows:

 

Ascorbic acid + Degradation products (18)

The reaction undergoes first order kinetics (Kirk M. ,
1976). so that the reaction rate can be described as:

dC/dt = - k c (19)
where:

C: concentration of the vitamin

t: time

k: first order rate constant
Integrating and substituting the initial condition C = CO at t = t0

yields :

C = C0 exp (—kt) (20)

The Role of Oxygen and Moisture Vapor Transfer
into the Package

The other factors influencing the vitamin degradation rates at
a constant terperature are oxygen and moisture. Assuming oxygen is a
non—limiting factor, then k is only a function of water activity inside

the package (a1):
15

16

k = f (ai) (21)

In this study, the relationship between the rate constant (k) and
water activity for each temperature condition was obtained from the
results of shelf-life tests.

The change of water activity inside the package due to increasing
moisture content of the model food system was calculated from the BET
equation ( 5). The BET constants were found experimentally by Bach ( 1974)
using the Paltnikar and Heldman method (1971).

The increasing moisture content of the model food system was
obtained from equation (16) assuming all the moisture transport
through the packaging film was absorbed by the model food system.

The computer simulation flow sheet at a constant tenperature

can be expressed as shown in Figure 1.
The Influence of Temperature on the Rate Constant

The degradation rate of the vitamin at any temperature at a

constant aW can be expressed by the well-known Arrhenius equation:

k = k0 exp (—E/RT) (22)
or:
In R = (-E/RT) + 1n k0 (23)
where:
k0: Arrhenius constant, time-1
E: activation energy, cal /mo1e

gas constant, 1.987 cal/OK—mole

absolute temperature, 0K

3'? F?

17

 

Start
t=0

I

Input: C . dt. M . a0. 1). x, Wm, 0, K. A, 1;]

 

 

 

O 0

Al

7

 

 

 

i i _ i
at/Mt(1-at) - l/wmc + (c—1)at/wmc

 

 

 

 

 

 

 

 

= Ct exp (-kt dt)

7

dM = (K/x) (A/ws) pdt (a0 - a

 

l Ct+dt

 

 

i
t)

 

 

 

 

 

 

 

 

 

Figure l. The computer simulation flow sheet at a constant tenperature.

18

Based on equation (23), the Arrhenius curve can be plotted using
the results of shelf-life tests for the rate constant of ascorbic acid
degradation at various temperatures.

By obtaining the Arrhenius equation for three or more different
water activities, a computer simulation using a least square fitting
method can be developed to calculate k at various aW values and to
establish the relationship of k as a function of aW at any terperature.
The computer simulation flow sheet for k as a linear function of aW is
illustrated in Figure 2.

This program, incorporated into the previous computer simulation
(Figure l) as a subroutine, makes the simulation capable to predict

the ascorbic acid degradation at any temperature .

The Influence of Temperature and Relative Humidity
Fluctuat ion on the Rate Constant

The product temperature and moisture content are influenced by
the changes of environmental temperature and relative humidity during
storage and transportation in the marketing channel .

Lee (1976) developed a computer simulation to calculate the

temperature fluctuation throughout a year using the Fourier series:

f(x) = (ac/2) + :1 (an cos(mrx/L) + 5n sin(nmx/L)) (24)
where:

a0 = (l/Ln qi‘mn ax)

an = (l/L) (£:f(x) cos(nmx/L) dx)

hn = (1/L) (£:f(x) sin(nmx/L) dx)

L: limit of cycle

x: time, days

19

 

 

Start

I

Input: kO(N), E(N), aw(N). T

 

 

 

 

 

 

 

 

A
r

 

k(N) = ko(N) exp (-E(N)/RT)
I

Y

 

 

 

 

 

 

 

 

 

 

 

mmnawm) - (MN) zaw‘NI)
C1 = N
z<aw(N))2 - (zawmnn2
N
‘32 = (MN) - c1 (Xawmnnn/N

 

 

 

N: number of Arrhenius equation

1,2,3, . . . , N
C1: slope of the linear curve for k-—f(aw)
C2: intercept of the linear curve

Figure 2. The corputer simulation flow sheet to establish the relation-
ship of k as a ftmction of aW at any temperature.

20

Since relative humidity is a function of temperature and dew point,
it is possible to predict the relative humidity fluctuation throughout
a year using the same equation.

The computer simulation flow sheet in Figure 1 can be modified to
predict the vitamin retention in the product as the temperature and
relative humidity fluctuates during a year. The modified flow sheet

is shown in Figure 3.

21

 

Start
t=0

I

Input: C6, dt, Mb, p, x, Wm, c, K, A, ws

1 i _ i
at/Mt(l-at) - 1/Wmc + (c—1)at/wmc

 

 

 

 

 

 

 

 

 

 

 

 

 

Ir

Predict T using the Fourier series
equation (24)

I

Establish k=f(a:) using the subroutine
in Figure 2

 

 

 

 

 

 

 

 

 

 

 

_ i
kt — f(at)
I

Ct+dt = Ct exp (-ktdt)

 

 

 

 

 

 

 

 

 

I.

Predict RH using the Fourier series
equation (24)

I

a: = RH/lOO

 

 

 

 

 

 

 

 

 

I

 

dM = (K/xxA/wsnpdt (a: - ab

 

 

 

 

 

t+dt' t

 

 

 

 

Figure 3. Computer simulation flow sheet at fluctuating tenperature and
relative humidity.

n1

8.

P};

(31)]

EXPERIMENTAL CONSIDERATIONS
Materials

A model food system was prepared in order to get an accurate and
uniform initial vitamin concentration. Its corposition was modeled
after cereal products and illustrated in Table 4. The preparation
method described by Kirk ial. (1976) was followed. The ingredients
were dry-mixed by a ribbon blender and water was added to obtain 40%
total solids. The slurry was heated to 60°C and honogenized in a
Manton—Gaulin horogenizer at 103.4 x 105 Newton/m2 gage (1500 psig)
in the first stage and 34.5 x 105 Newton/m2 gage (500 psig) in the
second stage. Ascorbic acid was added to the model as USP reduced
ascorbic acid at a level of 25% RDA per 100g of model system on a
dry weight basis. Then, the model system was freeze—dried in a Virtis
Model FFD 42 WS Freeze-Dryer, frozen at a tenperature of -40°C
and dried at 110°C and an absolute pressure of 5 qu.

