THEM“

,2 r

\
RABEI ES '

\\llll\l\\\\\ \ll llzllll ll

\llll

 

 

31
LIBRARY
Michigan State
University l
K t

 

 

This is to certify that the

thesis entitled

The Browning of Ketchup Due to Oxidation and
the Shelf Life of Ketchup Packaged in a
Gamma Bottle

presented by

Christine Maria Burgess

has been accepted towards fulfillment
of the requirements for

Masters degree in Agricultural Engineering

Wt ‘

Major préessor U

 

 

 

 

Date Oc’f‘ R7} [687

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

’fi 1/”

'.l

iii-

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or betore dde due.

DATE DUE DATE DUE DATE DUE ll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An AMrmdlve Action/Equal Opportunity Iii-titular!
empire-9.1

 

THE BROWNING OF KETCHUP DUE TO OXIDATION
AND ITS SHELF LIFE IN A GAMMA BOTTLE

by

Christine Maria Burgess

A THESIS

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

MASTERS OF SCIENCE
in

Agricultural Engineering

Department of Agricultural Engineering

1989

bosoqax

ABSTRACT

THE BROWNING OF KETCHUP DUE TO OXIDATION
AND ITS SHELF LIFE IN A GAMMA BOTTLE

by

Christine Maria Burgess

An experiment was performed to measure the oxygen transmission rate through the
Gamma squeeze bottle for ketchup and to determine the permeability constant for the
Gamma material itself. Another experiment was carried out to study the change in the
color of ketchup after long term exposure to an oxygen rich environment and to establish
a minimum acceptable redness level for ketchup as measured by a standard chroma
meter. The combined results were then used to determine the reaction rate between
oxygen and ketchup and to predict the shelf life for color stability of ketchup packaged in
the Gamma bottle. The predicted shelf life is 320 days.

Approved:

 

Robert Y. Ofoli, Major Professor

Date:

 

Approved:

 

Larry J. Segerlind, Department Chairman

Date:

 

To my parents

iii

ACKNOWLEDGMENTS

This is in grateful acknowledgement to the following people for their support and

assistance throughout my graduate program:

Dr. Robert Ofoli, for his constant help in answering questions, his aid in the
preparation of the final copy of this thesis, and for being an understanding and

patient major professor.

Dr. Larry Segerlind and Dr. George Mase for their encouragement in this endeavor

and for being on my committee.

Very special thanks are due Dr. Gary Burgess, without whose assistance and guidance
this work would not have been possible.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................... vi
LIST OF FIGURES ............................................................................................. vii
NOMENCLATURE ............................................................................................ viii
1 INTRODUCTION AND LITERATURE REVIEW ........................................... 1
1.1 Color Measurement for Tomatoes .............................................................. 2
1.2 Oxidation Reaction ..................................................................................... 10
2 OBJECTIVES ...................................................................................................... 12
3 EXPERIMENTAL METHODS AND RESULTS .............................................. 13
3.1 Ketchup Browning Experiment .................................................................. 13
3.2 Oxygen Diffusion ........................................................................................ 16
3.3 Combined Diffusion and Reaction .............................................................. 20
4 PERMEABILITY AND SHELF LIFE ESTIMATION ...................................... 31
4.1 Gamma Bottle Permeability ........................................................................ 31
4.2 Ketchup Shelf Life Estimation .................................................................... 38
5 DISCUSSION ...................................................................................................... 43
6 CONCLUSIONS ................................................................................................. 46
7 APPENDIX A ..................................................................................................... 47
8 APPENDD( B ...................................................................................................... 49
9 APPENDIX C ...................................................................................................... 50
10 REFERENCES .................................................................................................. 51

LIST OF TABLES

Table 1. Oxygen Concentration and Chroma Meter Values ................................. 15
Table 2. Oxygen Permeability Data for the Gamma Bottle .................................. 34

vi

LIST OF FIGURES

Figure 1. Munsell Color Disk ................................................................................. 5
Figure 2. Chroma Meter Color Space ..................................................................... 8
Figure 3. Setup for the Oxygen Consumption Experiment ................................... 14
Figure 4. Control Volume Used For Unsteady Diffusion and Reaction Analysis 21
Figure 5. Volume of Ketchup Used for Collision Theory of Reaction Rates ....... 25
Figure 6. Ketchup Redness Versus Number of Moles of Oxygen Consumed ...... 30
Figure 7. Diffusion through a banier .................................................................... 32
Figure 8. Measurement Types and Positions Taken on a Typical Band cut from

the Gamma Bottle ................................................................................................... 36
Figure 9. Error Analysis of dA on a Typical Band Cut. ........................................ 39

vii

:5“

agr‘r‘W'JO'“

NOMENCLATURE
exposed surface area, m2
desirable reactant characteristic
redness color attribute used by Chroma meter, dimensionless
primary color blue with wavelength 435.8 nm
undesirable product characteristic
yellow color attribute used by Chroma meter, dimensionless
permeability constant for Gamma material, cc-mil/day-mz-atm
concentration of oxygen, moles/liter
initial constant oxygen concentration, moles/m3
interface oxygen concentration, moles/m3
prescribed concentration on the surface of the ketchup, moles/m3
diffusion coefficient for oxygen in ketchup, mzls
diffusion coefficient for oxygen in the Gamma material, mz/s
permeability coefficient for the gas in the membrane
activation energy
fraction left to complete steady state
primary color green with wavelength 546.1 nm
depth of the ketchup, m
reaction rate constant, l/day
lightness value used by Chroma meter, dimensionless
perimeter, m
molecular weight, grams/mole

mass of oxygen molecule, kg

viii

N number of moles

order of reaction, dimensionless

:3

partial pressure of gas, atrn

critical oxygen consumption, moles/m2
dimensionless parameter

universal gas constant, 45.61 ml-atm/mole-°R
primary color red with wavelength 700 nm
permeation rate, moles/day

consumption rate, moles/day

solubility, cm3(gas at STP)/cm3(solvent)/atm

slant height, m

Hmwpngw-DO‘U

absolute temperature, °R

F.

time, days

average molecular speed, m/s
volume of bottle, ml

x bottle thickness, m

<=|

xo penetration distance of oxygen into the ketchup, m
X,Y,Z tristimulus values

VAR variance

collision rate parameter

symbol for ‘change in’

flux, moles/s/m2

symbol for surface integral

S—o-‘GD'G

ix

1 INTRODUCTION AND LITERATURE REVIEW

Secondary food quality indicators such as flavor, odor, consistency, texture and
overall appearance are intentionally regulated by the control of growing and processing
conditions. Once packaged in a transparent container or wrap, it is often the color of the
food product inside that the consumer notices first, and this visual observation often
creates preconceived ideas about the other quality factors. This is particularly true for
ketchup packaged in the plastic squeeze bottle [Gould, 1974]. Because color is a key
factor used by the consumer in evaluating the acceptability of the product, a major
function of the package must be to preserve the desired color of the product inside by
controlling a number of deteriorating environmental factors such as light, oxygen,
moisture, heat, and contamination. For ketchup in a squeeze bottle, heat, moisture loss,
and oxygen consumption lead to the browning over time [Hodge, 1953; Eckerle et al.,
1984]. Of the three deteriorating factors, oxidation is considered to be the major cause of
browning since moisture loss has not been a problem [Vilece, 1955], and distribution and
storage temperatures can be controlled.

