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.

COMPUTER SIMULATION OF LIQUID F000 '
QUALITY DURING STORAGE I

 

Dissertation for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
RAJINDER PAUL SINGH
1974
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ABSTRACT

COMPUTER SIMULATION OF LIQUID FOOD
QUALITY DURING STORAGE

BY

Rajinder Paul Singh

This dissertation is a discussion of a procedure
that can help a food engineer in predicting the quality
changes in a liquid food during storage. The procedure
is based on kinetics of quality degradation and computer—
aided prediction models. The specific objectives of this
study were to develop mathematical models that describe
(1) the kinetics of quality degradation and oxygen uptake
in a liquid food; (2) the oxygen diffusion accompanied by
a second-order chemical reaction in a liquid food during
storage; and (3) the influence of light intensity on rates
of quality degradation and oxygen uptake. A computer
simulation of these models was developed to predict the
quality history of a liquid food.

The quality index studied in this research was
reduced ascorbic acid. Infant formula was selected as the
model system. The overall reaction of ascorbic acid
degradation and oxygen uptake was assumed and confirmed

to be a second—order reaction under limited dissolved

Rajinder Paul Singh

oxygen concentration in the liquid. The second-order rate
constants were calculated for ascorbic acid degradation and
dissolved oxygen uptake in infant formula samples exposed
to light in l-cm deep exposure cells. These storage
experiments were conducted at five light intensities (dark,
1071 lux, 2142 lux, 3213 lux, and 4284 lux) and three
initial dissolved oxygen concentrations (1.0 ppm, 4.86 ppm,
and 8.71 ppm). Actual shelf-life tests were conducted to
compare with the computer predicted results.

The results showed that the vitamin loss occurred
within a 0-2 cm layer along the container wall. The
computer-aided results on vitamin degradation agreed with
the results obtained from actual shelf-life tests. The
standard deviations were within 1.43 to 5.10 percent of
initial ascorbic acid concentrations. The results obtained
in this study illustrate that the quality of a liquid food
can be predicted if the information on the rates of quality

degradation is available.

Approved:

m Nov. 7.1974-

Major Professor

 

N's/”'7“

Department Chairman

/

COMPUTER SIMULATION OF LIQUID FOOD

QUALITY DURING STORAGE

BY

Rajinder Paul Singh

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Agricultural Engineering Department

1974

To: Anila

ii

ACKNOWLEDGEMENTS

The author is greatly indebted to Dr. Dennis Ray
Heldman, Professor, Agricultural Engineering Department
and Department of Food Science and Human Nutrition, for
his interest and continuous guidance. Dr. Heldman's
inspiration and friendship will be always remembered with
gratitude.

Sincere appreciation is extended to Dr. J. L. Dye
(Chemistry), Dr. J. R. Kirk (Food Science and Human
Nutrition) and Dr. F. W. Bakker-Arkema (Agricultural
Engineering) for their valuable advice at various stages
of the research reported in this dissertation.

Appreciation is also extended to fellow graduate
student, Mr. Thomas Mack, for his help in the laboratory
experiments and Ms. Nancy Ting for conducting the vitamin
assays.

The financial assistance given by the Agricultural
Engineering Department and Department of Food Science and

Human Nutrition, Michigan State University, is acknowledged.

iii

. TABLE
ACKNOWLEDGEMENTS . . .
LIST OF TABLES . . . .
LIST OF FIGURES . . . .
LIST OF SYMBOLS . . . .
I. INTRODUCTION . .
II. REVIEW OF LITERATURE

OF

2.1 Ascorbic Acid

Scheme

CONTENTS

Oxidationu-General

2.2 Influence of Light on Ascorbic
Degradation in Milk . . . . . . .
Influence of Dissolved Oxygen on
Ascorbic Acid Oxidation . . . . .
Quality Degradation in Fruit Juices .
Computer Simulations of Food Quality .

2.3

2.4

2.5
III. THEORY

3.1

3.2

Kinetic Model of Vitamin Degradation
and Oxygen Uptake . . . . . . .
Oxygen Diffusion Accompanied by a
Second-Order Chemical Reaction in

a Liquid Food . . . . . . . . .
Influence of Light Intensity on Vitamin
Degradation and Oxygen Uptake . . .
Computer-Aided Prediction Model of
Vitamin Destruction in a Liquid Food .

3.4.1

Initial and Boundary Conditions

iv

Page
iii
vi
viii

xi

11
12

15

17

19
22
23
27

IV. EXPERIMENTAL MATERIAL AND PROCEDURES .

4.1

4.2 Experimental Procedures . . . . .
4 ' 2 ' 1 Light Exposure 0 o o o 0
4.2.2 Dissolved Oxygen Measurements
4.2.3 Storage Conditions . . . .
4.2.4 Vitamin Assay Procedure . .
4.2.5 Storage Trial with High Initial

Dissolved Oxygen Concentration
4.2.6 Storage Trials with 3-cm.-
Deep Cells . . . . . . .
4.2.7 Storage Trials with Regular-Size
Glass and Plastic Bottles . .
4.3 Description of Computer Program . .
V. RESULTS AND DISCUSSION . . . . . . .

5.1 Ascorbic Acid Degradation and Oxygen

5.2 Computer-Aided Prediction of Quality
Deterioration in Liquid Foods . .
VI. CONCLUSIONS . . . . . . . . .
6.1 Suggestions for Future Work . .
BIBLIOGRAPHY . . . . . . . . . . . .
APPENDIX A. Tables . . . . . . . .

Experimental Materials . . . .
1.1 Exposure Cells . . . .

4.
4.1.2 Liquid Food . . . . .
4.1.3 Light and Temperature Control

Uptake in Model System . . . .

5.1.1 Order of the Reaction . .

5.1.2 Influence of Depth with respect to.

Light Source on Rate of Vitamin

Degradation . . . . .

5.1.3 Influence of Light Intensity on the

Rate of Vitamin Degradation

5.1.4 Influence of Dissolved Oxygen on

Rate of Vitamin Degradation

5.1.5 Comparison of Results from Computer

Model and Storage Trials .

B. Computer Program Listing . .

Page
30
3O
30
31
34
36
36
36
38
39
40
41
41
43

45

45
46

52
55
57
63

69
82
83
84
89
98

LIST OF TABLES

Table I - Page

4.1 Nutritional Composition of Similac, Ready to
Feed Infant Formula . . . . . . . . . 34

5.1 Second-order Rate Constants of Ascorbic Acid
Degradation and Oxygen Uptake in Infant
Formula Exposed to 0, 1071, 2142, 3213 and
4284 lux Light Intensities . . . . . . . 49

A.l - Ascorbic Acid Degradation in Infant Formula
in 1 cm Cells Exposed to 0, 1071, 2142,
3213 and 4284 lux Light Intensities
(initial dissolved oxygen = 1.00 ppm) . . . 89

A.2 Dissolved Oxygen Uptake in Infant Formula in
1 cm Cells Exposed to Storage Conditions
Of Table A. 1 O O O O O O O O O O O 90

A.3 Ascorbic Acid Degradation in Infant Formula
in 1 cm Cells Exposed to 0, 1071, 2142,
3213 and 4284 lux Light Intensities
(initial dissolved oxygen = 4.86 ppm) . . . 91

A.4 Dissolved Oxygen Uptake in Infant Formula
in 1 cm Cells Exposed to Storage
Conditions of Table A.3 . . . . . . . . 92

A.5 Ascorbic Acid Degradation in Infant Formula
in 1 cm Cells Exposed to 0, 1071, 2142,
3213 and 4284 lux Light Intensities
(initial dissolved oxygen = 8.71 ppm) . . . 93

A.6 Dissolved Oxygen Uptake in Infant Formula
in 1 cm Cells Exposed to Storage
Conditions of Table A.5 . . . . . . . . 94

A.7 Dissolved Oxygen Uptake in Infant Formula
in 1 cm Cells Exposed to 1071 and 4284
lux Light Intensities (initial dissolved
oxygen = 60 percent oxygen) . . . . . . 95

vi

Table Page

A.8 Experimentally Measured Ascorbic Acid
Concentration History in Glass and
Plastic Containers from Five Storage
Trials . . . . . . . . . . . . . 96

A.9 Experimentally Measured Dissolved Oxygen
Concentration History in Glass and
Plastic Containers from Five Storage
Trials . . . . . . . . . . . . . 97

vii

.y ,1

 

Figure

3.1

3.2

4.1

4.3

5.3

5.4

LIST OF FIGURES

Factors influencing quality deterioration in

liquid foods during storage . . . .
A portion of a finite-difference grid of

liquid in a container exposed to light

and oxygen . . . . . . . . . .

An exposure cell . . . . . . . . .

Light transmission through plexiglass and high

density polyethylene . . . . . . .

Spectral distribution of F-40 cool white
fluorescent lamp. "A Practical Guide to
Westinghouse Fluorescent Lamps," Westing-
house Electric Corporation, Bloomfield,
N. J. . . . . . . . . . . . .

Experimental cells exposed to light . .
A 3-cm deep exposure cell . . . . . .

A second-order reaction model of vitamin
degradation and oxygen uptake for samples
exposed to 4284 lux light intensity
(initial dissolved oxygen - 4.86 ppm) .

Influence of transmitted light intensity on
second-order rate constants (initial
dissolved oxygen = 8.71 ppm) . . . .

Ascorbic acid degradation in infant formula
exposed to 4284 lux light intensity in a
3-Cm diVided C811 0 o o o o o o o

Dissolved oxygen uptake in infant formula

exposed to 4284 lux light intensity in a
3-cm divided cell . . . . . . . .

viii

Page

16

25

32

33

35
37
42

47

50

53

54

Figure

5.5

5.6

5.8

5.10

5.11

5.12

5.13

5.14

Ascorbic acid degradation in infant formula
exposed to 4284 lux light intensity in
3-cm divided and undivided cells . . . .

Ascorbic acid degradation in infant formula
exposed to 0, 1071, and 4284 lux light
intensities in l-cm cells (initial
dissolved oxygen = 8.71 ppm) . . . . .

Ascorbic acid degradation and dissolved
oxygen uptake in infant formula exposed
to 535 lux and 2142 lux light intensity
in l-cm cells . . . . . . . . . .

Dissolved oxygen uptake in infant formula
exposed to 0, 1071 and 4284 lux light
intensities in l-cm cells . . . . . .

Ascorbic acid degradation in the presence of
dissolved oxygen concentrations above
saturation with atmospheric oxygen . . .

Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in glass bottles
under 4284 lux light intensity . . . .

Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in glass bottles
under 535 lux light intensity . . . . .

Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in glass bottles
under 4284 lux light intensity . . . .

Computer predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in plastic bottles
under 1071 lux light intensity . . . .

Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in plastic bottles
under 535 lux light intensity . . . . .

ix

Page

56

58

59

61

62

65

66

67

68

70

Figure Page

5.15 Computer prediction of vitamin concentration
history in a glass container (for conditions
see page 71) . . . . . . . . . . . 72

5.16 Computer prediction of dissolved oxygen
concentration history in a glass
container (for conditions see page 71) . . . 74

5.17 Computer prediction of vitamin degradation

as a function of location inside a glass

container . . . . . . . . . . . . 75
5.18 Influence of light intensity on predicted

mass average vitamin concentration
history in a glass container . . . . . . 76

5.19 Influence of container size on vitamin
concentration history . . . . . . . . 77
5.20 Influence of initial dissolved oxygen

concentration on predicted mass average
vitamin concentration history (light
intensity = 535 lux) . . . . . . . . . 78

5.21 Influence of the type of container on
predicted mass average vitamin
concentration history . . . . . . . . 80

"I

 

 

 

 

(A)

(B)

LI ST OF SYMBOLS

concentration of quality index, mg/liter
(A)/(A)O, dimensionless

dissolved oxygen concentration, ppm

gas concentration in Equation 3—23, mg/liter
(B)/(B)O, dimensionless

diffusion coefficient of quality index in
liquid, cmZ/hr

diffusion coefficient of oxygen in liquid,
cmz/hr

diffusion coefficient of oxygen in container
wall, cmZ/hr

net rate of transfer of moles of oxygen,
mg/cm2 hr

solubility, moles/cm3 atm

second-order rate constant, liter/mg hr

average second-order rate constant, liter/mg hr
slope in Equation 3—28

light intensity, lux

the number of distance increments considered
in finite difference equation

permeability coefficient, cc.mil/day m2 atm

(A)O/(B) , dimensionless; partial pressure of
oxygen, atm, in Equation 3-26

surface area of container, cm

xi

 

   
 

 

 

s = DA/DB’ d1men31onless
t = time, hr.
(X) = concentration of A reacted at time 't', mg/liter
x = distance into liquid phase, cm.
y = distance into container wall, cm.
k(A)O
z = -IT———'(X)’ dimensionless
B
8 = k(A)Ot, dimensionless
2 a._l - 2a. + a. 1
6 (a. = 1 ,n 1,n 1+ ,n
1,n (Az)2
6 = thickness of container wall, cm
s = extinction coefficient of light
Subscripts
o = initial time for concentrations and zero depth
for light intensity 'L'
d = dark

xii

I . INTRODUCTION

Liquid foods in storage may undergo spoilage due to
several deteriorative mechanisms. These mechanisms affect
the quality resulting in degradation of nutrients,
development of off-flavors and change in the product color.
The overall emphasis in storage of any food product is on
keeping the deteriorative mechanisms at minimum rates. The
deterioration of quality of liquid foods is influenced by
several factors including temperature, light intensity and
dissolved oxygen content.

In this dissertation, a numerical procedure for
prediction of the quality index history in a liquid food
during storage is developed. The overall objective in mind
is the use of a computer-aided prediction model in selecting
storage environments best suited for liquid foods. As will
be discussed later, the prediction models require specific
information on rates of degradation of the given quality
index. This type of information is obtained through
laboratory-scale pilot studies.

The major emphasis in this research has been to
illustrate the procedures that are necessary to mathema-

tically predict the quality history of a liquid food. The

research is designed to assist in evaluation of storage
stability for new product package combinations. This type
of information is helpful to the product manufacturer in
selecting appropriate packaging material for new or existing
products. A second use of the simulation is the capability
to predict the nutrient concentration at any time during
storage and the use of such information for labeling
purposes.

For the purpose of this study, ascorbic acid
(vitamin C) was selected as the quality index. The liquid
food selected was an infant formula. Vitamin C is fairly
sensitive to the storage conditions including temperature,
light intensity, and presence of oxygen. The infant
formula was selected to assure better control of the
initial concentration of various nutrients and better con-
trol on microbial contamination. In addition, the product
is virtually oxygen-free in the bottles. The storage temp-
erature in this study was kept constant. The influence of
light intensity and presence of dissolved oxygen on vitamin
degradation was evaluated. The mathematical functions and
constants obtained in this study are specifically for
vitamin C in infant formula. The procedures for using this
information should be applicable to other liquid foods, with
minor modifications.

The specific objectives of this research were:

(i) to develop a theoretical mathematical model
to describe oxygen uptake in an infant formula accompanied

with a chemical reaction involving reduced ascorbic acid;

(ii) to incorporate the influence of initial
dissolved oxygen, light intensity and oxygen permeability of
a container wall into the mathematical model;

(iii) to develop a computer-aided mathematical
prediction of reduced ascorbic acid concentration and dis—
solved oxygen concentration in infant formula during
storage; and

(iv) to verify the computer-aided predictions of
reduced ascorbic acid and dissolved oxygen concentration
histories in infant formula by comparisons to results

obtained in the laboratory tests.

II. REVIEW OF LITERATURE

2.1 Ascorbic Acid Oxidation—-
General Scheme

Pure ascorbic acid (Vitamin C. L—threo-Z, 3, 4, 5,
6-pentahydroxy - 2 - hexenoic acid - 4 - lactone) occurs
as white, odorless crystals or powder, melting at about
190°C (374°F). It is optically active and is soluble in
water (1 gram in approximately 3 ml) (Hay §£_213, 1967).

It is a very strong reducing agent. In structure, it
resembles a simple sugar, but is modified to contain an
enediol and acid lactose group. It is easily oxidized in
air.

The most significant characteristic of ascorbic acid
is its reversible oxidation to dehydroascorbic acid. The
latter is reversibly reduced in the body to the physiolo-
gically active ascorbic acid. When dehydroascorbic acid
is allowed to stand in solution, the lactone ring gradually
Opens; the irreversible oxidation product, 2,3-diketo-l-
gulonic acid which is devoid of anti-scorbutic properties,
is obtained (Mazur and Harrow, 1971). Thus, the first

step of ascorbic acid oxidation is as follows:

 

 

 

CO CO -
I I
H-O-C 1 CO
I! O + .2. -02 ——I> ' + H20
H-O-C CO
I I
3'0 ———J HC-O -I
I I
H-O-C-H H-O-CH
I I
CH20 CHZO
l-ascorbic acid dehydroascorbic acid

The oxidation reaction is favored in the presence of
air, hydrogen peroxide, quinones, irradiation, enzymes
(ascorbic acid oxidase, peroxidase, cytochrome oxidase) or

+

metals (Cu++ and Fe+ ). The oxidative degradation is also

enhanced by pH values greater than 5.0.
2.2 Influence of Light on Ascorbic
Degradation in Milk

In a preliminary report, Hand gt_al. (1938) reported
a possible relationship of ascorbic acid and riboflavin
degradation to light intensity, oxygen concentration and
light catalyzed off—flavors in milk. Krukovsky and Guthrie
(1945) further concluded that the destruction of ascorbic
acid in milk was involved in the development of lipid
oxidized flavor resulting from light acting as a pro-
oxidant.

In one of the earlier reports, Burgwald and
JoSephson (1947) found complete disappearance of ascorbic
acid when milk was exposed for 1-2 hours to room daylight

for four days. Several investigators have observed

complete loss of ascorbic acid activity in milk exposed in
clear glass bottles for 10-30 minutes to sunlight (Buriana
(1937), Herried §E_§1, (1952), Holmes and Jones (1944),
Josephson gt_gl. (1946), Ron and Watson (1936). Containers
made of colored glass (yellow, green, brown, ruby, etc.)
‘ provided some protection to the ascorbic acid oxidation
(Houston gt_§l, (1938), Fomicheva (1962), Stull (1953)).

The light transmission in milk was studied by
Burgess and Harrington (1955a). They reported that sunlight
is capable of destroying ascorbic acid in milk at depths
approaching 26 mm. Their results indicate that at 546 nm
an 18-mm layer of whole milk transmitted more than one
percent of the incident light and at 365 nm a 4.5—mm layer
transmitted 2 percent of the incident light. In another
paper, Burgess and Herrington (1955b) reported the effec-
tive penetration depths of light into milk. The values of
effective depth of light penetration in whole milk ranged
from about 0.1 cm at 253 nm to 2 cm at 578 nm.

During the 19603, several papers have been published
on the influence of fluorescent lights on the ascorbic acid
content in milk stored in glass, paper and polyethylene

containers (Somogyi and Ott (1962), Hendrickx et'al.

 

(1964)). Radema (1962) reported a 35 percent loss of

‘Vitamdn C in milk after exposure at 8°C to 40-w lamps with
color temperature of 6500 K and light intensity of 500 lux.
The loss was at a lower rate when lamps with a color temp-

erature of 3000 K were used.

Aurand gt_al, (1966) studied the effect of ribo-
flavin, ascorbic acid and sunlight on the development of
oxidized flavor in milk. They reported that riboflavin was
the primary factor responsible for the development of light—
induced oxidized flavor, whereas ascorbic acid was only a
secondary factor and that riboflavin was unnecessary for
initiation or continuation of ascorbic acid destruction.

Hendrickx (1963) investigated the influence of
light on whole and skim milk. He observed greater loss of
vitamin C in skim milk than in whole milk. He indicated
that the serum of irradiated milk contributes most of the
light-induced flavors. Friedrich and Waiblinger (1969)
reported that milk, in clear polyethylene bottle, exposed
to fluorescent light of 1500 lux intensity at 10°C
resulted in a rapid breakdown of ascorbic acid from 14 to
4 mg/liter in 8 hours. After oxidation, the total content
of ascorbic acid, dehydroascorbic acid and 2,3-diketo-
gulonic acid decreased only slightly. The relationship
between the ascorbic acid destruction and the light intensity
in the range of 400-500 nanometers was reported to be
statistically significant. Thus, spectral transmittance
of polyethylene was found to be a controlling factor in
ascorbic acid oxidation.

Hansen gt_gl. (1972) published an abstract indicat-
ing that riboflavin and ascorbic acid breakdown in milk,
packaged in plastic containers, initiated after only 2

hours of storage under fluorescent light. The deterioration

of these nutrients was directly proportional to the amount
of off-flavor development. It was also reported that
plastic containers containing a special pigment gave 100
percent protection to the nutrients and flavor of milk
when exposed to fluorescent light.

Dimick (1973) reported that riboflavin destruction
in milk held in plastic and glass containers was not
significantly different and amounted to approximately 10—
17 percent loss following 72 hours of exposure. He
observed higher rates of ascorbic acid losses in milk
held in glass andplastic containers when compared with
fiberboard containers. Heldman and Kirk (1974) confirm
these losses in milk. In a related study, Sattar and
deMan (1973) reported significant losses of ascorbic acid
and riboflavin in milk held in clear plastic pouches at
5°C and exposed to 100 and 200 foot-candles light inten—
sity. These losses were minimal in opaque plastic pouches.

Recent research by Singh gt_gl. (1974) has illus—
trated the use of kinetic analysis in describing the
influence of light on riboflavin loss in milk during
storage. These results indicate that first-order rate
constants and activation energies are good parameters in
evaluating the ability of a container to protect the

product from light—induced loss of quality.

2.3 Influence of Dissolved Oxygen on
Ascorbic Acid Oxidation

In aqueous solutions, ascorbic acid degrades more
easily, especially in the presence of dissolved and head—
space oxygen. Theoretically, 1 ml of oxygen reacts with
15.7 mg of ascorbic acid (based on one mole of ascorbic
acid combining with one atom of oxygen) (Bayes, 1950).
This is equivalent to a reaction of 3.3 mgm of ascorbic
acid with 1 ml of air.