The measurerent of the packaging film moisture transfer coefficient
was carried out with anhydrous calcium chloride as the desiccant in
8-mesh ganulars which were free of 30-mesh fines as suggested by
ASI‘M Standard E 96 (1975).

To find the relationship between k and ai, a relatively large can of
303 x 406 size was used for a 15g sample in order to establish the

condition where oxygen is a non-limiting factor.

23

Table 4. Composition of model food system.

 

 

Conponent Percent
Protein 10 . 2
Fat 1 . 0
Carbohydrate 76 . 6
Reducing Sugar 5 . l
Sucrose 5 . 1
Salt 2.0

 

To determine the water diffusion into the product and to verify the
conputer simulation results, 21g (3/4 oz.) breakfast cereal boxes
containing a waxed paper film were used. The boxes were supplied by

General Foods, Post Division, Battle Creek, Michigan.

Procedures

Measurement of the moisture transfer coefficient

 

The anhydrous calcium chloride was reactivated by heating at 200°C
for one hour. Fifty grams of desiccant were placed in the waxed paper
film liners with and without cardboard boxes. The packages were stored
for seven days in cubicles at 30°C and 10, 40 and 85% relative humidities.
The cubicle conditions were controlled by a humidistat. The mass
difference after seven days was recorded as moisture transfer through

the packaging film.

24

Measurement of the rate of ascorbic acid degadation as a function of
water activity

 

 

Thin slabs of the model food system were equilibrated to 0.10,
0.24, 0.40, 0.50 and 0.65 water activities in an equilibrium chamber.
The air condit ion in the equilibrium chamber was regulated using an
Aminco—Aire unit which maintains constant humidity and tenperature.

Ten grams of equilibrated samples were put into 303 x 406 cans.
The cans were sealed and stored in cubicles at 10, 20 and 30°C. The
ascorbic acid degradation history was recorded for each water activity
until the half-life was reached, and the rate constant of vitamin
degradation was calculated by equation (20). The functional relation-
ship between the rate constant and water activity was then obtained by

plotting the rate constant at each water activity.

Shelf—life test for the model food system

 

Fifteen grams of the model food system was packed into the boxes
containing waxed paper film liners. The waxed paper was heat-sealed.
The boxes were stored in cubicles at 30°C and 10, 40, and 85% RH. The
moisture content on a dry weight basis was recorded until the equilibrium
condition was achieved to get the water adsorption history during storage.
The ascorbic acid degradation history was also recorded until the half-

life was achieved.

Measurement of the product moisture content

 

The moisture content was determined as described by Kirk et a1. (1976).

Samples of 2g were dried in a vacuum oven at pressure less than

25

4.6 x 103 Newton/m2 and at the same temperature as the product was stored.
A cold trap was inserted between the vacuum oven and the vacuum pump to
maintain a terperature differential between the inside and outside of
the vacuum chamber in order to aid in the water vapor transfer from the
chamber. The samnples were dried until they achieved constant weight.
Then, dried air at a rate of 15—20 ml/min was admitted into the chamber

to expell the remaining water vapor.

Measurerent of the ascorbic acid degradation

 

The ascorbic acid retained during the storage was determined by
the semi-automated O-phenylenediamine microfluorometric procedure
as described by Kirk and Ting (1975). The total ascorbic acid was
measured as dehydro ascorbic acid following oxidation of reduced
ascorbic acid with 2, 6 dichloroindophenol . Dehydlo ascorbic acid
was detected by fluoronepheloneter as the fluorescence product after

react ion with O-phenylenediamine.

Description of Computer Program

Based on the flow sheet presented previously, a computer program
was developed in order to predict:
1. The moisture content of the food product at
any time during storage.
2. The water activity inside the package.
3. The vitamin degradation at any time during

storage .

26

The input necessary to operate the program is as follows:

1.

2.

6.

BET constants of the food product.

Initial moisture content, initial vitamin concentra-
tion, and the mass of the food product.

Relationship of the rate constant of vitamin degradation
as a function of product water activity.

Moisture transport coefficient, film thickness, and
surface area of the package.

Temperature, relative humidity, and absolute pressure
of the air in the storage.

Time increment .

The conputer simulation was used to evaluate the influence of the

following operational parameters:

1.
2.

Initial moisture content.

Moisture transfer coefficient and film thickness
of the packaging material.

Mass of product per unit surface area of the
packaging material.

Storage temperature and relative humidity.

RESULTS AND DISIUSSIO‘IS

Measurenent of Moisture Transfer Coefficient

The experimental moisture transfer coefficients at various
relative humidit ies for waxed paper with and without cardboard boxes
are presented in Table 5. These data indicate that the cardboard box
does not have a significant influence on the moisture transfer. This
might be attributed to the sealing of the cardboard box which does not
maintain a different enviroment inside the box when corpared to the
outside storage condition .

The moisture transfer coefficient increases as the vapor pressure
differential increases. However, the increasing value which is in the
range of 0.25—0.83 x 10"5 gHzO—cm/mz-hr—rman has a small influence
in calculating dM in equation (16). If the average of all K values in
Table 5 is taken, the error is equal to £0.36 x 10-5 gHzO-om/mz-hr-nmflg
for K values from 10 to 85% RH. The average value, which is 7.25
x 10'5 gHzO-om/mz-hr—mmHg, was used as the moisture transfer coefficient

in the computer simulation.

27

Ni

III“

Inf

Inc.

00m1

(16);;

fire

attr

28

Table 5. Moisture transfer coefficient (K) for waxed paper with and
without cardboard box at various relative humidities.

 

 

Waxed Paper Vapor Pressure K
Differential ( O—cm)/(m2—
(% RH) r-mmHg)
Without cardboard box 10 7.00 x 10’5
40 7.25
85 7.67
With cardboard box 10 6.75 x 10'5
40 7.13
85 7.58

 

Water Diffusion into the Product

Influence of relative humidity

 

The results of computer prediction and experimental data on the
increases of moisture content of the model food systems stored at 10,
40, and 85% RH and 30°C are shown in Figure 4. The predicted moisture
contents are in good ageement with the experimental data. The standard
deviations between the conput er-predicted results and experimental data
are 0.22, 0.20, and 0.78 gH20/100g solids at 10, 40, and 85% RH,
respectively. However, at 85% RH, the computer results predicted
lower moisture contents than the experimental data. This may be
attributed to the BET equation used in the computer simulation to
predict water adsorpt ion .