Karel (1974) studied the effects of both oxygen and moisture on various packaged
products in general and found that protection from environmental gas and vapor
exchange through packaging depends as much on the permeability of the packaging
material used as it does on the integrity of the seals and closures. Since the squeeu bottle
is more than adequate as a barrier against moisture loss, the browning of ketchup in this
package is expected to depend almost entirely on the oxygen barrier properties of the
bottle material alone since the mouth of the bottle is usually sealed with foil. Whereas an
evaluation of the barrier properties of the squeeze bottle is relatively straightforward, a

study of the effects of oxygen on the color stability of ketchup is not. The browning of

ketchup by oxidation requires a knowledge of the reaction rate between oxygen and
ketchup, a means of measuring color, and a method for relating this to visual evaluation.

The latter two requirements are discussed first.

1.1 Color Measurement for Tomatoes

Ordinary light is the collection of electromagnetic waves having wavelengths within a
band known as the visible spectrum. The human eye responds to each wave differently by
producing the sensation of a particular color associated with the wavelength. In
particular, since all objects absorb certain wavelengths from incident light and reflect
others, it is only the reflected waves in combination which determine the object’s
perceived color [Williams et al., 1972]. If an object reflects all of the light rays it
receives, it is said to be white. An object is black if it absorbs all the light rays that fall
upon it. An object is red if it reflects red light and absorbs all other colors. Strictly
speaking however, color is not a property of the object since the illuminating source may
be deficient in certain wavelengths. Fluorescent lighting for example is undesirable for
color comparisons of tomato products as it makes them appear less red than they would
under natural light due to the deficiency of the wavelength perceived as red in fluorescent
light [Lamb, 1977]. Incandescent light on the other hand is rich in red and therefore
makes tomato products appear redder than they would under normal daylight [Lamb,
1977]. See-through packages may also change the color of tomatoes by attenuating
certain incident and reflected waves as they pass through the package. These are only a
few reasons why food color quality is difficult to judge [Robinson et al., 1951]. Even
without these problems with lighting and packaging, color quality is still difficult to

evaluate simply because it is difficult to measure and quantify.

It is the response of the human eye to light containing a collection of wavelengths that
makes color measurement complicated Through different studies conducted by
independent researchers [Evans, 1948; Wright, 1969; Clulow, 1972], it was found that
color perception may be described in terms of three fundamental variables called hue,
saturation, and lightness, using the terminology of the Optical Society of America (OSA).
These variables were also called hue, chroma and value, respectively, in earlier literature
[Evans, 1948]. The most important of these is hue which is the essential quality of a color
which leads the observer to call it primarily red (R), green (G), or blue (B). Physically,
hue is quantified by specifying the wavelength of the dominant primary color, R, G, or B,
in the mix. Saturation refers to the purity of the dominant primary color or alternatively,
the percentage of hue. More common terms associated with saturation are tint and tone
which are used to imply a desaturated color often by the addition of white, gray, or black.
Lightness refers to the overall brightness or brilliance of the color. Physically, lightness is
a measure of the energy or intensity of the collection of wavelengths forming the color.
Two colors are perceived as being nearly the same if their hue, saturation, and lightness
are the same. Note that this does not require that the complete spectra for the two colors
be identical, which indicates that the human eye is selectively stimulated.

Implied in the designation of hue, saturation, and lightness as the essential quantities
responsible for color perception is that the three primary colors, R, G and B, are the
fundamental building blocks for the entire color spectrum. While this is not entirely true,
it does provide the basis for the operating principles behind color television and the first
analog color measuring device to be discussed, the Munsell disk. The Munsell color
comparison system [I-land, 1953] consists of a disk containing adjustable sections of the
appropriate primary colors along with black and gray sectors. For some applications, one
or more of the primary colors may be replaced by mixtures of primary colors in order to

increase saturation. The Munsell disk used for the color grading of tomatoes for example
uses red, black, gray, and yellow (Figure 1). Spinning the disk gives the illusion of a
single color made up of a blend of these four. Visual scores for tomatoes are assigned
according to USDA standards [Lamb, 1977] by first adjusting the proportions of each
color sector mix to visually match the color of the tomato and then specifying the percent
of each as with a pie chart. The minimum requirement for USDA grades A and B for
ketchup is that the perceived color be equivalent to or better than (contains more red) the
color produced by spinning the Munsell disk adjusted to contain 65% red, 21% yellow,
and the remainder black or gray. The minimum requirement for grade C is that the color A
be equal to or better than the color produced using 53% red, 28% yellow and the
remainder black or gray. Any sample failing to meet the minimum color requirements for
grade C is assigned the substandard grade D, regardless of how the ketchup rates in odor,
flavor, and texture [Lamb, 1977]. The major drawback to this method is that color
matching is obviously very subjective.

The more elaborate digital color measuring system is completely objective and was
developed by the Commission Internationale de I’Eclairage (C.I.E.), also known as the
lntemational Commission on Illumination (I.C.I.). The basis for the color measuring
devices which rely on this system is again the observation that of all of the colors in the
visual spectrum, the three which can be used most successfully in color matching
experiments (calorimetry) are red, green, and blue. Consequently, R, G and B have been
designated as the primary colors [Williams, 1972]. Unfortunately, pure monochromatic
wavelengths for R, G and B or even narrow bands of wavelengths centered around these
three simply cannot be mixed in any way to produce certain colors perceived by the eye.
For example, the color cyan is a mixture of green and blue with red not added but taken

out. The C.I.E. overcame this difficulty with R, G, and B by postulating the existence of

Red

Figure 1. Munsell Color Disk

three theoretical but "unreal" primaries which are capable of covering the entire color
spectrum by purely additive mixtures. Because these theoretical primaries cannot actually
be produced nor appreciated by the eye if they could be produced, they are referred to as
"stimuli" rather than primary colors and denoted by tristimulus values X,Y, and Z
[Clulow, 1972]. The precise wavelengths of the stimuli in terms of those for R, G and B
are [Clulow, 1972]

X = 2.3646R -0.5151 G +0.00523 (1.1)
Y = 1.42640 -0.8965R —0.01448 (1.2)
Z = 1.00928 + 0.0887 G - 0.4681 R. (1.3)

Instruments such as the Hunter Color Meter [Gould, 1974] or the Standard Chroma
Meter [Minolta, 1988] are designed to capture light reflected off the surface of an object
and with the aid of special filters, analyze the spectrum and digitally display the
tristimulus values. The only problem with measuring color in this way is that the
tristimulus values are either too sensitive or too insensitive to color changes depending on
the dominant color (hue) being observed. In an attempt to remedy this situation, these
instruments were also designed to display their own individual versions of
perception-based stimuli related to the tristimulus values. For the Chroma Meter used in
this study, the chromaticity coordinates (a,b) and the lightness factor L are defined in

terms of the tristimulus values as

a = eta-ell
,, = “lei-ell

Y 5

L = 116(—) -16 (1.6)
Yo

where X0, Y0, and Z, are the tristimulus values of the illuminant used. For example,

daylight has the values of X°=98.041, Yo=100.00, and 20:1 18.103 [Minolta, 1988].