A Bayes (1950) studied the influence of oxygen on
ascorbic acid in aqueous standardized solutions stored
for 6 weeks at 35°C (95°F). He obtained a fairly good
agreement between the experimental and theoretical values
of ascorbic acid, indicating that the destruction of
ascorbic acid is directly proportional to the amount of
available oxygen in the containers.

One of the earliest investigations on the influ-
ence of dissolved oxygen on ascorbic acid degradation was
made by Guthrie gt_§l, (1938). They observed that the
destruction of ascorbic acid and the development of
oxidized flavor were largely or completely prevented by
removing the dissolved oxygen from the milk. Sharp gt_gl,
(1940) developed a continuous milk deaerating unit to
prevent the oxidized flavor and ascorbic acid degradation.
Guthrie (1946) reported an 8.27 percent loss of Vitamin C
in deaerated milk stored for 7 days at 40°F compared with

57.1 percent loss in aerated milk. The flavor of the

10

aerated milk was significantly "poor" and that of deaerated
mdlk was "good," after 7 days of storage.

.The kinetics of auto—oxidation of ascorbic acid in
sugar solutions in the presence of dissolved oxygen was
studied by Joslyn and Miller (1949a). They concluded that
the oxidation reaction was essentially first-order with
respect to the ascorbic acid concentration. They further
reported that under conditions of limited oxygen supply
the sugar solutions showed reduced initial rates of
oxidation (Joslyn and Miller, 1949b).

Khan and Martell (1967) worked on the influence of
‘ molecular oxygen on oxidation of ascorbic acid. The rate
of the uncatalyzed oxidation of ascorbic acid was found to
be proportional to oxygen concentration at 20 percent and
higher concentrations of molecular oxygen.

Significant losses of several nutrients in milk in
the presence of dissolved oxygen and exposure to sunlight
during storage were reported by Ford (1967). He recom—
mended the removal of dissolved oxygen from milk to
stabilize ascorbic acid and prevent degradation of such
'vitamins as Vitamin B12 and folic acid. Burton 35:31.
(1970) reported that the stability of Vitamin C and folic
acid is wholly determined by the level of residual oxygen

1J1 sterilized milk.

11
2.4 Quality Degradation in Fruit Juices

Researchers in the past have reported quality
deterioration, such as development of off-flavors, degrada-
tion in color, etc., in fruit juices held in storage.
However, published literature in this area is not as
exhaustive as for milk.

Tressler and Pederson (1936) reported no deterior«
ation of pasteurized grape juice packed in high vacuum or
in bottles containing negligible oxygen. However, they
found rapid deterioration when the bottles were partially
filled with the juice. They noted a change in color from
bright purple-red to brown. In addition, there were
detrimental changes in aroma and_flavor. These authors
also indicated that the presence of air in the headspace
of bottled strawberry juice resulted in increased
deterioration of color.

The degradation of ascorbic acid during storage
was observed by Beattie gt_§l, (1943). They noted that
in several fruit juices the changes in color occurred
concurrently with progressive losses of ascorbic acid
during storage. Nebesky gt_§1, (1949) reported that heat
and oxygen content were the most specific accelerating
agents responsible for deterioration of color during
storage. Deaerated juices stored at 21.1 to 26.7°C
retained their color and exhibited very little change
during storage for six months. They also reported that

anthocyanin pigments isolated from strawberries and

12

currants exhibited no deterioration when oxygen was excluded.
They found detrimental changes in the solutions of pigments
when the samples were exposed to light during storage.

Timberlake (1960) showed that oxidation of ascorbic
acid in the presence of copper and iron was significant in
black currant juice. He also discussed the effects of

some metal chelating agents on the ascorbic acid oxidation.
2.5 Computer Simulations of Food Quality

Recently researchers at Massachusetts Institute of
Technology have made attempts to mathematically predict
the shelf-life of dehydrated foods. Their main objective
has been to incorporate information (1) on laboratory
tests on the properties of food, (2) on the kinetics of
food deterioration reaction, and (3) on properties of
packaging materials, in developing prediction models of
packaging protection required for a given storage life
(Karel, 1972).

Mizrahi gt_§l, (1970a) studied the mathematical
prediction of extent of browning of freezeedried cabbage
stored in packages made of materials with different water-
vapor permeabilities. They developed a simulation that
incorporated the kinetic data of browning reaction, moisture
content inside the package and mass-transfer characteristics
of packages. They reported a fairly good agreement between
the experimental data and the predicted values. This pre«

diction model was later used in accelerated tests of

13

browning in dehydrated cabbage (Mizrahi §t_213 1970b).
The accelerated tests reduced the time required to obtain
browning rate data at low moisture contents from over a
year to only 10 days. This work emphasizes one of the
major advantages of computer simulation models. The
accelerated tests, along with computer simulations, pro-
vide a rapid determination of the storage stability of a
food component.

A computer-aided prediction of oxidative deterior-
ation of a shrimp product was presented by Simon et_§l,
(1971). They correlated the organoleptic degradation with
absorption of oxygen and with loss of carotenoid pigment.
They reported that the predictioncfifstorage stability was
comparable to actual storage tests based on the pigment
loss.

Quast gt_§l, (1972a)developed a mathematical model
to describe the oxidation of potato chips as a function of
oxygen pressure, extent of oxidation and equilibrium rela—
tive humidity. Quast and Karel (1972b) presented a simulae
tion of storage life of potato chips undergoing simultaneous
deterioration by two mechanisms, with interaction between
the mechanisms. The two mechanisms involved in deteriora-
tion were oxidation due to atmospheric oxygen and textural
changes due to moisture uptake. This simulation was later
used in determining optimal permeabilities which allow
simultaneous deterioration (Quast and Karel, 1973). They
also studied the influence of several packaging conditions

on these permeabilities.

14

Labuza gt_al, (1972) developed mathematical models
of food stability and incorporated information on sorption
isotherms in the simulations. They studied the moisture
gain in tea and moisture gain with a chemical reaction
(browning) in dry milk.

The computer-aided shelf-life simulation studies
have been limited to dry and dehydrated foods. However,
these studies demonstrate the capability of predicting

the quality changes in a food product.

I I I . THEORY

There are various changes which might take place in
a liquid food stored after packaging. Many of these
changes are influenced by the storage conditions and the
container material. As an illustration, a plastic con-
tainer containing a liquid food is shown in Figure 3.1.
The product has a certain initial vitamin concentration
and dissolved oxygen concentration. The container wall,
depending on its optical clarity, allows certain light
transmission. In addition, the container material has a
given permeability for oxygen from the atmosphere into the
product. The outside odors may permeate through the con-
tainer wall and influence the flavor of the product. The
container wall also allows loss of product ingredients via
absorption. In case of a carbonated beverage stored in
highly permeable plastic containers, carbon dioxide might
be lost via migration.

In this section, the following mathematical models
are discussed:

(1) Kinetic reaction model of vitamin degradation
and oxygen uptake in a liquid food.

(2) Oxygen diffusion accompanied by a chemical

reaction in a liquid food during storage.

15

16

STORAGE
TEIPERATLRE

LIGHT

 

I

I
I
I
I
I

OXYGEN
4_ PERI’EATION

OuALITY IORATION

I
I
l
Dunne TORAGE '

 

 

 

Figure 3.1.--Factors influencing quality deterioration in
liquid foods during storage.

17

(3) Influence of light intensity on vitamin degrad-
ation and oxygen uptake.

These models are incorporated in a computer
simulation to predict the vitamin concentration history
in a liquid food.

3.1 Kinetic Model of Vitamin Degradation
and Oxygen Uptake

In this study, the oxidative degradation of reduced
ascorbic acid in an infant formula is being investigated.
The kinetic reaction model is therefore developed for
reduced ascorbic acid oxidation. In the presence of dis-

solved oxygen, the reaction scheme is as follows:

A + B -—5¥——+ Products (3—1)
(reduced ascorbic (oxygen) (dehydroascorbic
acid) acid and H20)

where k is the rate constant.

If the dissolved oxygen, B, undergoes a second-
order reaction of finite speed with a dissolved reactant,
A, the rate of reaction can be expressed as:

'dIA) _ -
75-5- - RIA) (B) (3 2)

Initially (A) = (A)o and (B) = (B)o; let (X),
expressed as concentration, be the amount of A that has

reacted at time 't'. Then at any time,

18

(A) = mo - (x) (3-3)
(B) = (BIO ’ (X) (3-4)

The concentration units of (A), (B) and (X) are
moles/liter. The most commonly used units of vitamin
concentration and dissolved oxygen concentration are mg/
liter and parts per million, respectively. Therefore in
the rest of this dissertation the units of vitamin con—
centration (A) and dissolved oxygen concentration (B)
will be mg/liter and parts per million reSpectively, unless
otherwise stated.

From Equation (3-3),

0:

-d(A) _ (x) ._
TE— ‘ t (3 5)

0;

Substituting Equations (3-3) to (3-5) in Equation

(3-2) gives:

€391: egg: k (We - ‘X’H‘B’o" (XI) <3-6)

Integration from t=0 gives the concentration of X, or A
and B at any time:

(A)

-(X) (A)
ln[(B) (A)

0 _ _ _ 0 _
-(X)] - lnITB—T] - ((AIO (BIOIRt + IDITB-y-o-I (3 7)

O

A computer program, KINFIT, was used to fit the
experimental data in Equation (3-7) (Dye and Nicely, 1971).

The program is useful in plotting the data to the best

19

fit and calculating standard deviations on the calculated
parameters. The input of variables (e.g., dissolved
oxygen concentrations, vitamin concentrations, time) is
accompanied with their respective variances. This approach
assists in accounting for the internal errors of vitamin
assays and small variations in storage durations. The
program is specifically written for chemical reactions

and for evaluating kinetic parameters of these reactions.

The rate constants 'k' calculated from experimental
data are used in the computer simulation of the nutrient
history in a liquid food. The mathematical model used in
this scale-up is discussed in the following section.

3.2 Oxygen Diffusion Accompanied by a
Second«0rder.Chemica1 Reaction
in a Liquid Food

In this section, the diffusion of oxygen accom—
panied by second-order chemical reaction with ascorbic
acid in a liquid food is discussed. The theory is developed
with the following assumptions:

(1) The thermal convective diffusion in the liquid
is assumed negligible. This assumption neglects internal
diffusion of vitamin or dissolved oxygen due to any temper-
ature differentials within the container. The assumption
is valid if the storage temperature is maintained constant.

(2) The diffusion coefficients of oxygen and
ascorbic acid are assumed constant. The assumption is

valid at constant storage temperatures.

20

(3) The second-order rate constant 'k' varies with
depth inside the liquid. This assumption is discussed
further in section 3.3.