The BEl‘ model assured that (1) the heat of adsorption for the first
layer is constant, (2) the heat of adsorption in all layers above the
first is identical and equal to the latent heat of condensation, and

(3) adsorption occurs only on specific sites. Unfortunately, these

in;\ F\ C

s.».

— p.51 u a-F»...

r?~._#ruwnéd

Moisture content, gHzO/loog solids

29

 

 

 

 

 

 

24
T 30°C
M0 0.3%
0
20+ 0 o e ‘
o O
0 RH 85%
o O
16*-
O
O O
12 " O 0
8r-
RH 40%
. D D. . I . I
C]
4 ..
. V .V v V V v RH 10%
V V
V
0 . n n J n
0 4 8 12 16
Time, weeks
Figure 4. Computer prediction and experimental data for the

product moisture content during storage at various
relative humidities.

3O

assumptions are not entirely true. Labuza (1968) stated that the BET
equation usually holds only between water activities of 0.1 to 0.5,
arguing that the water surface area in most foods (100 to 250 mz/g)
is much larger than nitrogen surface area (0.2 to 2.0 mz/g) which is
the predicted adsorption BET value.

The BET model neglects horizontal interactions between the molecules
within the layer and vertical interactions, normal to the surface. At
higher humidities as many layers are adsorbed, the horizontal forces
between the adsorbate molecules can scarcely remain negligible because
their average separation is much less than a single diameter (Greg
and Sing, 1967).

Figure 4 also illustrates that a longer time is required to
reach the equilibrium condition at 85% Hi. Since the water adsorption
occurs in the capillary region at this high humidity, the completion
of water condensation in the pores of food may take more time than

in the mononolecular and multilayer region.

Influence of temperature

 

The influence of temperature on the moisture gained by the model
food system is illustrated in Figure 5. At lower tenperature conditions,
the food product will adsorb water at a slower rate. The product will
tend to achieve a higher equilibrium moisture content at the lower
temperature. This is indicated by the sorption isotherm curves at
various terperatures in Appendix 1.

The sorption isotherm curves at 20, 25, 30. and 37°C were established
by Bach (1974). The sorption isotherm curve at 10°C was developed by

measuring the moisture content of the model food system at various water

Moisture content, g water/100g solids

10

 

31

 

40%
1%

635

 

 

1 1 L I

0 2 4 6 8 10
Time, weeks

Figure 5. Computer prediction of the model food system
moisture content during storage at various
temperatures.

32

activities using the same method described by Bach (1974). The energy
constant (c) and the monorolecular moisture content (wm) were
calculated for each temperature (Appendix 2) and were plotted as a
function of tenperature (Figures 6 and 7).

The energy constant (C) decreases from 10°C to 22.5°C and then
increases to 37°C following a polynomial function, while the mono-
molecular moisture content (wm) decreases as an exponential function.

The adjusted curves were developed based on the modification of
c and wm at 30°C in order to get acceptable agreement between the
counter-predicted moisture content and experimental data. The adjusted
functions were used in the simulation to calculate the c and wm of the

model food system at any terperature.

Influence of packaging film

 

Film thickness and the moisture transfer coefficient (K) of the
package will affect the water diffusion to the product. An increase
in the film thickness will cause slower moisture transfer into the
package (Figure 8) so that the water diffusion into the product will
be reduced. An increase in the moisture transfer coefficient results
in greater moisture transfer rates into the package (Figure 9) and the

food product will reach equilibrium moisture conditions more rapidly.

Energy constant , c

33

 

 

 

  

 

 

80
c = 266 . 7-28 . 31T+1 .0431‘2- .0123’1‘3
(' = 116.8—12.68T+.482T2-.0057T3
70.- q
60F-
50b
40"
‘\
BOI— \
\
20..
/ I,
O
\ IL adjusted point
10- \ /
\d
M adjusted curve
0 n 1 I l l
10 20 30 40 SO 60
Temperature, °C
Figure 6. Energy constant (c) of BET equation as a function

of temperature.

Monauolecular moisture content, wm

(D

 

 

é
II

.0922 eXp(-.025T)

 

 

m
wm = .0868 exp(-.025T)

" O
L.
p

1 1 1 1 l
O 10 20 30 4O 50

Temperature, °C

Figure 7. Monomolecular moisture content (w ) of BET

equation as a function of tenpera't‘ure.

 

Moisture content, g water/100g solids

10

35

 

 

 

 

 

 

RH 40%
30°C
M0 1%
r
z I d _
’ f ‘ fl
’ I
/
/ ’ 0.009 cm film thickness
/ / --— 0.018 cm film thickness
I
// —--. 0.027 an film thickness
, L 1 n i
0 2 4 6 8 10
Time, weeks
Figure 8. Ccmputer prediction of the model food system

moisture content during storage at various
packaging film thicknesses.

$3“:va H~Xu~\.~$.u-3 Ha

. w :4». “w :A v. .

LL: grid—CS.

Moisture content, g water/ 100g solids

 

 

10
. RH 40%
T 30°C
a
MO In
8 .-
6 b

    

_s
K: 7.25 x 10 5

—--— K: 14.50 x 10‘5
---—-K: 21.75 x 10‘

 

l l

0 2 4 6 8
Time , weeks

-
P

Figure 9. Computer prediction of the model food system
moisture content during storage at various
moisture transfer coefficients, K (gH20-cm/m2

-hr-ang) .

 

10

37

Vitamin Retention During Storage

The relationship between the rate constant (k) and water activity (am)

 

The results from the experiments indicated that the rate constant
(k) increases as a linear function as water activity (aw) increases for
large cans (303 x 406 can) at 10, 20 and 30°C (Figures 10-12). Vitamin
retention data for small cans ('I‘DT can), provided by Kirk _e_t__ai. ( 1976),
were plotted in the same figures. All the experiments take into account the
range of 0.1 to 0.65 water activities which include only the monomolecular
and multilayer region and not the capillary region.

lee andlabuza (1975) presented the half-life of ascorbic acid
in another model food system at various water activities and temperatures.
Calculating and plotting the rate constants (k) against aW gave the
relationship of k with aW as illustrated in Figure 13. The rate constant
(k) begins to increase exponentially as aw reaches the range of 0.6 - 0.7.
This point is in the capillary region rather than in the nultilayer
region, while the starting point is 0.32 aw which is, most likely,
in the nultilayer region. ()1 the other hand, the model food system
used by lee and labuza (1975) has a different canposition (10g corn oil,
40g glycerol, 50g cellulose, 30mg ascorbic acid, and water) than the
model food system used in this study (Table 4).