Physically, the chromaticity coordinates are measures of redness (a) and yellowness (b),

respectively. Finally, the OSA key perception variables of hue, saturation and lightness

are defined as

Hue = g- (1.7)
Saturation = Vaz + b2 (1.8)
Lightness = L . (1.9)

Yeatman (1960 & 1969) discussed in detail the use of such measurements to quantify
color. To completely express the color of a product, a three-dimensional color space
covering the key elements of hue, saturation, and lightness must be used. Such a color
space based on the chromaticity coordinates and the lightness is shown in Figure 2. A
color may be quantified by its position using either rectangular coordinates (a,b,L) or
cylindrical coordinates (saturation, arctan (hue), lightness). The latter coordinate system
is used most frequently in the literature but with unconventional definitions of hue as alb
and hue angle as arctan(a/b) which amounts to nothing more than a change in reference
for the angle from counterclockwise from the x-axis to clockwise from the y-axis.

Little (1975) discusses the origin of the confusion over two definitions of hue and hue
angle in the Hunter system and points out that alb as hue turns out 'to be more appropriate
for tomatoes since this definition is more sensitive to changes in b. Still, there are

mathematical problems with either definition of hue. Regardless of which definition is

 

 

 

 

 

White
L
Yellow
+b
Green? -a +a __). Red
-b
Blue Gray
L*
Black

Figure 2. Chroma Meter Color Space.

used, if the chromaticity coordinate in the denominator is near zero and undergoes a
small change from say +0.000001 to -0.000001, the result is an enormous change in both
the magnitude and sign of hue. But common sense dictates that a small change in a
chromaticity coordinate like this cannot possibly produce such a large perceived
difference in color. Hue by either definition then may be unrealistically sensitive to small
changes in color and therefore may not be the best measure of color quality.

Ultimately, the perception of color rests with the human eye, which in all probability
does not rely on hue alone or saturation alone, but responds to particular combinations of
wavelengths in the visible spectrum depending on the illuminating source, the object
being viewed, and other factors not accounted for with conventional colorimetry
methodology. Perhaps the best way to proceed with evaluating color quality is to admit
that since color judgment under identical experimental conditions must still be somewhat
subjective, there is a need to statistically correlate objective color measurements with

visual scores. Yeatman (1960) found that the empirical formula

2000 a = T.C.I. = Tomato color index (1.10)
L To2 + b”)
correlated best with the visual scores assigned by trained observers for evaluating the
color quality of tomatoes. The higher the visual score, the better the product. The
correlation coefficient between the average of the visual scores and the formula was 0.97.
Kramer [1959] noted however that color scores based on visual evaluation alone are
suspect since observers Operating without reference guides tend to drift towards an
average evaluation whereby consistently high quality is downgraded and consistently
poor quality is upgraded Even though Yeatman’s visual scores are questionable, his raw

data for color measurements do reveal a general tendency for the Hunter color values a, b

10

and L to be related to each other. For example, whenever "a" is high, "b" is generally low
and vice versa which means that it may be possible to characterize browning reactions by
following the change in only one of these values as the color deteriorates.

One of the few researchers to study color changes resulting from deterioration was
Eckerle (1984) who found a correlation between sensory and instrumental testing
methods when studying the effects of storage temperatru'e on the deterioration of canned
tomato paste. The color of the product was analyzed by two sensory testing methods and
three instrumental testing methods. All three instrumental analyses indicated that the
product became browner as it deteriorated. Moreover, the Hunter colorimeter values a, b,
and L all decreased together as the paste became darker, less red, and less yellow.
Sensory tests also concluded that the flavor developed a hay, caramelized, burnt, prune or
bitter taste. This was one of the first studies to suggest that periodic color measurements

can be used to gauge the overall condition of the product.

1.2 Oxidation Reaction

Vilece (1955) found that oxidation plays an important role in many non-enzymatic
food discolorations based on the observation that darkening occurred concurrently with
oxygen absorption and carbon dioxide production. She added that acidic foods like
ketchup generally absorb oxygen slowly. Hodge (1953) emphasized the complexity of
browning reactions due to the many intermediate reactions involved. He discusses several
distinct routes leading to the final stage of browning, but adds that it remains to be
determined which of these reactions are operative and to what extent one affects another
in a given food under a given set of conditions.

Labuza (1982) proposed that for foods in general, the loss in nutrient value and other

less tangible quality attributes such as color could be described by the chemical reaction

11

A —» B (1.11)

where A is a desirable characteristic and B is an undesirable one. Applied to an oxidation
reaction with fresh ketchup, A could then be either a physical quantity or a color attribute
associated with fresh red ketchup and B the same but associated with brown ketchup.

Labuza further noted that the decrease in A per unit time could be described by an

expression of order n
M
—— = k A" 1.12
d: ( )

where k is the reaction rate constant, n is the order of the reaction, and t is time. For most
reactions, k is strongly temperature dependent [Latham, 1964] and n is 0 or 1, although
fractional orders have been found to occur [Labuza, 1982]. Fractional orders generally
indicate a complex multistage reaction. Once k and n are measured, the extent of reaction
for any length of time t can be determined, and the shelf life of the product with respect
to color degradation can be established when the barrier properties of the package are

also known. These ideas were applied to the oxidation of ketchup in a Gamma bottle.

12

2 OBJECTIVES

The objectives of the study are:

1. To measure the amount of oxygen consumed by a fixed quantity of ketchup in a
closed oxygen rich environment over time and relate this to appropriate color
measurements.

2. To measure the oxygen diffusion rate through a Gamma bottle without ketchup.
Since the Gamma bottle is a composite of polypropylene (PP) (for structure) and ethylene
vinyl alcohol (EVAL) (for barrier properties), a secondary objective of this part is to
evaluate the mix .

3. To predict the shelf life of ketchup in a Gamma bottle using the results of the two

separate experiments described above.

13

3 EXPERIMENTAL METHODS AND RESULTS
3.1 Ketchup Browning Experiment

In order to verify that browning does not take place unless ketchup is exposed to air,
several glass jars were filled to capacity with fresh ketchup and surface color readings
were taken using a Chroma Meter (Minolta, 1988). The average of the chroma values
were found to be a=l9.6, b=9.3, and L=28.2. Metal lids were then screwed onto the jars
and sealed around the rims with wax so that no air could get into the jars between the
threads. With the ketchup totally deprived of air in this way, the jars were then placed in
a cabinet held at 21.1°C. After 1 month, the lids were removed and the ketchup chroma
values were again measured. The average values were found to be a=l9.5, b=9.1, and
L=28.0. This slight change in color, most likely due to aging, was insignificant when
compared to the larger changes in color that occur when ketchup is exposed to air.
Although this identifies exposure to air as a requirement for browning, it does not prove
that oxygen is responsible nor does it show that oxygen is consumed during browning.

In order to verify that it is oxygen that causes browning and that oxygen is actually
consumed by the ketchup in the process, eleven 400 ml beakers fitted with lids containing
gas sample extraction ports were filled with 50 ml of fresh ketchup and sealed as shown
in Figure 3. The headspace contained an oxygen concentration of 21.4% when the
beakers were sealed and stored under standard conditions of 21.1°C and 50% RH. After 3
days, a gas sample was extracted from one of the beakers and analyzed on the gas
chromatograph (GC) for oxygen concentration. The result was 21..102% as shown in
Table 1. The sealed lid was then taken off the beaker and a surface color measurement

was taken using the same Chroma Meter. Similar measurements were taken from the

14

Oxygen Sample Extraction Port

   

 

  
  

Aluminum Lid

 

 
       

 

e . .
. S l
Headspace (390 ml arr) 0 ea
0 . 0
Initially 21.4% 02
e ' e . e
. O
O 0 7.1 cm '.D.
o . Glass Beaker
. \—>
. 0
e e e .
e 02 . 9
0 . 0 Surface Color
. Measurement
0
. . O . 0
50 ml Ketchup X; “I

 

 

 

Figure 3. Setup for the Oxygen Consumption Experiment.