The equations which describe the variations of the
ascorbic acid concentration (A) and dissolved oxygen
concentration (B) in time and space within the liquid in
the presence of a second-order reaction (Equation 3-1)

are the following (Danckwerts, 1970):

 

2

DA i—4%1-= 3§%l + k(A)(B) <3-8)
3 x

n 32‘3’ - 3‘3) + k(A)(B) (3-9)

39x2 ' at.

with the initial condition

(3) = (3)0 . (A) (A)o x a o. t=o (3—10)

When the liquid food is stored in a glass bottle,
the boundary conditions on the dissolved oxygen and vitamin
concentration are allowed to vary with time. In a situation
when the liquid food is stored in a plastic container
permeable to oxygen, the dissolved oxygen concentration at
the wall is expressed as a function of the oxygen permea-
tion through the wall. The way in which these boundary
conditions are handled for these specific cases is dis-
cussed in Section 3.4.1.

An analytical solution encompassing these para-

meters in functional form is impossible (Brian et a1, 1961).

21

Therefore, the differential equations (3-8, 3-9) were
approximated by the implicit finite difference techniques.
It can be seen that the number of separate solutions
necessary in this method for each variation of the para-
meters becomes excessive. To resolve these problems, the
equations were put into dimensionless form through the

following substitutions:

E

 

 

 

 

a =
(Me
(B)
b =
(BIO
P = (M0
(3)0
D
s = EA
B
k(A)
z = o (X)
DB
6 = k(A)ot

The dimensionless form of Equations (3-8) and

(3-9) is:
32a 8a
8p—7 - S '—6- = ab (3-11)
32
32b b

22
with the initial conditions
a = l, b = l at 6 = 0, z a 0 (3-13)

Equations (3-11) and (3-12) can be solved along
with information on the rate constant, diffusion coeffi-
cient for oxygen and ascorbic acid and initial concentra-
tions of ascorbic acid and dissolved oxygen. The numerical
method used in this study is presented in section 3.4. The
rate constant 'k' is evaluated for a given light intensity.
The influence of light intensity on rate constant 'k' is
discussed in section 3.3.

3.3 Influence of Light Intensity on Vitamin

Degradation and Oxygen Uptake
The second-order rate constant describing vitamin

degradation and oxygen uptake can be expressed as a func-

tion of the light intensity. Thus
k = f(L) (3—14)

The light intensity is a function of depth inside
the liquid. Assuming an exponential extinction of light

inside the liquid medium gives

L = L e‘ex (3—15)
0
Thus, the second-order rate constant can be
expressed as a function of incident light intensity and

depth inside the liquid medium, as follows

23

k = f(Lo e'ex) (3-16)
where the function can be evaluated from experimental data.

As discussed in Chapter II, the light extinCtion
in a liquid food, e.g., milk, is in a thin layer along the
walls of the container (Burgess and Herrington, 1955b).

The light penetration inside a liquid food depends upon
the incident light intensity and the extinction coeffi—
cient, e. Specially designed experimental trials, such
as the ones that will be discussed in this dissertation
are helpful in investigating the effective depth of light
penetration for the given liquid food.

The experimentally determined function of Equa-
tion (3-16) is used in solving Equations (3-11) and (3—12)
numerically. The mathematical procedure is presented in
section 3.4.

3.4 Computer-Aided Prediction Model of
Vitamin Destruction in a
Liquid Food

Equations (3-11) and (3-12) can be solved numeri-
cally provided the following information is available:

(a) Rate constant 'k' as a function of light inten-
sity and depth obtained from experimental data (Equation
3-16).

(b) Light and oxygen transmission through con—

tainer'walls.

24

(c) Diffusion coefficients of ascorbic acid and
oxygen in the liquid.

Equations (3-11) and (3-12) are solved by the
following time-centered, implicit finite-difference
equations according to the Crank and Nicolson formulation

for the geometry shown in Figure 3.2:

 

 

 

1 2 1 2 _ ai,n+1 ' a1,n
Spl'z'Gzaimfl + 'z'dzaim] P I A8 1
a. - a.
_ 1 n+1 1 n _
[--—’-——-———--‘-—2 J (hi.n+%—) (3 17)
b b.
12 12 1ng 1J1
[2dzb1,n+l + 2dzbi,n] [ A8 ]
[bi,n+l + biyn] ( 1
2 ai,n+§-—) (3-13)

The implicit equations have been solved by a method
similar to the method presented by Brian et a1. (1961).
The method of solution is as follows:
1. Assume that the values a. and b. are known
1,n 1,n
at some time-step n for i = 0,1,2,. . . M.

2. The values ai,n+%-(1 = 1,2,. . . M) were cal-

<3u1ated by using the explicit finite-difference equation

 

2 éi,n+% - ai,n
SP‘Gzaiml ‘ P‘ A672: r) = ai,n bi,n (3‘19)

3. Inserting these values of ai into Equation

Iné

03-18), a system of M simultaneous linear equations is

25

 

A

A
J
I

I

 

LIGHT

OXYGEN

 

 

 

 

 

 

 

 

I» z

(a) liquid in container exposed to light and oxygen

 

T en+1

> (i, 11”!)

LL an

1.1 1 1+1

A

 

 

 

 

(b) Crank-Nicolson Method

Figure 3.2.--A portion of a finite-difference grid of
liquid in a container exposed to light
and oxygen.

26

obtained which, together with the boundary conditions to
be discussed later, was solved for the values bi,n+l
(i = 1,2,3 . . . M). The tridiagonal method of solving
equations was used to solve these simultaneous equations

(Carnahan et a1., 1969).

4. The calculated values of b. were used to
1,n+l
calculate bi,n+% as
b l = bi,n+l + bi,n
ipn+§ (i = 1' 2 o o o M) (3-20)
5. These values of b. 1 were inserted into

1,114":
Equation (3-17) to obtain a system of M simultaneous linear

equations. These equations, along with the boundary con—
ditions, were again solved by the tridiagonal method to

yield values a. (i = O, 1, 2, . . . M). Thus, the

1,n+1

complete set of future-time concentration ai and

,n+1

b was obtained.

i,n+l
This procedure was repeated as the calculation
proceeded from one time-step to another.

The above implicit finite-difference method was
chosen in order to avoid severe-stability limitations
encountered when an explicit method is used (Perry and
Pigford, 1953).

The forward and backward difference forms used in
finite differences leadtxadiscretization errors of

0(At + sz). The central difference form of Crank-

Nicolson method used in this study reduces the dependency

27

on the time increment from O(At) to O[(At)2] (Carnahan,
1969). This method converges with discretization error
OHAt)2 + (Ax)2].

Brian gt;al, (1961) used a similar method for
infinitely rapid chemical reaction and reported that the
results deviate from true solutions to the differential
equations by less than 2 percent. In this dissertation,
the predicted values are compared with the actual experi-
mentally measured values to confirm the validity of this
method.

The boundary conditions for these difference equa-

tions are discussed in section 3.4.1.

3.4.1 Initial and Boundary Conditions

 

The initial and boundary conditions for the dif-
ference equations were handled as follows:
(a) Initial condition:
at time t=O,

a. = l
} (i=O,l,2,3 . . . M) (3-21)

b. = 1
(b) The boundary conditions for a container with
no oxygen permeation through the walls, such as glass, are:
(i) at the wall:
The vitamin and dissolved oxygen are consumed
at a finite rate as determined from Equation 3‘7.

The equation is solved at each time step to

Fill-p

 

 

 

28

calculate new concentration values for vitamin
and oxygen at the boundary node.

(ii) at the center:

- (3-22)
bm,n - bm-l, n-l

(c) The boundary conditions on oxygen concentra-
tion at the wall for a container permeable to oxygen are
developed for a one-dimensional case.

Assuming a concentration gradient %§~exists across
the two sides of the film, the net rate of transfer of
moles of oxygen across a unit area of a plane perpendi—

cular to x'axis at a given moment is given by Fick's first

law of diffusion:

_ 3C -
F-Dc—f (3 23)

This equation can be integrated between

C = C1 (gas concentration in the surrounding
atmosphere)

and C = C2 (gas concentration in the liquid) at

x = O and x = 6 respectively, as follows:

_ It
F — "6' (cl - c2) (3-24)

The flux can be expressed as number of diffused
molecules per unit time. Thus for a given area of the

film, 8:

29

D S

- C _ _
F - -3— (C1 C2) (3 25)

Assuming Henry's law is valid, the concentration,
C, of oxygen on the surface of the container wall is a

function of the partial pressure of oxygen:
C = H p (3‘26)

Combining Equations (3-25) and (3-26)

 

F (3-27)

II
D
a:
U)

o,

The outside partial pressure of oxygen, p1, is
0.21 atmosphere. The quantity (DCH) is commonly known as
the permeability coefficient. This coefficient can be

defined in terms of the following quantities:

D H = (amount of gas)(thickness)
c (area)(timeI(pressure diEIerence)

Several types of units have been used in the past
to express this coefficient. In this study, the following

units were used:

cc mil
_____1r.___
day m atm

Equation (3-27) is used in the computer program to
calculate the amount of oxygen transferred at the boundary
into the container during small steps of time. The

computer program is discussed in section 4.3.

IV. EXPERIMENTAL MATERIAL AND PROCEDURES

Experiments were conducted primarily to generate
data in order to calculate the rate constant 'k' described
in section 3.1. This required obtaining:

. (1) Mass average vitamin concentration data as a
function of storage time,

(ii) Mass average dissolved oxygen concentration
data as a function of storage time.

The storage temperature was held constant (at 7.2°C)
in these experiments. Light intensity and initial dis—
solved oxygen concentration were varied.

In addition, experiments were conducted to observe
the influence of high initial dissolved oxygen concentra-
tion (above saturation with atmospheric oxygen) on vitamin
degradation. Scale—up experiments with larger-size

containers were also conducted.

4.1 Experimental Materials

4.1.1 Exposure Cells

In order to maintain better control on experimental

‘variables, special plexiglass cells were fabricated for

30

31

light exposure studies. The cells are 1 cm in depth with
an exposed surface area of 31.67 cm2 (Figure 4.1). The
top surface of these cells is made out of clear plexiglass.
The bottom and sides of the cells are made of opaque
plexiglass. These cells have two small openings (1 mm
diameter), on the sides, for filling and removal of
samples. The light transmission curve for clear plexi-
glass and polyethylene (used in plastic bottles), obtained

from a spectrophotometer, is shown in Figure 4.2.
4.1.2 Liquid Food

The liquid food system selected for this study was
an infant formula. The infant formula was selected for
the following reasons:

(a) The infant formula from the same batch has
uniform initial concentration of various
nutrients, as well as overall composition.

(b) Infant formula in bottles provides a better

I control on the initial microbiological
contamination.

(c) The product is deaerated before bottling.

This results in low initial dissolved oxygen
concentration.

The infant formula, Similac, was obtained directly
from the Ross Laboratories, Columbus, Ohio. The product
‘was contained in 4-oz. ready-to-serve glass bottles. The
nutritional composition of this infant formula is presented

in Table 4.1.

32

 

~——-—-¢=6.35cM as] CLEAR

I PLEx
IGLASS
JL1m

I? LIQUID SANPLE V
1%
I

%
a2za2zazaazazzaazzezaazzaazazzaa’

 

 

 

      
    
 

Figure 4.1.--An exposure cell.

33

 

PLEXIGLASS
----- POLYETHYLENE
I\

100 -

m I-
2 A—
o 80 V
0
II
m 70 "
8
«3 60
.3
E 50 I
In
5
H to r ”a“...
E‘. ,fl"’
1:” 30 “ ,..»”’
s -—”
.4 20 I— /__,-—’

I
10 5””
0 1 J 1 1 1 1

 

 

Figure 4.2.-—Light transmission through.plexiglass and
high density polyethylene.