lee and Labuza's model food system shows sorption isotherms of
type III (Figure 14) while the sorption isotherms of the model food
system used in this experiment indicates type II or a signoid isotherm
according to the classification by Brunauer 313311 . (1940). A type III
isothenn is characterized by its being convex to the water activity

axis (Gregg and Sing, 1967) . This suggests that the attractive forces

The rate constant (k), x 10 days

38

 

 

 

 

0.7
O
0.6.. .
large can
0.5..
O 0
$1113.11 can
0.4 r-
O
0.3 i-
2
o—-o k = (0.279+0.360 aw).10"
2
0—0 k = (0.307+0.557 aw).10‘
0.2 L 1 4 l
0 0.2 0.4 0.6 0.8

Water activity

Figure 10. The rate constant of ascorbic acid degradation

(k) as a function of aW at 10°C.

1.0

The rate constant (k), x 10 days

39

 

 

 

 

 

2.5
2'07-
1.5-
1.0..
0.5- (D 2
o——o k = (0.436+1.620 aw).10'
__2
0—4 k'= (0.583+2.049 aw).10
O L L I l
0 0.2 0.4 0.6 0.8 1.0

water activity

Figure 11. The rate constant of ascorbic acid degradation

(k) as a function of aw at 20°C.

The rate constant (k), x 10 days

10

4O

 

 

 

 

2

O-—O k = (0.039+7.779 aw).10-

2

H k = (l.073+7.635 aw).10_

large can
snall can
L L l l

0 0.2 0.4 0.6 0.8 1.0

Water activity

Figure 12. 'lhe rate constant of ascorbic acid degradation
(k) as a function of aw at 30°C.

l

2

days

The rate constant (k), x 10

41

 

140

120 r-

g

20-

 

l

 

35°C

 

23°C

 

J J

 

0 0.2 0.4 0.6 0.8 1.0

Figure 13.

water activity

The rate constant of ascorbic acid
degradation (k) as a function of
in Lee and Labuza'SImodel food sys GHL

Moisture content, gHZO/ 100g solids

20

16

12‘

42

 

      
   
  

.. type III isotherms
(temperature not statem

r

.. type II isotherms

(30°C)

H model food system I
(Lee and Labuza's)

O——-O model food system II

(experiment)

 

 

l I L

0 0.2 0.4 0.6 0.8

Water activity

Figure 14. Sorption isotherms of model food system I and
model food system II.

 

1.0

43

between the molecules of water are greater than the attractive forces
between the water vapor as adsorbed gas and the model food system as
adsorbent. (11 the contrary, a type II isotherm occurs when the attractive
forces between the molecules of water are smaller than the attractive

forces between the water vapor and model food system.

Verification of computer prediction of vitamin retention during storage

Computer simulation, as illustrated in Figure 1 (flow chart in
Appendix 3), was developed using the mathematical model of k as a function
of aw. The carputer-predicted ascorbic acid retention in the model
food systen (Figure 15-17) gives good agreement with the experimental
data. The standard deviation of camarison between the computer-
predicted results and experimental data are 5.84, 4.15, and 6.58% at
10, 40, and 85% RH, respectively.

The canputer result is slightly slower in ascorbic acid degradation
than the experimental data for 10% RH. This may be due to the diffusion
effect of water which can occur at the monarolecular region. Duckworth
3131. (1963) showed that the water soluble canpounds have substantial
mobility and may be diffused out of the specific sites in cells and
react with each other in this low water activity. If this is true,
the ascorbic acid as a water soluble ccmpound may also diffuse out
of the specific sites and be exposed to oxygen. Hence, it might
accelerate the ascorbic acid degradation .

Sane scattering in the experimental data might be due to lack
of uniformity of the surface area of the waxed paper bag because

folding and heat sealing were done manually.

44

At 85% RH, the canputer predict ion results indicated higher
ascorbic acid retention compared to the experimental data. This might
be due to several factors. First, the mathematical model of k as a
flmction of aW was developed only for the range of 0.1 to 0.65 water
activities. Thus, k for 0.85 aW is obtained by extrapolating the
unthenatical model which probably results in some error.

Secondly, the BET equation is not satisfactory to predict water
adsorption in the capillary region as discussed previously. It
predicted lower moisture contents than the experimental data, hence,
the predicted vitamin degradation was also lower.

lee and Labuza (1975) postulated the effect of decreasing
viscosity at higher water activities which may cause the exponential
rate of ascorbic acid degradation in their model food system. The
decreasing viscosity will increase mobilization of the reaction
species in the aqueous phase so that the ascorbic acid and metals
were more easily mobilized.

Influence of tanperature

 

The influence of temperature on the rate constant of ascorbic acid
degradation is expressed in the Arrhenius equation at various water
activities as illustrated in Figure 18 for 303 x 406 cans. The
activation energy (E), calculated fran the function, is 15.1, 16.4,
and 19.6 kcal/mole for aw of 0.10, 0.40, and 0.65, respectively.

The objective of developing the Arrhenius curves is to determine
a mathanatical relationship among k, aw, and tarperature. Using

the Arrhenius equations, k for various aw at any temperature can be

‘70

 

Ascorbic acid retention,

45

 

lOr

computer prediction

 

o 0 experimental data

 

 

 

! J l 1
0 4 6 8 10
Time, weeks

Figure 15. Oxmputer prediction and experimental data for
ascorbic acid retention in the model food systen
during storage at 10% RH.

Ascorbic acid retention. %

 

46

 

—— computer prediction

 

 

 

- O 0 experimental data
1 J_ l J
0 4 6 8 10

Time . weeks

Figure 16. Computer prediction and experimental data for
ascorbic acid retention in the model food system
during storage at 40% RH.

0'
IO

Ascorbic acid retention,

 

47

 

_. commuter predict ion

 

 

,.. o 0 experimental data
1 L n 1
2 4 6 8 10

 

Time, weeks

Figure 17. Computer prediction and experimental data for
ascorbic acid retention in the model food system
during storage at 85% RH.

l

2

days

The rate constant (k). x 10

10

0.8

0.6

0.4

0.2

0.1

48

 

 

    

 

 

_ o——00.1 aw: 1n k = ~7585/T + 21.053

_ H04 aw: In R = —8241/T + 23.929
p

V—V0-65 aw: 1n k = -9862/T + 29.724
P
b
r
1 1 1 1
3.2 3.3 3.4 3.5 3.6 3.7
I/T, x 10'

Figure 18. The Arrhenius curves for ascorbic acid degradation

in the model food system packed in large cans.