15

Table 1. Oxygen Concentration and Chroma Meter values

 

 

 

 

 

 

 

 

Beaker # Days Headspace O, a b L
tested concentration, (red) (yellow) (lightness)
%

1 0 21.40 19.67 9.33 28.66
2 3 21.10 19.36 8.07 27.75
3 6 20.97 18.61 7.47 83.72
4 10 20.89 18.52 7.87 27.75
5 17 20.70 18.05 7.67 27.77
6 27 ' 19.98 17.27 7.71 27.72
7 30 19.90 17.04 7.77 27.92
8 33 19.81 16.92 7.41 27.36
9 36 19.80 16.46 6.79 27.82
10 52 19.65 15.70 7.61 28.00
1 1 55 19.60 15.50 5.32 26.20
12 90 18.70 13.72 3.93 25.82

 

 

16

remaining beakers at regular intervals. The results in Table 1 clearly show that the
oxygen concentration inside the beaker continued to decrease over time and that the
surface color changed from red to brown as shown by the decline in the chroma value "a"
indicating that oxygen had been consumed in the browning process. Since the changes in
oxygen concentration and redness were small, separate sensitivity experiments were
performed on the GC and the Chroma Meter to determine their respective instrument
errors. This was done to verify that the measured changes were not the result of
instrument imprecision alone.

To determine the precision of the GC, 50 samples were taken from still lab air using a
syringe and analyzed. Precautions were taken to minimize the possibility of taking air
samples contaminated by human or plant respiration. From the fifty air samples, only the
maximum and minimum GC results for percent oxygen content were used to calculate the
instrument error, defined here as half the range expressed as a percent of the average

%ERROR = Mm. (3.1)
max+m1n

The instrument error for oxygen measurement was found to be 0.54%.

To determine the associated error for the Chroma Meter, thirty color measurements
were taken at various locations on the surface of fresh ketchup. Again using only the
maximum and minimum chroma "a" values in Eq. (3.1), the Minolta Chroma Meter
instrument error was found to be 1.73%. This error may also include color

non-homogeneity of ketchup.

3.2 Oxygen Diffusion

Having shown that oxygen is consumed by ketchup during browning, it is now

necessary to determine the extent to which it reacts chemically with ketchup. It is entirely

17

possible that browning requires oxygen only as a catalyst and that oxygen consumption is
the result of diffusion alone. It is more likely however that both diffusion and reaction
take place simultaneously. In order to gauge the extent to which diffusion plays a role in
the potentially combined diffusion/reaction process, pure diffusion was studied first.
Oxygen molecules were assumed to diffuse through the ketchup with no direct
involvement in a chemical reaction. Fick’s law for diffusion in the downward direction
(Figure 3) states that the flux of oxygen molecules through each layer of ketchup is

proportional to the oxygen concentration gradient:

3c
(b — -Dg; (32)

where 41 is the flux (moles/s/mz), c(x,t) is the concentration of oxygen x (m) below the

surface at time t (s), and D is the diffusion coefficient for oxygen in ketchup (mzls). A
mass balance for oxygen diffusing through a control volume fixed in space leads to the
one-dimensional transient diffusion equation in a homogeneous substance [Holman,

1986],

8’ 3
Di; = 33-. (3.3)

Since glass and metal are impermeable to oxygen [Dow, 1984], the beakers used in
the browning experiment allowed no oxygen to enter from the outside so that the
assumption of one-dimensional diffusion is justified. The solution to Eq (3.3) for a
prescribed constant concentration c(0,t)= c, at the boundary x= 0 of the ketchup and no
flux (ac/ax =0) at the bottom (x=h) of the ketchup with an initial constant oxygen
concentration c(x,0)=ci is given in Appendix A. At the bottom of the ketchup, the oxygen

concentration c(t) is

18

 

 

€0-00) _ 4 Q9 qzs Q49
c,-c, ’ «(q-3+?'7+"° (3.4)
where
-7tth
= 3.5
q cxv[ 4h, ] ( )

Please see Appendix A for the derivation of Eq. 3.4.

The numerator on the left hand side of Eq (3.4) represents the change in oxygen
concentration at time t needed to reach steady state and the denominator represents the
change required from the start. Therefore, the left hand side will be denoted by f(t) and
referred to as the instantaneous fiactional change left to go to reach steady state. A value
of f=1 then means that the diffusion process has just begun and corresponds to q=l and
t=0 while a value of f=0 means that steady state has been reached with q=0 and t = co. For
values of t>0, Eq (3.5) gives q<1 so that the infinite series in brackets in Eq (3.4) is
dominated by the first term q. Using only the first term on the right hand side with f(t) on
the left hand side and solving for t from Eq (3.5) gives the time required to reach the

fraction f left to achieve steady state,

= 53% 1n [$1 (3.6)
Since ketchup is essentially hydrated cellulose (tomato pulp) held in suspension by
water which accounts for at least 70% of the product by volume [Lamb, 1977], the
diffusion coefficient for oxygen in water will be used [Geankoplis, 1983] as an estimate,
D = 3.25x10‘9 mzs‘} (3.7)
In the oxygen consumption experiment (Figure 3), the beakers were filled with
ketchup to a depth of 1 cm. With x=0.01 m, D=3.25 x10" mzls, and f=0.05 in Eq. (3.6),
the time required to reach 95% of steady state is 40,370 8 or 11.2 hours. In other words,

19

the ketchup should have been nearly saturated with oxygen through diffusion alone in
about a half a day. This means that if oxygen had acted only as a catalyst in the browning
reaction with the concentration of oxygen inside the ketchup controlled by diffusion
alone, then the compositions of the headspace air in all of the beakers referred to in Table
1 should have been the same. The fact that they were not supports the conclusion that
oxygen was actually consumed in a chemical reaction during browning. Of course this
conclusion does not hold if the diffusion coefficient in Eq (3.7) is in error. Since the
headspace air composition continued to change up to 90 days, the diffusion coefficient
for oxygen in ketchup would need to be smaller than the value in Eq (3.7) by a factor of
90x24/11.2=193, or about two to three orders of magnitude in order to support the
alternate conclusion that oxygen acts purely as a catalyst.

The case for oxygen being consumed in the browning reaction is further supported by
examining the solubilities of oxygen in both ketchup and air. Again assuming that
ketchup is essentially water, these room temperature solubilities under exposure to

normal air are [Masterton and Slowinski, 1973]

S 1 = 2.82x10'4 moles oxygen per liter water (3.80)

S, = 86.9x10'4 moles oxygen per liter air. (3.8b)

Therefore, the maximum amount of oxygen that can by absorbed by the 50 ml of
ketchup is (2.82 x 10‘)(0.05)= 1.41 x 10” moles. In comparison, the amount of available
oxygen in the 390 ml headspace above the ketchup in the beaker is (86.9 x 10“)(O.390)=

3.39 x 10 '3 moles which says that the ketchup is capable of consuming only

1.41x10'5
3.39x10’3

)100 = 0.42% ' (3.9)

20

of the available oxygen in the headspace by diffusion alone. However from Table 1, the

ketchup did actually consume as much as

(0214’0'187) 100 = 12.6% (3.10)

 

0.214

of the available oxygen after 90 days which amounts to 12.6/0.42 = 30 times more than
saturation by diffusion will allow. Therefore, diffusion alone without reaction does not
account for the amounts of oxygen consumed. This can only mean then that oxygen is
involved directly in the browning reaction. Moreover, because of the results in Eqs. (3.9)
and (3.10), the evidence suggests that oxygen is consumed much faster than it can
diffuse. This should halt the diffusion of oxygen altogether at sorrre depth below the
surface and confine browning to the surface layers only. The extent of the affected region
is expected to be determined by a balance between the diffusion rate and the reaction rate.