34

TABLE 4.l.--Nutritiona1 Composition of Similac, Ready to
Feed Infant Formula.

 

 

Nutrients Per Liter Vitamins Per Liter

Fat 36 gm Vitamin A 2500 USP unit
Carbohydrate 71 gm Vitamin D 400 USP unit
Protein 15.5 gm Vitamin E 9 Int. unit
Minerals 3.7 gm Vitamin C 55 mg
Calcium 0.6 gm Vitamin B1 0.65 mg
Phosphorus 0.44 gm Vitamin B2 1 mg
Magnesium 0.04 gm Niacin 7 mg

Iron trace Vitamin B6 0.4 mg

Copper 0.4 mg Folic Acid 0.05 mg
Iodine 0.04 mg Pantothenic Acid 3 mg

Water 901.8 gm Vitamin 312 I 1.5 mcg

 

4.1.3 Light and Temperature Control

 

General Electric lamps (40W, Coolwhite) were used in
these studies. The spectral distribution of these fluores-
cent lamps is presented in Figure 4.3. It should be noted
that the radiation intensity is very high in the area of
450 nanometers. As indicated earlier, this is the critical
area with respect to light-induced and oxidized flavors.

A reflector-holder with two fluorescent lamps was hung
from the ceiling. The height of the lamps above the cells
was adjusted to achieve the desired light intensity
measured on the top surface of the cells. A constant-
temperature water bath (American Instruments Model 4—8600)

was used to control temperature around the cells. A

35

 

 

 

 

cheomm/mz AT 60 CM

 

 

 

l l l l l

383 460 RIO 620 7(1)

WAVELENGTH m

.Figure 4.3.--Spectra1 distribution of F-40 cool white
‘fluorescent lamp. "A Practical Guide to
Westinghouse Fluorescent Lamps,“ Westing-
house Electric Corporation, Bloomfield,
N. J.

36

Tektronix J16 digital photometer was used to measure light

intensities.

4.2 Experimental Procedures

4.2.1 Light Exposure

 

The infant formula was transferred from the bottles
into the cells using a 50 cc hypodermic syringe with a
l7-gauge needle. Random checks on dissolved oxygen content
showed no increase in dissolved oxygen when this transfer
was done carefully with the hypodermic syringe. The
openings in the cells were closed using surgical tape.

The cells were arranged on a platform in the
constant-temperature water bath with their sides submerged
in water. 'The top surface of the cells was kept above
~water, as shown in Figure 4.4.

After completion of the desired time exposure, the
liquid sample was removed from the cell using a hypodermic
syringe. The sample was then either assayed for ascorbic

acid or analyzed for dissolved oxygen concentration.
4.2.2 Dissolved Oxygen Measurements

The dissolved oxygen measurements were conducted
using a Beckman Laboratory Oxygen Analyzer Model 777.
The instrument consists of a polarographic electrode that
is used to determine the oxygen content in gaseous samples
or dissolved oxygen in aqueous or non~aqueous solutions.

The operation of the sensor is as follows: The sensor is

37

 

 

LIGHT
OUTSIDE TENPERATIRE

= 72° C

 

 

 

 

 

 

 

WATER BATH

Figure 4.4.-—Experimental cells exposed to light.

 

 

 

placed
is app
The 0)
reduo
a our
and t
of '1
obte:

cali

ccn
ti:
111
t1)
‘tk

cal

38

placed in the sample and a potential of approximately 0.8 V
is applied between the gold cathode and the silver anode.
The oxygen diffuses through the Teflon membrane and is
reduced at the cathode. The reduction of oxygen causes

a current flow. The current produced is then amplified

and the oxygen content is indicated on the dial in units

of "percent oxygen.” The instrument was calibrated to
obtain the values in "parts per million, oxygen.“ The

calibration procedure is described by Mack (1974).

4.2.3 Storage Conditions

 

The following storage experiments were conducted:

(a) Three trials with initial dissolved oxygen
concentration of 1.0 ppm, 4.86 ppm and 8.71 ppm; respec-
tively were conducted. The dissolved oxygen concentration
in the infant formula (measured immediately after opening
the bottle) was 1.0 ppm. Using a laboratory gas diffuser,
the liquid samples were saturated with atmospheric air to
obtain a dissolved oxygen content of 8.71 ppm (at 7.2°C).
The 4.86 ppm dissolved oxygen samples were obtained by
mixing infant formula from bottles and the samples saturated
with atmospheric oxygen in equal ratios by volume.

I All storage experiments were conducted at 7.2°C
(45°F) and five light intensities: 1071 lux (100 ft-c),
2142 lux (200 ft-c), 3213 lux (300 ft-c), 4284 lux
(400 ft-c) and dark.

39

The vitamin assay and dissolved oxygen measurements
were conducted on duplicate samples at 0, 4, 8, 15 and 24

hour storage durations:
4.2.4 Vitamin Assay Procedure

The vitamin assay procedure is described in detail
by Kirk and Ting (1974). A summary of procedures is as
follows: A 25-m1 sample was pipetted into a 50-ml volume-
tric flask. Then 6 percent metaphosphoric acid was added
to make the solution to the SO-ml mark. Thelcontents of
the flask were well shaken and the solution was filtered
using Whatman filter paper No. 41. The filtrate was then
analyzed in the Technicon Autoanalyzer for ascorbic acid
as follows.

The reagents used in the autoanalyzer were:

1.: 2,6-dichloro-indophenol: 2% in water then

filtered

2. Thiourea: 5% in 50% ethanol

3. Metaphosphoric acid: 6%

4. Sodium acetate: 50% of NaOAc. 3 H20

5. Boric acid: 3 g in 100 ml of 50% sodium

acetate 5% H

6. O-phenylene diamine hydrochloride: 0.1%

The autoanalyzer was allowed at least 20-30 minutes
warm-up time. Reagents were then pumped until the system-
stabilized (10-15 minutes). The baseline on the recorder-

chart was adjusted to 5 percent transmission. The sample

4O

probe was placed in a high standard (dehydroascorbic acid
100 mg/ml). On achieving steady state, the full-scale
record was adjusted to give a 95 percent transmission
reading. The full range of standards was then sampled at
a rate of 50 samples/hour with a sample wash time ratio
of 2:1. Blanks were run with boric acid-sodium acetate.

The standard curve for vitamin concentration
against percent transmission was obtained using a stock
solution of ascorbic acid prepared by adding 500 mg/ml of
ascorbic acid in 6 percent metaphosphoric acid to make the
final concentrations of standard ascorbic acid to 20 mg/ml,
40 mg/ml, 60 mg/ml, 80 mg/ml and 100 mg/ml.

An aliquot of the stock solution was transferred
into a lOO-ml volumetric flask, along with approximately
50 m1 of metaphosphoric acid. 2,6-Dichloroind0phenol
solution was added to make the solution pink. A few dr0ps
of thiourea were added until the solution was colorless.
The solution was then made to the lOO—ml mark with meta—
phosphoric acid (6 percent). The final concentration was
100 mg/ml of dehydroascorbic acid. This was then used to
obtain the 95 percent transmission on the recorder.

4.2.5 Storage Trial with High Initial
Dissolved Oxygen Concentration

 

A trial was conducted to observe the influence of
very high initial dissolved oxygen concentration. The
purpose of this trial was to determine the order of

nutrient degradation reaction when the dissolved oxygen

 

 

isin
pure c
"60 p1
that
perce
high
cell
ligh
OXYE

inte

‘wit
EH11
de;
tr:
liI

ti

CC»

The

41

is in abundant supply. The infant formula was purged with
pure oxygen to obtain a dissolved oxygen concentration of
"60 percent oxygen" on the Beckman oxygen analyzer (note
that 100 percent saturation with air is equivalent to '21
percent oxygen"). The samples of infant formula with
high initial dissolved oxygen were transferred into l-cm.
cells. These cells were exposed to 1071 lux and 4284 lux
light intensities. Both ascorbic acid and dissolved
oxygen were monitored at 0, 2, 4, 8 and 15 hour time
intervals.
4.2.6 Storage Trials with

3-cm.-Deep Cells

Storage trials were conducted in 3—cm-deep cells
with and without partitions, as shown in Figure 4.5. The
'purpose of these trials was to determine the effective
depth of light penetration in infant formula. These
trials were conducted under 4284 lux light intensity. The
liquid formula had an initial dissolved oxygen concentra-
tion of 8.71 ppm.

4.2.7 Storage Trials with Regular-Size
IGIass and Plastic Bottles T'

Several storage trials were conducted to verify the
computer-predicted results for vitamin loss in infant
formula stored in larger-size containers. The glass bottle
'used in this trial was 6 cm in diameter and 6 cm in height.

The plastic container measured 6 cm diameter by 10 cm

42

 

 

I
in
s

 

 

 

 

 

ETEI

 

% 3””
E SNVPLE
fill/ll/l/l/l/j/II/ll

OPAGUE

PLEXIGLASS

1...-
seek

 

 

Figure 4.5.--A 3-cm deep exposure cell.

hej

sit

(4C

tic

dBV‘

 

par

ror

It

inc

prj

re;

$1.11

Sul

81:]

tr

th
tr

 

 

43

height. These trials were conducted at three light inten-
sities, 535 lux (50 ft-c), 1071 lux (100 ft—c) and 4284 lux
(400 ft-c). The two initial dissolved oxygen concentra-

tions observed were 8.71 ppm and 4.86 ppm.
4.3 Description of Computer Program

The various components of the computer program
developed in this study are discussed in this section.

(1) PROGRAM MAIN: This program reads the input
parameters, it sets the initial conditions, calls sub—
routine QUALITY to obtain new time concentration values.
It then modifies the boundary nodes for the next time
increment. The concentrations of oxygen and vitamin are
printed at specified time intervals. This procedure is
repeated for the next time interval.

(2) SUBROUTINE QUALITY: This subroutine calls
subroutine RATE to obtain rate constant values. It calls
subroutine DIMEN to obtain non-dimensional parameters,
subroutine OXYGEN to obtain new time oxygen concentrations
and subroutine VITAMIN to obtain new time vitamin concen-
trations.

(3) SUBROUTINE RATE: This subroutine calculates
the rate constants for the given dissolved oxygen concen—
trations and light intensity. This subroutine includes
the experimentally determined functions from Equation 3u28.

(4) SUBROUTINE DIMEN: This subroutine calculates

the non-dimensional parameters discussed in section 3.2.

 

 

 

subrouti
to calcu
values f

subrouti

simultar

Carrahar

in Apper

 

 

 

44

(5) SUBROUTINE VITAMIN AND SUBROUTINE OXYGEN: These
subroutines use the time-centered finite difference approach
to calculate the new time oxygen and vitamin concentration
values from old time values. Both of these subroutines call
subroutine TRIDAG to solve the simultaneous equations.

(6) SUBROUTINE TRIDAG: This subroutine solves the
simultaneous equations. The subroutine is obtained from
Carrahan (1969).

A fortran listing of the computer proqram appears

in Appendix B.