49

obtained and later a mathematical model can be established to express
the relationship between k and aw by utilizing the least square fitting
method.

Omputer Simulation of Vitamin Degradation

Influence of various input parameters

 

The computer simulation developed in this study is based on (1) the
first order kinetic reaction between ascorbic acid and oxygen, and (2)
the assmption ttet oxygen is not a limiting factor. Thus, the
simulation can be used to predict the vitamin degradation in dry foods
during storage when those assmptions are met.

The output from the carputer simulation is in the form of product
moisture content and vitamin retention in the food product as a
function of time. The simulation can be used to evaluate the effect
of packaging film materials, the characteristics of food products, and
the storage environments. The parameters involved as input data and
an example of each quantity and unit are listed in Table 6. An
illustration of some of the cmputer predictions with various input
parameters indieates the value of the simulation approach.

The influence of varying RH (Figure 19) with all the other input
conditions held constant at the values. given in Table 6, shows that
the vitamin degrades more rapidly as RH increases.

Figure Z) illustrates the influence of temperature with all other
parameters held constant . As temperature decreases, the vitamin

retention in the food product will increase.

50

Table 6. Various input parameters for the computer simulation.

 

 

Parameter Quantity and Unit
Storage temperature affects: At 30°C:
1. energy caistant (c) l. c = 25
2. monarolecular moisture 2. wm = 4.1
content (w ) -
3. k as a metion of aw 3. = (1.073+7.765aw).10 2
4. absolute pressure 4. pS = 33.26 mmHg
Storage relative humidity (RH) 40%
Initial moisture content (M O) 1%
Product mass per unit of 0.088 g/cm2
packaging surface area (wS/A)
Packaging film thickness (x) 0.009 cm
Moisture transfer coefficient (K) 7.25 x 10-5 gHzO—am/mz—hr
—mmHg

 

An increase in the initial moisture content (Figure 21) provides
more rapid vitamin degradation if the other parameters are held constant.
Figure 22 illustrates the influence of moisture transfer
coefficient (K). The destruction of vitamin occurs more rapidly at

higher K values.

A larger packaging film thickness (Figure 23) will give higher
vitamin retention, but at a certain point increasing packaging film
thickness will not give an effective increase of vitamin retention.
The influence of product mass per unit packaging surface area

(Figure 24) is quite similar to packaging film thickness.

Vitamin retention, 5'6

20

10

 

51

 

 

 

 

\ \ 40% RH
‘ \
. \. \
\ \
\\ \
. 85% \
RH \
P \\ \
\ \
\\‘
L. \‘
\\
.- \\
\\
\\
, \
I I I
0 4 6 8 10
Time, weeks
Figure 19. Computer prediction of vitamin retention in a

food product during storage at various relative
humidities (see Table 6).

Vitamin retention , 9'0

100

8

5.1
O

52

 

 

b
p

 

 

Figure 20.

2 4 6 8 10

Computer predict ion of vitamin retention in a food
product during storage at various temperatures
(see Table 6) .

Vitamin retention, %

53

 

 

 

1%MO
———- 2%M

—-o——--— 3% M0

 

 

L 1 1
0 4 6 8 10
Time, weeks
Figure 21. (Imputer prediction of vitamin retention in a

food product during storage at various initial
moisture contents (see Table 6).

%

Vitamin retention.

 

 

 

5
K= 7.25 x 10‘5
— — — K=l4.50 x 10’5
—.-—.— K=21.75 x 10'

 

 

 

1 u 1 I n
2

4 6 8 10
Time, weeks

Figure 22. Computer prediction of vitamin retention in a
food product during storage at various moisture
transfer coefficients (see Table 6).

C.‘
10

Vitamin retention.

55

 

 

 

—-— 0.009 cm film thickness
— -— 0.018 on film thickness
21» """"'" 0.027 cm film thickness

 

 

l l I

 

0 2 4 6 8 10
Time. weeks
Figure 23. Computer prediction of vitamin retention in a

food product during storage at various packaging
film thicknesses (see Table 6).

Vitamin retention. %

 

 

 

 

 

 

)-
r
.. 0.088 g/cm2 (wS/A)
._..._. 0.282 g/em2 (wS/A)
...-_.- 0.623 g/cm2 (wS/A)
1 1 l J
0 2 4 6 8 10

Time . weeks

Figure 24. Computer prediction of vitamin retention in a
food product during storage at various product
mass per unit packaging surface area (see Table 6).

57

Influence of independent variables

The ccmputer simulation developed so far uses the time increment
as the indepeident variable (Appendix 3). Another possibility is to
use the inside water activity increment as the independent variable
(see flow sheet in Appendix 4). Figure 25 exhibits both of the computer
prediction results at 40% RH.

The advantage of using the water activity increment as the indepen-
dent variable is the possibility of applying the trapezoidal rule,
as illustrated in Appendix 4, which theoretically gives better
predictions. 0n the other hand, the accuracy in the carputer simulation
using the time increment as the independent variable could be
increased if a smaller time increment is used. The simulation using
the water activity increment as the independent variable has a
disadvantage. As the vapor pressure differential between outside and
inside water activity decreases and approaches zero, dt (Appendix 4)
approaches infinity. This limits the prediction of the vitamin
degadation after food precinct achieves the moisture equilibrium where

the vapor pressure differential is zero.

Influence of storggg temperature and relative humidity fluctuation

 

In the real environment, food products will be subject to the
fluctuation of storage temperature and relative humidity which are
influenced by weather.

lee (1976) successfully simulated the temperature fluctuation by

the Fourier series. Based on this method, a carputer simulation was

Ascorbic acid retention. ‘70

40

10

 

 

 

 

Ye
“ \
O
. . .
0 ~ 0
0 .
I- .
O
O
O
aW as independent —-" (it as independent

variable variable
P
r

O O 0 experimental data
r
L I 1 1
0 2 4 6 8 10
Time, weeks

Figure 25. Computer prediction using (it and as independent

variables compared to experimental data for ascorbic
acid retention in a food product during storage at
40% RH and 30°C.