A quantification of this can be made only by studying diffusion and reaction together.

3.3 Combined Diffusion and Reaction

The fundamental differential equation for combined diffusion and reaction can be
derived by first considering an element of ketchup in the form of a thin rectangular slab
of ketchup as shown in Frgure 4. The diffusion constant for oxygen in ketchup is assumed
to be unaffected by the change in chemical makeup during the reaction. Oxygen can
leave the slab in two different ways. The first is by a difference in fluxes at each face of
the slab and the second is by consumption due to reaction. The net number of moles ND

of oxygen leaving the slab in time At by diffusion alone is

ND = [%Ax](AAT) (3.11)

and the net number of moles NC consumed in the browning reaction in time At is

21

 

flow area A

9(x.t) ¢(x+Ax,t)

 

 

.AJLLJC

 

 

 

Ax=thickness

Figure 4. Control Volume Used for Unsteady Diffusion and Reaction Analysis.

22

NC = (k c”At)(A Ax) (3.12)

where the Labuza (1982) reaction rate from Eq (1.12) was used. Since the total amount of

oxygen leaving the slab must equal the reduction in the amount of oxygen in the slab,

34>

. _ -9.
'81-(AAXAI)+I€C (AAxAt) .. 81(CAA")A" (3.13)

Dividing each term by AAtAx, rearranging, and using Eq (3.2) gives

BC 826 ,.
a — D-ax—z-kc. (3.14)

Since Eq (3.14) is a nonlinear partial differential equation, it is doubtful that it can be
solved analytically. Fortunately, a steady state solution exists which provides the
information sought. If steady-state conditions exist, then Bela: is zero everywhere, c

becomes a function of x only, and Eq (3.14) reduces to

dzc ,.
DEX—2 = kc. (3.15)

The solution to Eq (3.15) is obtained by introducing z=dc/dx so that

 

dzc dz dz dc dz

_ = _ = __ = — .16

4x2 dx dc dx 2 dc. (3 )

Substituting this into Eq (3.15) gives

D 2 dz = kc” dc (3.17)

and integration leads to
22 3+!
D 5 = n + 1 + constant. (3.18)

Eq (3.18) shows that the steady state solution cannot be c(x)=co as with pure diffusion

alone since z=dcldx must depend on c and is therefore nonzero. Since 250 in Eq (3.18)

23

for obvious physical reasons and c starts out at c0 when x=0, the concentration must
eventually reach zero at some location x, presumably inside the ketchup. Beyond this

point, there is no oxygen so that

dc
f 2 , = —-
orx x0 c 0 and dx

II
P

(3.19)

Forcing Eq (3.18) to fit these internal boundary conditions requires the constant of

integration to be zero so that
dc , I 2k c" *1
— = — —— .2
dz (7: + DD . (3 0)
Integrating and using the boundary condition that c=co at x=O gives

(1-"): _ (1-,” n ’1 ka
c — co +—2 _—(n +1”) (3.21)

or in terms of x0,

210-»)
C x
Co [1 - x0 ] (3.22)

2 +1Dc§"")
x, = 1 \j (" ’ (3.23)

 

 

 

l - n k

As expected, Eq. (3.23) predicts a decrease in the penetration distance as the reaction
rate k increases relative to the diffusion rate D. In addition, this steady state solution
makes physical sense only for n < 1, since xo would otherwise be negative and the
concentration would increase with depth into the ketchup. Because the browning reaction
is known to be complex, a fractional order of reaction 11 < l is expected [Latham, 1964].
Using n= 0.5 for example, D= 3.25 x 10‘9 mZ/s from Eq (3.7), c, = 0.282 moles/m3 from
Eq (3.8) and the fact that in each browning experiment, the discolored portion was found

 

24

to be confined to a thin surface layer approximately 1 mm thick regardless of exposure
time, Eq (3.23) gives k= 0.021 moles°"’/m"5/s as an estimate of the oxidation reaction
rate. Used in this way, Eq (3.23) may be viewed as a relationship between n and k
involving ketchup properties D and c and a measurable quantity x,. Unfortunately, this
appears to be as far as the results of the browning experiment will allow the analysis to
go and falls somewhat short of the desired goal of finding n and k separately. However,
even if n and k could be determined individually by sorrre experiment, the interpretation
of the results would be difficult since both may change values during the different stages
of the browning reaction depending on whether separate reactions occur in sequence
(series reactions) or several reactions occur concurrently (parallel reactions). The
browning reaction probably involves both series and parallel reactions and for this
reason, 11 and k in Eq (3.23) are most likely weighted averages of the individual n’s and
k’s for the separate reactions.

The preceding analysis has shown that browning is essentially a surface phenomenon
and that n and k in the context of Eq (1.12) may be too complex in meaning to be of any
real value. A simpler approach based on the collision theory of reaction rates [Frost,
1961] will be used to produce a more practical version of the reaction rate equation.
Consider a volume of pure ketchup with an exposed surface area A that has not yet
absorbed any oxygen as shown in Figure 5. Of all the molecules of oxygen immediately
surrounding the surface of the ketchup, only 1/6 of these are expected to hit the surface
since on the average there are equal numbers of molecules moving in six perpendicular
directions, one of which may be considered to be directed toward the surface. Since the
average speed of a molecule is (Frost, 1961]

25

 

 

 

O
I . o ‘
O
. l ,
l . . .
e I 0
O
O I. O
O
Exposed ' I . .
° Surface ' 0
Area A
. —Il .— «‘— —- -
O O
/ e '
. 2 ' '
/ e
/0 . Fixed Air
/ Volume V o
I. O

 

 

 

Figure 5. Volume of Ketchup Used for Collision Theory of Reaction Rates.