 

of a
is .
det-
pro
res
sec
ill

chc

CO:

CO

91
1‘s
in
de

ex

V. RESULTS AND DISCUSSION

The primary objective of this study was to develop
a computer-aided prediction model to describe the history
of a quality index in a liquid food. The first section
is a presentation of experimental results necessary to
determine specific input requirements for the computer
program. The computer-aided predictions and experimental
results from storage studies are also compared in this
section. The second section in this chapter involves the
illustration of the computer program output with a set of
chosen input conditions.

5.1 Ascorbic Acid Degradation and Oxygen
Uptake in Model System

One of the important input variables for the
computer-aided mathematical model is the second-order rate
constant. . The rate constant is obtained from laboratory
storage trials on degradation of a quality index in the
given liquid food. For the purpose of this study, the
rate constants were obtained for ascorbic acid degradation
in an infant formula. The experimental procedures were
described in Chapter IV. The results from laboratory

experiments are discussed in this section.

45

 

 

Ln
I-‘

I:

atmc
the)
0X1".
or I
and
rep
lin
tio:
Und
non
OXY
of

fol

in

vel
Se:
0f

in

a11c

(3-

the

46

5.1.1 Order of the Reaction

 

The liquid foods prior to storage may be exposed to
atmospheric oxygen. During canning or bottling operations,
they may be deaerated. Thus, during storage, the dissolved
oxygen in the liquid food is present in concentrations at
or below that of saturation with atmospheric oxygen. Khan
and Martell (1967) and Joslyn and Miller (1949b) have
reported that the kinetics of ascorbic acid oxidation in a
liquid is first-order when oxygen is present in concentra-
tions above that of saturation with atmospheric oxygen.
Under conditions of limited oxygen supply they indicate a
nonlinear dependence of the initial rate of oxidation on
oxygen concentration. In this study, the overall kinetics
of this reaction under limited oxygen supply was assumed to
follow second-order mechanism. The discussion of results
in this section justifies this assumption.

From Equation (3-7), a plot of logn [(A)/(B)]
versus storage time should be a straight line if the
second-order reaction (Equation 3-2) is followed. The plot
of logn [(A)/(B)] versus storage time for samples exposed
in 1 cm cells to 4284 lux (initial dissolved oxygen =
4.86 ppm) is shown in Figure 5.1.. (The data on vitamin
and dissolved oxygen concentrations is tabulated in
Appendix A.) The second-order rate constants were calcu-
1ated from the slope of the straight line using Equation
(3-7). The computer program KINFIT was used to obtain

these rate constants for the various storage conditions.

 

1N (A/B)

5.4 »—
5.2 ~
5.0 -

4.8 ”
4.6 »

LIA ~
4.2 E

“I0 '—
18 _

3.6 e

3.2 L

3.0 I/

2.8

 

1N (NB)

5.4
5.2
5.0

4.8
4.6

4.4
4.2

4.0
3.8

3I6

3.4
3.2

3.0
2.8

47

 

 

 

 

LI 8 12 16 20 - 24
STORAGE Tm; HR

Figure 5.1.--A second-order reaction model of vitamin

degradation and oxygen uptake for samples
exposed to 4284 lux light intensity
(initial dissolved oxygen = 4.86 ppm).

 

 

 

 

three
intens
are be
measu;
devia
the r
const
units

repo:

4.86
in j
difj
tior
dien
The:
dar’

iJlt

the:
Sat;
Of'

9151
EraJ

48

The calculated second-order rate constants for
three initial dissolved oxygen concentrations and five light
intensities are presented in Table 5.1. The rate constants
are based on the average of duplicate trials with five
measurements during each storage trial. The low standard
deviations obtained for these rate constants confirm that
the reaction follows second-order kinetics. The rate
constants were also calculated using concentrations with
units in moles/liter, the results were similar to those
reported in Table 5.1.

The increase of dissolved oxygen concentration from
4.86 ppm to 8.71 ppm in samples exposed to light results
in increased rate constants. There is no significant
difference in rate constants (based on one standard devia-
tion on each rate constant) for samples with initial
dissolved oxygen concentrations between 1.00 and 4.86 ppm.
The rate constants show an increase when samples held in
dark are compared with samples under 1071 lux light
intensity.

The rate constants calculated for the trial when
the initial dissolved oxygen content was 8.71 ppm (or
saturation with atmospheric oxygen) is plotted as a function
of transmitted light intensity in Figure 5.2. The plexi-
glass used in this study allowed 82 percent light
transmission. The light intensity values were adjusted

accordingly.

49

 

 

mm.m mmm.ma ovN.H Hm~.mH omb.m mco.m «mmv
mH.m omm.oa oom.a «Ha.m o¢~.~ Hum.m mHNm
mm.H mmH.mH on~.~ th.oa oo~.v vma.ma «can
~m.a mmn.~a ~mm.o mmh.v ona.~ vmm.m Head
He.o moH.H mom.o th.H ~mm.o mnm.a sumo
He mE\uouHH no mE\uou«H we mE\HouwH st
as x as x x ca x as x x as x as x x mesmaauaH
v v w v v v unmaq
.>oo ucoumcoo .>oo acoumcoo .>oo acoumcoo usocaomH
.oum ovum .cvm oumm .cum ovum .

 

an“ HF.“ " oOoQoH

L

Ede mm.¢ u .o.o.H

 

Ema oo.H u .o.a.H

 

.nowuwmcoucH
snags use same can mean .maaa .Hboa .o o» emaoaxm essence ucmmcH as

oxcumo commxo com cowumcoumoo wand oanuoomd mo mucmuusou oumm HooHOIosooom11.H.m mummy

50

 

RATE CONSTANT leOLl LITER/MGHR
9 9° '95 [<5 25' .5 ES .8

 

 

 

0 800 1600 2400 3200 £000
TRANSMITTED LIGHT INTENSITY Lux

op:

Figure 5.2.--Influence of transmitted light intensity on
second-order rate constants (initial
dissolved oxygen - 8.71 ppm).

 

 

of ligh

mitted)

 

the rat
above 1
scatter
signifi
obtaine
and 4.E
incider

ence i]

functi

cells

51

The rate constants increase linearly as a function
of light intensity with a peak value at 1756 lux (trans—
mitted) light intensity. From Figure 5.2 it appears that
the rate constant decreases with increasing light intensity
above 1756 lux. However, based on one standard deviation
scatter, the rate constants above 1756 lux do not change
significantly. Similar observations with rate constants
obtained at initial dissolved oxygen concentrations of 1.00
and 4.86 ppm indicate that above 1756 lux (or 2142 lux
incident light intensity) there is no significant differ-
ence in the rate constants.

Thus Equation 3-16 can be modified for the linear

function as follows:

k = kd + k' Lo e"ex (3-28)

The rate constants, K} obtained from l—cm deep

cells are average rate constant values, or

E'= ~4§§§- (3—29)
Substituting Equation (3—28) in (3—29) gives

f(kd + k' Lo 3‘“)dx ,
E'= fax (3-30)

 

Integrating from O to l (for 1 cm cell)

L
E'= kd - k' EQ-(EP - 1) (3—31)

 

coeffic
extinC‘
for mi

discus

intens

at any

measur

routir

5.1.2

“—

Perce
fOrmu
is jt
mehts
are I
Deon;
and 1
The '
FiQU:
the <

Signj

52

Equation (3-31) is solved for k'. The extinction
coefficient is calculated by assuming 99 percent light
extinction in the 1-cm layer. This assumption is valid
for milk and similar opaque liquid foods. Further
discussion on this assumption is presented in section 5.1.2.

With the knowledge of k', kd' E and incident light
intensity, Equation 3-28 is used to calculate rate constant
at any depth inside a liquid medium.

The information obtained in the experimental
measurements of rate constants is incorporated in the sub-
routine RATE of the computer program.

5.1.2 Influence of Depth with Respect to
Light Source on Rate of Vitamin
Degradation

In section 5.1.1, it was assumed that there is 99
percent light extinction in the l—cm layer of infant
formula along the walls of the container. This assumption
is justified from the results obtained from storage experi-
ments when 3-cm deep, divided cells were used. The results
are presented in Figure 5.3. Maximum loss of vitamin
occurred in the top 1 cm layer. The losses in the middle
and bottom layers are comparable to those of dark storage.
The dissolved oxygen concentration. history is shown in
Figure 5.4. The second—order rate constants obtained from
the data of middle and bottom layer did not show any

significant difference.

ASCORBIC ACID CONCENTRATION IB/L
O s e; s s s e a; s s E

 

+ + 0—1 CM
V—V 1-2 CM
0 o 2-3 CM

 

 

A

+\
+¥

 

 

STORAGE TIIE HR

Figure 5.3.-—Ascorbic acid degradation in infant formula

exposed to 4284 lux light intensity in a
3'cm divided cell.

 

10.0
9.0

800
7.0

6.0
5.0

“I0

300
2.0

1.0

DISSOLVED OXYGEN CONCENTRATION PPM

54

 

 

 

 

 

 

 

+ + O-lCM
v V l-ZCM
0 0 2—3CM
v\
v
o
v
_ +~e--‘\“~“~
.. +— +
1 I l L l l

 

 

 

O ’4 8 12 16 20 24

STORAGE TIRE HR

liigure 5.4.--Dissolved oxygen uptake in infant formula

exposed to 4284 lux light intensity in a
3-cm divided cell.

55

In another trial, 3-cm deep divided and undivided
cells were used. The ascorbic acid concentration data
plotted as a function of time is presented in Figure 5.5.
The calculated mass average of the concentrations in three
layers is comparable with the concentration values for the
undivided cell. It is acknowledged that there is 82
percent light transmission through plexiglass. Therefore,
in a divided cell, there is less light intensity reaching
the middle layer than in an undivided cell. These results
indicate that the outside layer (approximately 1 cm)
experiences vitamin loss influenced by light. These
results on light extinction in infant formula are comparable
with the studies of Burgess and Herrington (1955b).

The above results indicate that the vitamin
degradation in liquid foods exposed to light occurs mainly
in a thin layer along the walls of the container. The
thickness of this layer depends on the incident light
intensity. The contents in the central region of the
container do not experience any losses due to light. There
is, however, degradation of the vitamin in the central
region due to the dissolved oxygen concentration. The
vitamin losses in the central region would be comparable to

losses under dark conditions.

.§;l.3 Influence of Light Intensity on the
W

The reduced ascorbic acid concentration history in

infant formula exposed to light in experimental cells is

 

‘V 'V
O-——O
D— --[3

O- - -—..

56

0-1 CM

1-2 CM

2-3 CM

UNDIVIDED CELL

Mass AVERAGE CONCENTRATION

 

 

 

 

 

 

 

ASOORBIC ACID CONCENTRATION I‘B/L
o s s s 5 ET 8 a; s s E

O

STORAGE TIRE HR

Figure 5.5.--Ascorbic acid degradation in infant formula
-exposed to 4284 lux light intensity in 3-cm

divided and undivided cells.