59

developed to predict the relative humidity for a one-year period
(Appendix 5) and the result is presented in Appendix 6. The commuter-
predicted relative humidities are in excellent agreement with the
weather data. Ten-day averages of the daily average dry bulb and dew
point tetperatures as reported by the National Weather Service for
Lansing, Michigan for 1975 were used to cmpute the relative humidity
data. Usually, storage temperature is maintained above a minimum
temperature in the warehouse. Taking 10°C as the minimum
temperature and using the weather data for inlet air temperature and
relative humidity, carputer predict ion remlts are exhibited in
Figure 26.

A computer simulation (Appendix 7) was developed incorporating the
Fourier series to predict the warehouse temperature and relative
humidity fluctuat ion , the Arrhenius equation to determine the rate
constant (k) at any temperature, and the least square fitting to
establish the relationship of k and aw. The results of carputer
prediction for ascorbic acid degradation and moisture uptake in the
model food system during a one-year storage are illustrated in
Figures 26 and 27 along with the predicted temperature and relative
humidity.

Fifty percent of the ascorbic acid degrades in about 5 months,

3 months, 1.5 months, and 4 months after the food product stored in
the beginning of January, April, July and October, respectively.

In January to April, food product is kept under low temperature
and relative humidity in the warehouse so that the vitamin degrades
slowly. As the temperature and relative humidity begin to increase

in May, the vitamin retention decreases rapidly.

60

The food product stored in May follows the same pattern as the
food product stored in January but at a much higher rate of vitamin
degradation.

Since the temperature and relative Immidity are high in July,
the food product stored during this period starts to lose the vitamin
content quickly and then destruction becomes gradually slower when the
temperature drops in September .

The October storage period illustrates a rate of vitamin degra-
dation which is slower ttan the food product stored in April or July
but more rapidly than in January because of the high relative humidity
and low temperature.

Figure 27 illustrates that the food product stored in the warehcuse
adsorbs moisture until 15—20g HZO/IOOg solids because of the high
relative humidity and temperature during spring and summer, and then
the moisture content begins to decrease in October as a result of
decreasing storage relative humidity and temperature .

lfthispheiomenonoccursintherealwarehmsesystem, thefood
product will lose its crispimess. However, the moisture transfer
into the package is also influenced by the bulk of food product stored
in the warehouse and the stacking system. Small volume of air compared
to large volume of food product stored in the warehcuse might yield
a microenviroment different from what indicated by the weather data.
The stacking system, for exarmle, the secondary container merein
the boxes are placed, my act as a barrier against moisture transfer
into the product.

.5535. £533 5 2.2 9:8
3325: 9,328 on.» 530959 ongoing.» 63582 583? no 830395 young .8 0.”...me

 

 

n58... .25
one 82 e8 acne we sea. was .3. Guns can. one 5:.
OH: / a . 4 A d . q a d a a 1
. z z. . c. e e
/../ / / E O. O
./ / . .8880 . .l .| Guns I l I.
.. / 32. o ILI guns.
0 w /. / ,/ n no mcegfimoo one 5 8.35 semen coca
# /. x . Eco... nfi 5 83898 can»;

 

e

 

 

J

 

OH

8

8
% ‘HOI went mm

 

8H

fioH

 

10¢

£832: 4583 5 2.2 mane

 

 

 

spaces—E 03.53.“ pod 832095» 0331233 one #8500 cascade 530.3 «0 83030.3 859.8 SN chum?”
nausea .85.
08 >02 poo poem. as 33. 0:2. hi. dune coed: com can. 0
\
s\ e\ \
.\ N \ \
\
.. . .\ \ .4 n
\ .\ \ O O
\. \ \ O O O m
. \ 0 o m
o w b\ o o
I.” . \ e eeeeeeeeeewam
- e e e e e e .\ \ o
x \ m
\ \ .
1 JFIO 0 W\ . \K . +H ~m
IOHOIIOQv o w \ . . 0
O, I II I. II. 0‘ o . O o o U
o o .888 - .l . .l. m
0 O 0 his. oil c .l
o o o 0 98 l I l m
u Susan. .8 N
”no wfinfimnn one 5 unseen Sense “.81“ m.
Hence one 5 2380 madness 588a
a O 0
mm 0 O

 

 

 

(INCLUSICNS

l. The mathemtical model of the relationship between the rate
constant of ascorbic acid degradation (k) and water activity (aw)
is found to be a linear function of temperature at 10, 20, and 30°C.

2. The corputer simulation successfully predicts the ascorbic
acid retention and the moisture uptake in the model food system
corpared to experimental data.

3. The computer simulation accmmts for the influence of storage
temperature and relative humidity as well as various product and
packaging film claracteristics.

4 . The simulation is applicable for prediction of the vitamin
degradation in dry foods based on the following conditions:

(a) the reaction between the vitamin and oxygen follows first
order kinetics,

(b) the mathematical model of the relationship between k and
aw, and the sorption isotherms of the food products are known,

(c) oxygen is not a limiting factor, and all the moisture
transferred through the packaging film is assumed to be adsorbed by
the food product.

64

5. The computer simulation using subroutines including the
Fourier series to predict the storage relative humidity and temperature
fluctuation, the Arrhenius equation to determine the rate constant of
vitamin degradation (k) at any temperature, and least square fitting
to establish the linear relationship of k and aw, provides an excellent
prediction of vitamin retention in food products during a one-year

period.

WIQISKBI‘URI‘HERSIUDY

The auttor sugests that further work is required:

1. Tb experimentally verify the computer simulation in pre-
dicting vitamin degradation and product moisture content at lower
storage terperatures. '

2. Tb experimentally verify the computer simulation in predicting
the ascorbic acid degradation and product moisture content in a
commercial breakfast cereal stored at a commercial warehouse.

3. Tb utilize sorption isotherm equations other than the BET
equation for higher water activities in the corputer simulation.

4. Tb establish mathematical models describing the relationship
between the rate of vitamin degradation and product water activity for
other vitamins and to develop corputer simulation based on these models.

5. Tb develop commuter simulation to optimize the product
composition, packaging material ctaracteristics, and storage environ—
ment to get maximum vitamin retention.

REFERENCES

Anonymous, 1975. Standard methods of test for water vapor transfer
of materials in sheet form. In: The Annual Book of ASIM
Standards, Part 20.

Bach, J. A., 1974. Thiamin stability in a dehydrated model food
system during storage. 16 Thesis, Department of Food Science
and Human Nutrition, Michigan State University.