26

I; = V331 (3.24)

where T is the absolute temperature (R), R is the universal gas constant (45.61

ml-atm/mole-°R), and M is the molecular weight (grams/mole), the number of moles that

 

hit per unit time is
1 concentration x volume __ _l_ c(AE dt) _ l _
6 dt — 6 “(it — 6 C A u. (3.25)

Of these, only a fraction, f, is expected to adsorb and react with the ketchup with the
fraction (l-f) rebounding back into the surrounding air. Since molecular speeds are
distributed normally with E as the average, and since the browning reaction is expected to
take place only if the kinetic energy of an individual oxygen molecule equals or exceeds
the required activation energy EA [Frost, 1961], f should be related most strongly to the
distribution of speeds. For example, if EA just equals mr-t'2/2 with m the mass of an oxygen
molecule, then f should be about 0.5. Even with the required activation energy however,
an impacting oxygen molecule may still not cause a reaction simply because of a
deficiency in the number of favorable impact sites on the surface of the ketchup which
would allow the molecule to adsorb. This suggests that f may be dependent on the oxygen
concentration as well since increasing c would have the net effect of positioning more

molecules over favorable impact sites. From Eq (3.25) then, the flux of oxygen molecules

reacting with the ketchup is
1 dn

where B =fr'i/6 is a function of temperature through 17 and possibly c through f. This

result is similar in structure to the defining equation for heat transfer by convection

[Holman, 1986] with (p analogous to the heat flux, 0 to temperature, and B to the average

27

surface heat transfer coefficient. Since the browning experiment was performed at
constant temperature, B was taken as a function of c alone with B = kc“'l so that the

modified reaction rate equation becomes
4) = kc" (3.27)
where k now is the reaction rate and n is the order of the reaction.
The reaction constants in Eq (3.27) were determined by fitting this relationship to the
observed data in Table 1. Substituting n==cV into Eqs (3.26) and (3.27) gives

1519. _ -322 = kc» (3.28)

4) Ad: — Ad:

with V the headspace air volume. Integrating the last equality gives

 

620 = am)? (3.29)
where

(Iggy? (3.300)

p = 1:" (3.3011)

and c, = initial oxygen concentration = 8.85 moles/m3.

After taking the natural log of both sides of this equation, p and z were chosen so that
the overall difference between the actual and the predicted results (the variance) was a
minimum,

N . 2
VAR = £[ln -:—'-pln (1—zt,-)] = minimum (3.31)

3.1 a

28

where (t,, c,) are the N actual data. Differentiating VAR with respect to p and 2 then
setting the derivatives equal to zero for a minimum results in two independent equations
for p in terms of z,

N ct e
.2 Inc-1n (1 - 2t) .2 —

r-l

N 'N—_—_'
2 11120-211) .2 "——

iBl i=1 ‘

 

(3.32)

'6
I

The computer program in Appendix B calculates c,/co from the data in Table 1 as the
ratio of percent compositions and uses Eq. (3.32) to obtain the solution for p and 2 by
trial and error. The results of the fit are p=—0.983 and z=-0.00191 day". With V=390 ml =
3.9 x 10“ m3 and A=3.96 x 10'3 m2 from Figure 3, the order of the reaction and the
reaction rate are found from Eq (3.30) to be n=2 and k=2. 15 x 10'5 m‘lday/mole. Since
these results apply to the modified Labuza reaction rate equation in Eq (3.27) instead of
Eq (1.12), a fractional order for 11 should not necessarily have been expected.

The specific information required for shelf life calculations is the relationship between
redness and the amount of oxygen consumed. The amount of oxygen consumed is
determined from Table l as the reduction in oxygen concentration co - c(t) converted into
a reduction in oxygen partial pressure and then into the number of moles using the gas
law. For example, after 33 days of exposure to headspace air at room temperature

(sample 8 in Table 1), the number of moles of oxygen consumed was

(0.214 - 0.1981) (390)
(45.61) (530)

 

2.57x10" moles. (3.33)

Since this amount was consumed only by the exposed surface whose area was 3.96 x
10” m’, the consumption rate required to produce a corresponding redness of 16.92 from
Table l is 0.065 moles/m2. This procedure was applied to the remaining data and ketchup

 

29

surface redness was graphed against moles/m2 of oxygen consumed in Figure 6. After 52
days, the exposed surface of the ketchup developed a redness of 15.7. This color level
was chosen by a small test panel to be the minimum level required for an acceptable

surface color when compared to fresh ketchup. Therefore, from Figure 6,

moles oxygen

= 0.072
Q m2 surface

(3.34)

must be absorbed by the ketchup before its color can be considered unacceptable.

Chromameter Redness Value

30

191

18.

17‘

16‘

 

 

15v

Test Panel Results For
Unacceptable Color Level

11»

 

 

I L l J

«1-

 

db
«1-
ult-
di-

T

.02 .09 .06 .08

Holes of Oxygen Consumed

d‘b
0

Per m2 of Exposed Ketchup Surface

Figure 6. Ketchup Redness Versus Number of Moles of Oxygen Consumed.

31

4 PERMEABILITY AND SHELF LIFE ESTIMATION
4.1 Gamma Bottle Permeability

The two processes by which gas and vapor move through packaging materials are
flow through imperfections like pinholes and cracks in the package and diffusion through
the pore structure of the material itself. Since the mouth of a Gamma bottle is sealed with
foil after it is filled with ketchup, diffusion through the exposed surface of the bottle is
the only way that oxygen can reach the ketchup. In general, diffusion through a banier is
driven by a difference in concentration in gas or vapor molecules across the barrier.
Molecules adsorb on the surface of higher concentration, diffuse through the barrier
toward the side of lower concentration, and then desorb as shown in Figure 7. Fick’s Law
in Eq. (3.2) may be used to describe gas transport through the bottle with D now the
diffusion coefficient for oxygen in the Gamma material (m2/day). If D is constant and the
bottle wall thickness is small, then the concentration gradient may be expressed as a finite

difference and Fick’s law for the diffusion rate in moles/s becomes

dn (01"(32)
d1 — DA Ax

 

(4.1)

where c1 and c2 are the surface oxygen concentrations inside and outside the bottle, A is
the bottle surface area, and Ax is the wall thickness. Since c, and c, are usually difficult to
measure experimentally, the concentrations in Eq. (4.1) may be related to the gas partial
pressures through Henry’s law ['I‘obolsky, 1971]

c = S p (4.2)
where S is the equilibrium solubility constant for a given gas-polymer system in cm3 (gas
at STP)/cm3 (polymer)/atm and p is the gas partial pressure in atrn. Substituting Eq. (4.2)
into Eq. (4.1) gives the permeability equation [Dow, 1984]

 

32

    

oee}€€0w
90¢ 09¢ .

           
 

 

o .
..909 009
xwmv.§2V

. . ..
....... .. m
a... N.... ........ o

 

  

 

Figure 7. Diffusion Through a Barrier.

33

dn (Pr‘Pz)
dt — CA Ax

 

(4.3)

where C = DS is the permeability constant for a given gas-polymer system.

To experimentally determine the oxygen permeability constant for the Gamma
material, twelve empty bottles were flushed with 100% nitrogen at 1 atrn, sealed, and
stored under standard conditions (22.8°C, 1 atrn, 21% Oz and 50% RH.). The bottles were
flushed for a period of three hours before they were sealed. After 49 days, a gas sample
was extracted from each bottle with a syringe and analyzed on the same gas
chromatograph used in the browning experiment to determine the percent oxygen
content. This result was then converted into an equivalent volume of oxygen under
standard reporting conditions of 1 atrn and 22.8°C using the gas law and the measured
bottle volume of 720 ml. For example, if after 49 days the GC measured an oxygen
content of 3.5% inside the bottle, then the oxygen partial pressure was 3.5% of 1 atm =
0.035 atm and the equivalent STP volume of oxygen was 3.5% of 728 ml = 25.5 cc since
the experiment was already conducted under STP conditions. Since the bottle was
initially flushed with nitrogen, this volume of oxygen also represents the amount of
oxygen which had permeated into the bottle, and the oxygen transmission rate under
standard conditions was 25.5 m1/49 days = .52 cc/day. The actual oxygen transmission
rates for the 12 bottles tested are shown in Table 2. The average oxygen transmission rate

was found to be
OTR = 0.56cc/day. (4.4)
The oxygen transmission rate in moles/day may be obtained from the rate in cc/day
using the gas law result that one mole = 24,173 cc at STP. It is more common, however,

to find the permeability equation in Eq (4.3) written as [Dow, 1984]