 

 

pr*

ex;
tha

vit

vit

a de
los:
ShOV
fall
the

hon:

tior
inte
lux)

(l.(

grad

StOr

57

presented in Figure 5.6. In this trial, the initial dis-
solved oxygen concentration in the infant formula samples
was 8.71 ppm. The rate of vitamin degradation in samples
held in dark storage is small compared to the samples
exposed to light during storage. These results indicate
that increase in light intensity increases the rate of
vitamin degradation.

Trials conducted at 535 lux (50 ft—c) showed more
vitamin loss than the trials under dark conditions (Figure
5.7). This indicates that even a low light intensity has
a detrimental effect on the vitamin. The trends of vitamin
loss and oxygen uptake between 0 to 4 hour intervals are
shown in Figure 5.7. The two-hour concentration values
fall in line with 0 to 4 hour values. This trend confirms
the validity of measuring vitamin concentration at four-
hour intervals.

The experimental data of ascorbic acid concentra-
tion and dissolved oxygen concentration at five light
intensities (dark, 1071 lux, 2142 lux, 3213 lux and 4284
lux) and three initial dissolved oxygen concentrations
(1.00 ppm. 4.86 ppm and 8.71 ppm) are presented in Tables
A.l, A.2, A.3, A.4, A.5, and A.6 (Appendix A).

5.1.4 Influence of Dissolved Oxygen on
Rate of Vitamin DegradaEion

An important observation from Figure 5.6 is the

gradual decrease in the rate of vitamin degradation as the

storage time increases in samples exposed to light. This

58

--——: DARK

0 1071 LUX
+-——+ 4284 LUX

O

 

 

1.0

Olg
0.8

007
0'6

0'4 _ fi+\\
0.3 _. +

 

 

 

 

 

 

0.2 r

0.1 -

01) I l l , I l 1
0 4 8 12 16 20 24

STORAGE TIME HR

'Figure 5.6.--Ascorbic acid degradation in infant formula
exposed to 0, 1071 and 4284 lux light
intensities in l—cm cells (initial dissolved
oxygen = 8.71 ppm).

 

Figu

59

 

. 535Lux (ASCORBIC ACID)

 

 

 

 

 

+—-+ 2142 LUX (ASOORBIC ACID)
.-----. 5351le (DISSOLVED OXYGEN)
+---..+ 2142 LUX (DISSOLVED OxYGEN)
1.0 + 1.0
009 _ 009
0.8 ‘ —-1\ - 0.8
0.7 - \ \xm. . ‘ 0'7
\ + ~"\‘
006 — ‘*_ ~ “‘ '1 006 g
\ ‘~
g” 0.5 _- \ + - 0.55"
\ .
0.4 ‘- \ ~ 0'4
I?‘ +
0.3 — "K - 0'3
0.2 - \‘I--~~~ -‘ 0.2
0.1 .. IN“ " 0-1
0.0 ‘ ' l '
0 LI 8 12 16
STORAGE TINEHR

Figure 5.7.--Ascorbic acid degradation and dissolved
oxygen uptake in infant formula exposed
to 535 lux and 2142 lux light intensity
in l-cm cells.

60

indicates that the reaction rate is initially high, and
reduces with time. The dissolved oxygen concentration
history in different cells, exposed to same conditions

as in Figure 5.6, is shown in Figure 5.8. This figure
confirms that dissolved oxygen is consumed very rapidly
and is in limited supply. The limited presence of oxygen
results in the observed reduction of the rate of vitamin
degradation at longer storage times.

An attempt was made to observe the vitamin degrada—
tion when dissolved oxygen is present in abundant supply.
Joslyn and Miller (1949b) earlier reported that the
ascorbic acid oxidation in a liquid medium is first-order
when oxygen is present in concentrations above saturation
with atmospheric oxygen.

The ascorbic acid history in infant formula with
dissolved oxygen concentrations above atmoSpheric satura-
tion is presented in Figure 5.9. The straight line rela-
tionship obtained on semi-log coordinate paper indicates
that the vitamin degradation is first-order. The dissolved
oxygen concentration during the experiment was above 0.21
atmosphere (or above saturation with atmospheric oxygen).
The dissolved oxygen concentration data is preSented in
Table A.7 (Appendix A). The experiment confirms that the
vitamin loss is first-order when oxygen is present in
abundant supply. Under realistic conditions, however,
liquid foods are exposed to oxygen concentrations at or

below saturation with atmospheric oxygen, as a result

61

 

 

 

 

 

 

 

 

STORAGE TIME HR

Figure 5.8.—-Dissolved oxygen uptake in infant formula
exposed to 0, 1071 and 4284 lux light
intensities in 1—cm cells.

1.0
0.9
0.8

0.7
006

0.5

0.4

0.3

0.1

62

 

 

 

 

 

 

0"“‘O 1071 Lux

+ + 4284 Lux

1 l l l

0 LI 8 12 16 20

STORAGE TIME (HRS)

Figure 5.9.--Ascorbic acid degradation in the presence of

dissolved oxygen concentrations above
saturation with atmospheric oxygen.

.7 ____-—.
, I

 

 

oxygen
Um as

second

 

on as
are c
earli
geome
Cylin
for m
to th
from

(Appe

Conce
The,
Same
Weas
Coef
0.67
0,06
DeCr

net

63

oxygen is present in limited supply. Under these conditions,
the ascorbic acid oxidation can be best described by a
second-order reaction as discussed in section 5.1.1.

5.1.5 Comparison of Results from Computer
Model and Storage Trials

 

In this section, results from five storage trials
on ascorbic acid degradation in glass and plastic bottles
are compared with computer-predicted results. As indicated
earlier, the computer model was developed for rectangular
geometry. The storage trials were, however, conducted in
cylindrical shaped bottles of 6 cm diameter commonly used
for marketing infant formula. These bottles were exposed
to the desired light intensity on two sides. The results
from storage trials are presented in Tables A.8 and A.9
(Appendix A).

The computer program was provided with the initial
concentration values of ascorbic acid and dissolved oxygen.
The diffusion coefficients of ascorbic acid (assumed to be
same for glucose molecule) and oxygen were obtained from
Weast (1971) and Danckwerts (1970), respectively. These
coefficients are 1.36 x 10-5 cmz/sec (for oxygen) and

5 cmZ/sec (for vitamin). A space increment of

0.673 x 10'
0.0625 cm and a time increment of 0.125 hr was selected.
Decreasing these increments to still smaller values did

not change the mass average concentrations significantly.

 

 

 

 

light i
oxygen
measure
time h.
tions

tion a.

CODCCD

oxygen
expose
result
trated
Percer

Percel

OXYge
exPOs
resul
trate
peIce

of ir

64

Trial l.—-Infant formula was expOsed to 4284 lux
light intensity in a glass bottle. The initial dissolved
oxygen concentration was 8.71 ppm. The experimentally
measured concentrations along with the computer predicted
time history are shown in Figure 5.10. The standard devia-
tions are 5.10 percent of initial ascorbic acid concentra-
tion and 2.86 percent of initial dissolved oxygen

concentration.

Trial 2.--Infant formula with initial dissolved
oxygen concentration of 4.86 ppm in a glass bottle was
exposed to 535 lux light intensity. The experimental
results and computer-predicted concentrations are illus-
trated in Figure 5.11. The standard deviations are 1.43
percent of initial ascorbic acid concentration and 5.71

percent of initial dissolved oxygen concentration.

Trial 3.--Infant formula with initial dissolved
oxygen concentration of 4.86 ppm in a glass bottle was
exposed to 4284 lux light intensity. The experimental
results and computer-predicted concentrations are illus-
trated in Figure 5.12. The standard deviations are 2.53
percent of initial ascorbic concentration and 5.65 percent

of initial dissolved oxygen concentration.

Trial 4.--Infant formula was exposed to 1071 lux
light intensity in a plastic bottle. The initial
dissolved oxygen concentration was 8.71 ppm. The results

are illustrated in Figure 5.13. The standard deviations

65

 

 

 

 

 

 

PREDICTED ASCORBIC ACID
_____ PREDICTED DISSOLVED OXYGEN
9 MEASURED ASCORBIC ACID
+ I’EASLRED DISSOLVED OXYGEN
10)
g) I 9.0
gm 3 800
s . 7.0 5’
:70 $5
50 " 6.0 a
a) '- \\ O T500 g
at“ ‘- \\\ '4 L‘00 g
2 \ + g
gm .— \\\‘ U 310
&m I- ‘~‘~~‘~- '200
10 - + - 1.0
0 1 L l I l l 0
O 6 12 18 24 3O 36
STORAGE Tm: HR

Figure 5.lO.--Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in glass bottles
under 4284 lux light intensity.

66

 

PREDICTED ASCORBIC ACID
_____ PREDICTED DISSOLVED OXYGEN

0 I’EASIRED ASCORBIC ACID

+ PEASIRED DISSOLVED OXYGEN

 

 

 

 

 

110

100

g) 9.0
E 80 8'0 9
g 70 7.0 g
I- I'-
E 60 6.0 0
g m "I‘- "‘ 500 g
e I.\\+ «40 E
s “0 "x ' i

\
2 30 .- \\ ‘ 3.0
\

g 20 .. ‘+~~_~‘+ ~ 2.0

m - ~~~~~~-—.1.0

0 1 l J I J 0

O 6 12 18 24 30 36
STORAGE TIRE HR

Figure 5.ll.—-Computer—predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history

'in infant formula in glass bottles
under 535 lux light intensity.

67

—— PREDICTED ASCORBIC ACID
——-- PREDICTED DISSOLVED OXYGEN

MEASURED ASCDRBIC ACID

+ MSWED DISSOLVED OXYGEN

 

 

 

 

110
100
g) D 9.0
_J
E a) - 8.0
E70 .. 730 E
- . 8
$60 _ \o 60 g
- 5.0
53 50 Kb ------‘___ g?
2 L0 -\ " “'0 9?.
L) \~ :2
"" 33 t - 3.0
§ .. \\\ g
m - \\\~‘ " 2:0
10 - + ~+~“‘--——~ 1.0
O 1 l l I l 0

 

12 18 24 30 36
STORAGE TIME HR

0
Ch

Figure 5.12.--Computer-predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in glass bottles
under 4284 lux light intensity.

ASCORBIC ACID CONCENTRATION [VG/L

ossssssaes§

68

_""“' PREDICTED ASCORBIC ACID
---- PREDICTED DISSOLVED OXYGEN
0 MEASURED ASCORDIC ACID

+ MEASURED DISSOLVED OXYGEN

 

 

 

l

 

 

STORAGE Tm: HR

Figure 5.13.-Computer predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in plastic bottles
under 1071 lux light intensity.

9.0
8.0

7.0
6.0
5.0
4.0

3.0

NOIlWJNSZJNOj) N39AXO aamossm

[‘3
c3
“dd

1.0
0.0

69

are 2.74 percent of initial ascorbic acid concentration and

7.01 percent of initial dissolved oxygen concentration.

Trial 5.--Infant formula with 4.86 ppm initial
dissolved oxygen concentration in plastic bottle was
exposed to 535 lux light intensity. The results obtained
from storage trial and those predicted are shown in Figure
5.14. The standard deviations are 3.68 percent of initial
ascorbic acid concentration and 3.78 percent of initial
dissolved oxygen concentration.