Brunauer, S., P. H. Emmett, and E. Teller, 1938. Adsorption of gases
in multimolecular layers. J. Am. (hem. Soc. 60:309.

Brunauer, S., L. S. Deming, W. E. Deming, and E. Teller, 1940.
Ch a theory of the van der Waals adsorption of gases. J. Am.
Chem. Soc. 62:1723.

Duckworth, R. B., and G. M. Smith, 1963. Diffusion of solutes at
low moisture levels. In: Recent Advances in Food Science,
vol. 3. J. M. Leitch and D. N. Rhodes, editors. Buttermrths,
London, England.

Dye, J. L., and V. A. Nicely, 1971. A general purpose curve-fitting
program for class and research use. J. Chem. Edu. 48:443.

Gregg, S. J., and K. S. W. Sing, 1967. Adsorption, airface Area and
PDrosity. Academic Press, New York, N.Y.

Heldman, D. R., 1974. Computer simulation of vitamin stability in
foods. Paper presented at Seminar on Stability of Vitamins
in Foods for the Association of Vitamin Chemists, Chicago, Ill.

Jensen, A., 1967. Tbcopherol content of seaweed and seameal, 3. In-
fluence of processing and storage on the content of tocopherol ,
carotenoids and ascorbic acid in seaweed meal. J. Sci. Food
Agric. 20:622.

Karel, M., 1972a. Calculation of storage stability of foods on the
basis of analysis of kinetics of deteriorative reactions
of foods and of mass transfer rates through packaging materials.
Paper presented at the International Symposium on Heat and Mass
Transfer Problems in Food Engineering, Wageningen, The
Netherlands.

Karel, M. , 19723. Qiantitative analysis of food packaging and storage

stability problems. ‘ Paper presented at the session on advances
in Food Preservation and Packaging on AIChE meeting, New York, N .Y.

67

68

Karel, M., S. Mizrahi, and T. P. Labuza, 1971. Canputer prediction
of food storage. Modern Pack., August 1971:54.

Kirk, J. R., and N. Ting, 1975. Fluorametric assay for total vitamin
C using continuous flow analysis. J. Fbod Sci. 40:463.

Kirk, J. R., D. Dennison, P. Kokoczka, D. R. Heldman, and R. P. Singh,
1976. Degradation of ascorbic acid in a dehydrated food system.
Accepted for publication in J. Food Sci.

Kwolek, W. F., and G. N. Bookwalter, 1971. Predicting storage
stability from tiine-terperature data. Fbod Technol. 25:1025.

Labuza, T. P., S. Mizrahi, and M. Karel, 1972. Mathematical models
for optimization of flexible film packaging of food for
storage. Trans. of ASAE 15:150.

Labuza, T. P., and S. R. Tannenbaun, 1972. Nutrient losses during
drying and storage of dehydrated foods. CRC Critical Reviews
in Food Technol. 3: 217.

Labuza, T. P., S. R. T‘annenbaun, and M. Karel, 1970. Water content and
stability of low-[misture and intermediate-moisture foods.
Food Technol. 24:543.

Lee, S. H., and T. P. Labuza, 1975. Destruction of ascorbic acid as
a function of water activity. J. Food Sci. 40:370.

lee, Y. C. , 1976. Vitamin composition of tomato culture and carputer
simulation of ascorbic acid stability in canned tarato juice.
PhD Thesis, Department of Food Science and Human Nutrition,
Michigan State University.

Mizrahi, S., T. P. Labuza, and M. Karel, 1970. Computer-aided
predict ions of extent of browning in dehydrated cabbage.
J. Food Sci. 35:799.

Neter, J ., and W. Wasserman, 1974. Applied Linear Statistical Models.
Richard D. Irwin, Inc., Hams-wood, Ill.

Paltnikar, M. P. and D. R. Heldman, 1971. Equilibrium moisture
characteristics of freeze-dried beef components. J. Fbod
Sci. 36:1015.

Qiast, D. G., and M. Karel, 1972. Effects of envimmental factors
on the oxidation of potato chips. J. Food Sci. 37:584.

mast, D. G., and M. Karel, 1972. Computer simulation of storage life
of foods undergoing spoilage by two interacting mechanisms.
J. Food Sci. 37:679.

Qiast, D. G., and M. Karel, 1973. Simulating shelf life. Modern
Pack., March 1973:50.

69

Simon, 1. B., T. P. Labuza, and M. Karel, 1971. Cerputer-aided
predict ions of food storage stability: oxidative deterioration
of a shrimp product. J. Food Sci. 36:280.

Singh, R. P., and D. R. Helchan, 1976. Simulation of liquid food
quality during storage. Trans. of ASAE 19:178.

Vojnovitch, C., and V. F. Pfeifer, 1970. Stability of ascorbic acid
in blends with wheat flour, (SM and infant cereals. Cereal
Sci. deay 15:317.

Wanninger, Jr. , L. A. , 1972. Mathematical model predicts stability
of ascorbic acid in food products. Fbod Technol. 26:42.

APPENDIX

Moisture content. g H20/100g solids

16

12

Amemflxl.

Sorption isotherm curves for the model food

system.

71

 

‘

 

IZIIZ

10°C
20°C
25°C
30°C
37°C

 

1 l

0.4 0.6

water activity

0.8

 

1.0

Appendix 2.

Galculat ion of energy constant (c) and monmolecular
moisture content (Wm) of the model food system.

72

 

BET equation:
aw/M(1-aw) = 1/wm + (C--1)aw/wm

aw:

M:

water activity
moisture content, gHZO/ 100g solids

energy constant

monarolecular moisture content

Least square fitting of BLT equation, c, and wm for each temperature

are as follows:

 

Range of

 

 

T, BET monolayer 0 wm
8‘" C’C equation
0.1 - 0.4 10 y = .1236x+.0018 69.7 7.97
0.1 - 0.5 20 y = .1898x+.0163 12.6 4.85
0.1 — 0.5 25 y = .1939x+.0136 15.2 4.82
0.1 - 0.5 30 y = .2236x+.0132 17.9 4.22
0.1 - 0.4 37 y = .2507x+.0129 20.4 3.79
where: y = aw/M(l-aw)
x = a

73

Appendix 3. Carmter flowchart to predict the moisture content and
ascorbic acid degradation in the model food system during
storage at a given storage temperature and relative humidity .