Table 2. Oxygen Permeability Data for the Gamma Bottle

34

 

 

 

 

 

 

 

 

 

Bottle % 0, from cc/day {it C
Number GC dx cc-mil/mz-day-atm
after 49 days m’lmil

l 6.30 0.94 0.00124 3581

2 4.97 0.74 0.00133 2646

3 2.10 0.31 0.00141 1052

4 2.45 0.36 0.00126 1371

5 5.88 0.87 0.00100 4160

6 6.58 0.98 0.00129 3608

7 3.01 0.45 0.00142 1500

8 2.87 0.43 0.00122 1665

9 2.24 0.33 0.00121 1314

10 4.55 0.68 0.00129 2494

11 2.38 0.35 0.00117 1434

12 2.17 0.32 0.00126 1214
Average 3.79 0.56 0.00126 2170
Std. Dev. 1.67 0.25 0.0001 1 1046

 

 

35

£0. = CAAP

day -x— (4.5)

where Ap is the difference in oxygen partial pressures (atrn) inside and outside the bottle,

x is the wall thickness of the bottle (mil), A is the exposed surface area of the bottle (m2),
and C is the permeability constant (cc-mil/mz-day-amr) for oxygen in the Gamma

material. When the thickness varies over the surface of the bottle, the permeability

equation is replaced by
cc dA
22; = C Ap f:- (4.6)

where fdAlx is the integral over the exposed surface of the bottle. The integral was

estimated by cutting the bottle into thin bands as shown in Figure 8. Four thickness
measurements, x, at the center of each band were taken at locations A, B, C and D using a
vernier caliper along with the four corresponding slant heights S and the perimeters L of
the top and bottom of the band. The measurements for a single bottle are given in
Appendix C. The contribution of each band to the total integral was then approximated
by

(twam )(s‘u, +sc+so)

”4% = 2(9, +1., new“) _ (4'7)

4
The individual results for each band were added to obtain fdA/x for the entire bottle.

Eq (4.7) was also used for the base of the bottle by taking the bottom L equal to zero, the
top L equal to the circumference, and the slant heights as the radii. The results for the 12
bottles cut and measured are given in Table 2. The average value for the integral is

12.639 cmzlmil.

36

 

 

 

 

bot

Figure 8. Measurement Types and Positions Taken on a Typical Band cut from the
Gamma Bottle.

37

The final quantity in Eq (4.6) required for the calculation of the permeability constant
C is Ap. Since the oxygen partial pressures found in the bottles after 49 days were on the
order of a fraction of a percent, the partial pressure difference was essentially constant at
Ap = 0.21 atrn. Using Eq (4.6), the results for the permeability constant are shown in the
last column of Table 2. The Gamma material is primarily polypropylene (PP) for
structure with a thin layer of ethyl vinyl alcohol (EVAL) to provide barrier properties.
The permeability constant was expected to be a weighted average of the permeability
constants for oxygen in PP and oxygen in EVAL, respectively. The reported permeability
constant for oxygen in PP is C = 1,300 to 6,400 cc-mil/mz-day-atm [Packaging
Encyclopedia, 1985] and for oxygen in EVAL is C = 0.16 to 1.4 cc-mil/mz-day-atm
[Dow, 1984]. Since the average permeability constant obtained for the Gamma
copolymer in Table 2 is much closer to that for PP than for EVAL, the thickness of the
EVAL layer was probably very small.

The variations in data found in Table 2 are due both to measurement errors and
manufacturing differences between bottles. Because of precision of the GC, the
concentrations of oxygen found in the bottles after 49 days and therefore the oxygen
transmission rates may be in error by as much as 0.54% from an earlier calculation.
Another source of error in the area integral is the measurement of the band dimensions in
Figure 8. Using a vernier caliper with a sensitivity of 1 mil, the average thickness taken
over the various band locations was found to be about 50 mil so that an error of +/-1%
may be attached to each thickness measurement in Table 2. The measurement errors
associated with the slant heights and perimeters are much smaller on a percent basis since
the measurements themselves are much bigger. Possibly the greatest source of error is the
approximation itself in Eq (4.7 ), because average values for L, S, and x were used This
error is difficult to quantify because it depends on how S and x vary between

38

measurement locations. More importantly, within this approximation there was an
additional error due to the way in which the band areas (numerator in Eq (4.7)) were
calculated. After the bottle was sectioned into bands, the bands were cut and unfolded
into flat strips as shown in Figure 9. Inevitably, the long sides of the band were rough and
jagged The maximum error associated with the length measurement in Figure 9 was 0.51
cm and the maximum error on width was 0.191 cm. The length and width measurements

are

L = 20.45 i 0.51 cm (4.80)

W = 1.272t0.19l cm (4.8b)
so that the band area A = LW is bounded between 21.52 cm2 and 30.62 cm’, or

A = 26.07 :I: 4.55 cmz. (4.9)

Using the error in the measurement of band dimensions, the total error associated with
the calculation of fdA/x was less than 20%. This explains part but not all of the variation
in the calculated permeability constant in Table 2. The rest is attributed to material

composition and manufacturing differences.

4.2 Ketchup Shelf Life Estimation

Shelf life is defined as the period between manufacture and retail purchase during
which the product is of satisfactory quality [Eckerle et al., 1984]. In order to estimate the
shelf life of ketchup with respect to color degradation when packaged in a Gamma bottle,
certain results from the browning and permeability experiments described in this and the
previous chapter are required. For convenience, they have been summarized below.

Gamma bottle oxygen permeation rate and relevant data are:

permeationrate = R, = CAp f? (4.10a)

39

 

0.191
1777‘ ’1 W

0.51
-—>-

 
      

0.51
Actual Strip 0.127

  

 

 

 

 

 

-( 20.45 —>

All Measurements in cm

Figure 9. Error Analysis of dA on a Typical Band Cut.

4o

Ap = 02 partial pressure difference (atrn)

C = 2170 [cc—mil] da;y"m"zatm'1 = permeability constant

{is = 0.00126 mzmil'l = area integral

A = 0.067 m2 = exposed bottle surface area.

For ketchup, the oxygen consumption rate and related adsorption data are:

Consumption rate = R, = k A c’I

c = 02 concentration in surrounding air (moles m’3)
k = 2.15x10‘5 m‘[mole - day]"1 = reaction rate

n = 2 = order of reaction

A = 0.067 m2 = exposed ketchup surface area

S,‘ = 2.82x10‘4 moles/liter = solubility of oxygen in ketchup

:4
II

, 86.9x10'4 moles/liter = solubility of oxygen in air

Q — 0.072 moles m2 = critical oxygen consumption for browning.