The small deviations between the predicted and the
experimentally measured concentrations are due to one or
more of the following reasons: (1) the assumed permea-
bility constant for the plastic container, (2) the inherent
errors in experimental measurements, and (3) the assumed
rectangular geometry for the cylindrical shaped containers.

In the following section, a general discussion on
the various capabilities of the computer program developed
in this study are discussed.

5.2 Computer-Aided Prediction of Quality
Deterioration in Liquid Foods

The mathematical model developed in this study is
based on a second—order reaction between the quality index
and oxygen. Thus, a quality degradation reaction in a
liquid food which follows a second-order rate kinetics can
be predicted by this computer program. The computer output

includes information on the quality index and dissolved

7O

----- PREDICTED ASCORBIC ACID
————— PREDICTED DISSOLVED OXYGEN

0 MEASlRED ASCORDIC ACID

+ MEASURED DISSOLVED OXYGEN

 

 

 

 

 

 

“0 l
100 0: o
E m " 0 o -‘
S
r: 30 _ 4
E m >- d
60 _ J
9..
as 50 +=---+-.._ ‘
2 “~#
g m _ ~~‘4;-_ 1
30 ~ ‘“‘-
m .. .—
10 - -I
0 l 1 J l L
O 6 12 18 24 3O 36
STORAGETINEI'R

Figure 5.14.--Computer predicted and experimentally
determined reduced ascorbic acid and
dissolved oxygen concentration history
in infant formula in plastic bottles
under 535 lux light intensity.

9.0
8.0
7.0
6.0

5'0
“I0

3.0
2.0

1.0
0

Ndd NOIIvalNBONOj N39AXO aamossm

71

oxygen concentration as a function of time at various loca-
tions inside the container. In addition, the program
predicts the mass average concentrations of the quality index
and dissolved oxygen as a function of time.

As an illustration, the following information was
provided as input conditions to the computer. The quality
index used in this illustration is vitamin concentration.

Type of container = Glass

Initial vitamin concentration = 100 mg/liter

Initial dissolved oxygen content = 8.71 ppm

Incident light intensity = 2142 lux

Cross-sectional width of the container = 6.0 cm

Sides exposed to light = 2 (opposite)

Diffusion coefficient of oxygen - 1.36 x 10'-5

cmZ/sec
Diffusion coefficient of vitamin = 0.673 x 10'"5
cmz/sec

Space increment = .0625 cm

Time increment = 0.125 hr

Total time of storage = 36 hr.

For the above input, the vitamin concentration
history along the container wall and at the center are
plotted in Figure 5.15. As expected, the vitamin
degradation along the wall is very rapid. The decrease in
vitamin concentration occurs at a much slower rate in the

central core of the container. Figure 5.15 illustrates

the mass average concentration of the vitamin, also. The

VITAMIN CONCENrRATION WL

ossssseaes'é

Figure S.lS.--Computer prediction of vitamin concentration
history in a glass container (for conditions

 

O

72

 

ATCENTER

--—-- MASS AVERAGE
——— AT CONTAINER WALL

———— AT 0.5 CM FROM HALL

 

 

~ ~~_——T———

l i— l I

6 12 18 24
STORAGE TIME HR

see page 71).

30

 

36

73

time history of dissolved oxygen concentration at these
locations is plotted in Figure 5.16. The decrease is very
rapid initially, indicating a rapid uptake of oxygen by
contents due to oxidation reactions within the container.

The vitamin concentration at various locations and
times inside a container is presented in Figure 5.17. The
significant decrease in the vitamin concentration occurs
in the 1 cm layer along the wall of the container. The
vitamin destruction rate in the l to 2 cm layer increases
due to diffusion as the storage time increases.

The influence of different light intensities on the
rate of vitamin destruction is shown in Figure 5.18. The
input parameters are the same as in Figure 5.15, except for
the light intensity value. As expected, the mass average
vitamin degradation is greater at higher light intensities.

The influence of the container size on rate of
mass average vitamin loss is presented in Figure 5.19. The
input variables were held constant except for the cross-
sectional width of the container. The vitamin loss is
increased as the size of container is decreased. This
indicates that light intensity is more detrimental to the
nutrient when the liquid food is stored in smaller size
(or smaller cross-sectional width) containers.

The initial dissolved oxygen content is another
important variable which determines the rate of vitamin
degradation in a liquid food. The influence of this factor
is illustrated in Figure 5.20. The high initial dissolved

oxygen concentration results in accelerated loss of vitamin.

74

AT CENTER

 

—-—-— MASS AVERAGE
—-— AT CONTAINER WALL
————— AT 0.5 FROM WALL

50
O

 

”*1
9°
c:

PPN
c: c: :3

EN
CD

 

DISSOLVED OXYGEN CONCENTRATION
F
O

L" L"

O O
I l
’—
’

 

 

t
l
I
L

 

0 6 12 18 24 30 36
STORAGETINEI‘R

Figure 5.16.--Computer prediction of dissolved oxygen
concentration history in a glass container
(for conditions see page 71).

75

 

 

 

 

 

 

VITAMIN CONCENTRATION ML
0 s B a: s s 8 a 23 25 §

0 1.0 2.0 3.0
(WALL) DISTANCE FROM WALL (CENTER)

Figure 5.17.--Computer prediction of vitamin degradation
as a function of location inside a glass
container.

76

0Lux
__-_ 535LUX

 

 

 

 

-———- leIZLux
1(1)
\
95 ' \ ~
\\ \
SI) \ ‘
85 ~ \ \
—l n—
E 80 \\ .
§ 75 3 \ \
I— L. \\ ,
70 \\ \
65 - \ .
E. 50 .- \\ \
5 \\ '
E 55 “' \\\ \
\
50 L \\\ \
45 F ““-
“-
no .-
11: l l l 1 l
0 6 12 18 24 30 36
STORAGE Tm: HR

Figure 5.18.--Influence of light intensity on predicted
mass average vitamin concentration history
in a glass container.

77

HALF-DEPTH
6 CM

—-—— 3CM

——.—— 2cm

 

 

1(1)
90-\\
_l
\
E80“ \\\~
§70— \
F’ ‘\ .
60* \\ \
50 h \n\ ‘\“-.~“‘-
.2. \\ .\.
Em” \
F- “~‘
$30.. \\
\\
\\
20" “~
10-
0 I I I l I

 

 

0 6 12 18 24 30

STORAGE TIME HR

Figure 5.19.-—Inf1uence of container size on vitamin
concentration history.

 

78

 

4.86 PPM

—-—- 8.71 PPM

 

 

VITAMIN CONCENTRATION WL
assassamssasé

 

 

i; I I I I I

0 6 12 18 24 30 36
STORAGE TIME HR

Figure 5.20.--Inf1uence of initial dissolved oxygen
concentration on predicted mass average
vitamin concentration history (light‘
intensity = 535 lux).

79

An attempt was made to compare the rate of vitamin
degradation in a plastic bottle (permeable to oxygen) with
rate in a glass bottle. The oxygen permeability coefficient
for plastic is 3000 cc mil/day m2 atm (Karel, 1974). The
results are plotted in Figure 5.21. These results show
the significance of light transmission through the con-
tainer wall. The rate of vitamin degradation in a glass
bottle is more accelerated than the rate in a plastic con-
tainer with 20 percent light transmission (through the
wall). During the storage time the dissolved oxygen
concentration in the plastic container is maintained at a
higher level than in glass container. It is apparent that
light transmission through the container wall plays a major
role in the light-induced destruction of vitamin..

The preceding results illustrate the capabilities
of this computer-aided prediction model. As indicated
earlier, the program requires specific values for rate
constants describing vitamin degradation and oxygen uptake.
These rate constants are obtained from experimental studies
as discussed in the Experimental section.

An attempt was made to observe the influence of
smaller time increments on the predicted results. It was
found that with a time increment of .0625 hr the mass
average concentration value changed by less than 0.25
percent. Similarly decreasing the depth increment from
.0625 cm to .03125 cm did not significantly change the

Predicted results. The computer time used for the time

80

 

PLASTIC CONTAINER

— - — GLASS CONTAINER

 

VITAMIN CONCENTRATION VG/L

 

 

1; . . I .

 

 

0 6 12 18 24 30
STORAGE TIME HR

Figure 5.21.--Inf1uence of the type of container on
predicted mass average vitamin
concentration history.

81

increment of 0.13 hr for total storage time of 36 hours
was 10 seconds.

In developing the theory in section 3.2 it was
assumed that the thermal convective diffusion in the liquid
is negligible. In a real situation if there is a large
temperature differential present inside the container, it
may result in convective currents in the liquid. The
convective currents in this situation would result in
increased light-induced loss of vitamin than predicted
from the simulation developed in this study. Similarly,
the diffusion coefficients will vary depending on the
temperature and may influence the total light-induced
vitamin loss. The predicted results, as indicated in the
assumptions, are valid for a situation where the storage
temperature is maintained constant.

The results obtained in section 5.1.5 indicate that
the computer model developed in this dissertation can be
successfully used in predicting ascorbic acid degradation
in infant formula stored at constant temperature. The
method can be used for describing concentration history of
other quality factors in liquid foods. This information
can help the food processor in predicting in advance the
quality of an existing or new liquid food product, and in

designing the package containers.

VI. CONCLUSIONS

1. The experimental results indicate that the
ascorbic acid degradation and oxygen uptake in a liquid
food under limited oxygen presence can be described by
second-order rate kinetics.

2. The computer-predicted and experimental studies
confirmed that the rate of vitamin degradation in liquid
foods during storage is more accelerated in the presence
of light than under dark conditions.

3. Infant formula with an initial dissolved oxygen
concentration at.g§¢nnmjgn' with atmosPheric oxygen, in a
typical glass bottle (6 cm diameter) showed approximately
50 percent ascorbic acid loss after 36 hours of storage.
This loss occurred under 4284 lux light intensity at 7.2°C
storage temperature.

4. The computer-predicted and experimental results
confirmed that the rate of ascorbic acid degradation
increases as initial dissolved oxygen concentration is
increased.

5. The computer-predicted results showed that the
influence of light on rate of ascorbic acid degradation
increases as container size (cross-sectional width) is

decreased.

82

83

6. A typical polyethylene container provides more
protection to ascorbic acid than a glass container. The
protection was obtained even with high dissolved oxygen
levels present at all times compared with levels in glass
containers.

7. The computer predictions and experimental
results illustrate that the major portion of light-induced
ascorbic acid degradation occurred within 0%? cm layer
along the container wall.

8. The computer-predicted results on vitamin
degradation provided agreement with results obtained from
actual shelf-life tests. The standard deviations were
within 1.43 to 5.10 percent of initial ascorbic acid
concentrations. A similar agreement was obtained for
results on dissolved oxygen concentrations. The standard
deviations were within 2.85 to 7.01 percent of initial

dissolved oxygen concentrations.
6.1 Suggestions for Future Work

The author concludes that further work is needed:
(1) to determine rate constants and computer
prediction of ascorbic acid degradation in fruit juices;
(2) to determine rate constants and computer
simulation of color deterioration in liquid foods; and
(3) to incorporate the influence of thermal

convective diffusion in the computer model.

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APPENDIX

89

 

 

 

 

 

 

 

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