 

 

Cam)

/ READ CD,DI‘,T,(M),WS,AO,PS,X,WM,C,K,A,K1,K27

fpmmrammm]

 

 

 

 

 

 

 

 

 

 

M = T/DT

(11(1) = (M)

C(l) = (I)
l no N = 1, M

 

 

 

XA = Q! (N) ' (C—l)
XB =‘(CM(N) ° C -- 2 ° CM(N) - C-WM)
XC = ~24}! (N)

l

AI(N) = (fi- XB + sQRr (X32 - 4.XA.XC))/2.XA

[

mm) = Kl.AI(N) + KZ

cm) = cow) exp (-K<N> - Dr)

F

m = (K.A.PS.(A0 - AI(N)).DI‘)/(X.WS)

Y

(MOM) =‘ cum + m
I

i

NEXTPAGE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

74

 

r mm N,AI(N) ,CM(N) and

 

The rate constant of ascorbic acid degradation
Initial ascorbic acid concentration, %
Time differential, day
Storage time, days
Initial moisture content, gHZO/lOOg solids
Product mass, g
Energy constant of the model food system
lkxxnrflecularrmxunnneecontent of the:mxkfl.fbod.sysbem
Outside water activity, RH/100%
Inside water activity
Saturated vapor pressure,rmdmg
Packaging film thickness, cm
Lbisture transfer coefficient, gHZO - cm
m3 - hr -tndm;
Packaging surface area,1n2
Constants from the mathematical model describing the

relationship of KR as a function of AI

75

Appendix 4. The computer simulation flow sheet using water activity
increment as independent variable.

 

 

, o
[INPUL Co,da,Mo,a,p,x,wm,c,K,A,wS

 

 

 

 

 

ai.w .c
'3‘ . .
f d((l—al) + (c—l) (1—a1)a1) da1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M :-
dai
k = f —-§—)—df ”‘1 dai
dai
an = u - no
@).x.w3
dt = I d K.A.ps.(a°-a1) dai

 

i

 

 

da

 

l _

C=Coexp(-kdt)J

I

ai=a1+dai

 

 

 

 

 

 

 

 

 

76

Appendix 5. Flow chart of carputer simulation to predict RH based on the

Fourier series.

 

 

 

(8:04 .

/ READ KK,M,DATAJ KK:

 

 

 

 

 

No. of data points
No. of coefficients to
be calculated

DATA: Array name for RH data

 

1
—----I Do N=1,KK >
1

—-—[ A(N)=B(N)=0.0

 

 

 

 

 

l AA= 0.0, P= 3.1416, AM= M

c l
-— II) I = 1,1!

l >

’ j

 

 

 

 

 

——r AA= AA + (DATA(I) x I - (DATA(I) x(I-1)))l—-—[ AA= a 1

O

 

 

AA=AAIAM

. j
,———-[ Do J=1,KK>
T I '

I x - (2.0 PJ)/AM |

{MI >

 

 

 

 

 

 

 

[ A (J) = A (J) + DATA (K) x sin (XX)
A (J) = A (J) - DATA (K) x sin (X(K—1))
B(J)=B (J) +DATA (K) xcos (XX)
I

—[ B (J) = B (J) - DATA (K) x cos (X(K-1))

 

J

 

 

L _
B (J) = B (J>/(-PJ) I

_ 1 .
_____| A<J)=A(J)/(PJ> ]

Next
Page

 

 

 

 

 

 

Appendix 5. (continued)

 

C = 2P/365.

. l #
r-—-——Lm L=1,M >

I i '
[arson

1

Do N= 1mm)
1

 

 

 

 

 

 

 

 

 

 

 

 

 

l RH=RH+A(N)xccs(10(NL)1-——-—

 

 

 

 

 

L—[ RH=RH+B(N)xsin(10CNL)j

 

 

lm=mi+AA|

 

 

 

PRINT III+DQTA(L)|

 

 

 

78

 

 

228. .85

 

 

 

one 82 p8 Enm mi 33. was an: fine one 5a.
a q . a q . q .1 J e 1 o
.m5m§ 5 teams 90:98.3
BB .3 83.885
an 3625: 9322 o O
E 830303 933980 0 O O
n m wee.
. . . o O . L
0 0 ca
0
0
O O O O O L 8
e e
e e
o e e e e e ..
om
8H
.wofiuoo poison
one :0 pawns 3325: 9332 new awesome 5338.3 Havana .o 59.3%

‘HH

79

Appendix 7. Computer flow chart to predict the moisture content and
ascorbic acid degradation in the model food system
during a one-year period.

 

MAINpaoGRAM
Cm)
- F

[ READ CO,UI‘,TI,CM),WS,X,K,A/

 

 

 

 

 

J
M = TI/DT
(11(1) = cm
C(l) = 00

 

 

 

CALL TEMP (T(N))

f

c = 116.8 - 12.68 T(N) + .4:82(T(N))2 - .0057(T(N))3
WM = .0868 exp (-.025T(N))

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
XA = CM(N) . (0-1)
x3 = -((M(N).C - 2CM(N) - C.WM)
xc= -2.(M(N)
I
AI(N) = (-XB + soar (x132 - 4.XA.XC))/2.XA
I
CALL (DEFF (E(N), K2(N))
1
mm) = K1(N).AI(N) + K2(N)
T

 

 

LC(N) = C(N) exp (-K(N).DT)

 

Next
Page

80

Appendix 7 . (continued)

 

 

[CALL an (mam j

 

 

Ao (N) = RH(N)/100. j

_ 1
l m = (K.A.PS. (A0 - AI(N)).DI‘)/(X.WS)

 

 

 

. I
l (M (n+1) = cam) + m

 

 

 

fPRINT‘ m,AI(N),Od(N).C(N)]

®
w

 

81
Appendix 7. (continued)

SLBROJTINETEMP

The flowchart of Sibmutine TEMP is similar to flowchart in
Appendix 5 if all parameter RH is changed to T.

SIBRCIII‘INE RH
See flow chart in Appendix 5.

smmmmm
C MD
- 1' -
[ READ AKO(I),E(I),A(Ij
L
no; =l,N >

AKRU) = WI) eXP (-E(I)/RT(I))
I

 

 

 

 

 

 

 

 

 

 

 

A
B + A(I)

C + AKR(I).A(I)
D + B2

 

 

 

 

 

 

 

 

 

 

"IT'lelllll'lll'llllT