(4.10b)

(4.10c)

(4.10d)

(4.10e)

(4.110)
(4.11b)

(4.116)

(4.11d)

(4.11e)
(4.11f)
(4.11g)

(4.11h)

Under actual storage conditions, the rate at which ketchup adsorbs oxygen is limited

by the rate at which the bottle allows oxygen to permeate inward. From Eq (4.10), the

bottle permeation rate is determined by Ap alone since the remaining quantities are fixed

bottle properties. The maximum possible R1, is obtained by using an inside oxygen partial

pressure of zero. Therefore, the maximum R1, (in monay) is

R, = (2170) (0.21 -0) (0.00126) = 0.57 cc/day = 2.38x10‘5

(4. 12)

41

where the conversion 1 mole = 24,173 cc at STP has been used. Now assume that the
actual inside oxygen partial pressure is in fact zero. Then the oxygen concentration c, at
the interface between the ketchup and bottle must also be zero which makes the
consumption rate Rc = 0 from Eq (4.11). But this cannot happen because oxygen entering
the bottle through permeation is forced to react with the ketchup as soon as it appears at
the interface. The ketchup has nowhere else to go. The true interface concentration must

therefore be chosen so that R, and R, are equal, which means that c, cannot be zero.

The permeation rate when c, is not mm is most easily obtained by converting Ap in

Eq (4.10) back into a concentration difference using the ideal gas law. This in essence

amounts to reverting back to Fick’s Law. Using p= (n/V)RT= CRT,

R = CRT(co-c,)f% (4.13)

P

where R: 45.61 ml-atm/mole-°R is the universal gas constant, T= 530 °R is the assumed
absolute storage temperature, c, = S, = 86.9 x 10“ moles/liter is the outside oxygen
concentration, and ci = is the unknown interface concentration. Substituting the required
quantities into Eq (4.13) and making the appropriate conversions gives

_ 217045.61 _,_
R, .. 24173 1000 (530)(86.9x10 C,)(0.00126) (4.140)

 

01'

R

P

(2.38110'5-0.00273c,) moles/day (4.14b)

provided that c, is in moles/liter. The corresponding consumption rate is

R = 2.15x10"(0.067)(1000c,.)2 (4.15a)

R = 1.44 c? (4.15b)

42

again with ci in moles/liter. The condition that R, = Rt leads to a quadratic equation in c,
c} + 1.9x10'3c, - 1.65x10" = 0. (4.16)
The solution to Eq (4.16) gives the interface concentration

c. = 32.2x10" mole/liter (4.17)

which when substituted back into either Eq (4.14b) or Eq (4.15b) gives the true

permeation and consumption rates:

R = R = 1.51110" moles/day. (4.18)

p c

The actual permeation rate is less than the maximum rate in Eq (4.12) as expected but
the predicted interface oxygen concentration in Eq (4.17) is greater than the assumed
solubility of oxygen in ketchup (water), Sk = 2.82 x 10“ moles lliter. One possible
explanation of this result is that ketchup is capable of holding much more oxygen than
previously assumed, about 322/282 = 11.4 times more. This is the situation if a volume
property such as solubility can even be considered to apply to a surface phenomenon.
The more likely explanaan which is consistent with oxidation and browning as a surface
effect is simply that the browning reaction dictates this concentration based on supply
and demand, regardless of solubility. In any case, Eq. 4.17 must be true since the
permeation and consumption must be equal.

The shelf life for browning may now be deduced from the oxygen consumption rate in
Eq. 4.18 and the ketchup properties in Eq. (4.11e) and Eq. (4.11h). The calculation gives

. QA (0.072) (0.067)
Sh um = — = = 320da . 4.19
c e R. 1.5x10’5 ys ( )

 

43

5 DISCUSSION
The actual shelf life of ketchup in the Gamma bottle could not be measured directly

due to difficulties encountered in the color measurement process. The average shelf life
of 320 days is based on an unacceptable redness level of 15.7 for ketchup by itself, not
for ketchup packaged in the translucent Gamma bottle. This was done because both the
measured and perceived redness of the ketchup is altered considerably when viewed
through the bottle. The true color quality of the ketchup can be evaluated only when the
bottle is opened and some ketchup is removed. But this process alters the color since
browning is a surface defect and the act of removing ketchup from the bottle by whatever
means tends to mix surface ketchup with fresh red ketchup underneath. The result is a
mixture whose surface redness measurement varies too much with location to be of any
real value.

This was the case with several new unopened battles placed in storage at room
temperature at the beginning of the browning experiment. After six months, the bottles
were opened and some ketchup was removed by simply pouring it out into a dish. The
measured redness levels varied with surface location and were anywhere from about 16
to 19. It is difficult to conclude on the basis of these measurements that the predicted
shelf life is correct. In support of this conclusion is the unwritten industry standard for
ketchup and many similar perishable products that the package be designed to give the
product a shelf life of at least one year [I-Ieinz, 1988]. Whether or not it was the intention
of the Heinz Company to adhere to this standard when considering color quality is not
known since performance data related to the Gamma bottle was never released It was
found in the permeability experiment, however, that the Gamma bottle was adequate for

this purpose. It was also found that the effectiveness of the EVAL layer in the

44

predominantly PP bottle wall as a barrier improvement is questionable since the overall
permeability constant for the Gamma copolymer was well within the range of
permeability constants for PP alone.

Some environmental factors not studied in this research which may influence the color
degradation of ketchup in a Gamma bottle are temperature, humidity, exposure to light,
and age. Storage temperature is expected to effect both the oxygen transmission rate
through the bottle and the consumption rate by ketchup. Increased temperature typically
increases permeation through a material by expanding the pore structure of the material
[Karel, 1974]. In terms of the parameters which determine the permeation rate in Eq
(3.6), the permeability constant C = DS increases primarily because the oxygen solubility
S increases. Increased temperature will most likely also increase the oxygen consumption
rate of ketchup by increasing the activation energy of the oxygen molecules consumed in
the browning reaction. It would appear that increasing the storage temperature should
reduce the shelf life considerably.

Humidity is known to affect permeability in a number of ways. For most packaging
materials, absorbed moisture may either reduce the oxygen transmission rate by blocking
pathways through the material or increase it by making oxygen more soluble in the
hydrated material [Karel, 1974]. In reality, absorbed moisture probably does both
simultaneously and the net increase or decrease in permeation rate with environmental
humidity is determined by pore size and structure. For the Gamma bottle, the effect of
humidity on permeability is not known.

Exposure to light is another factor which may affect the color of ketchup in opposite
ways. Radiation delivering heat to the surface will most likely accelerate the browning
process for reasons mentioned above and at the same time may whiten the surface by

bleaching. The extent to which the separate effects occur is expected to depend on the

45

type of light the ketchup is exposed to and the exposure time. The effect of exposure to
fluorescent store lighting over the duration of its shelf life in a Gamma bottle is not
known but the shelf life under these conditions may not be very much different from the
calculated value of 320 days since both the permeability and browning experiments were
conducted under lab lighting which is very similar to storage conditions.

Color deterioration due to age alone is the final factor not accounted for in this study.
The very first browning experiment performed in this research was done to establish that
oxygen was required for browning. As described in the beginning of Chapter 3, sealed
glass bottles full of ketchup were stored in a dark cabinet at room temperature for one
month. The redness value was found to change from 19.6 to 19.5 in spite of the fact that
the ketchup was deprived of oxygen, moisture, and light. This color change can only be
due to age and if it is assumed for simplicity that the rate of aging is constant, then the
change in redness over the 320 day shelf life would be (19.6 - 19.5) x (320/30) = 1.07 due
to age alone. Since the total change in redness required to turn the ketchup brown is 19.67
- 15.5 = 3.97 from Table 1, age must then be considered to account for (1.07/3.97) x 100
= 27% of the change in color over the 320 day shelf life and the combined effects of
oxidation, light, and heat, the rest. Even though this analysis is somewhat simplistic, it
does identify aging as an important factor related to color deterioration which should be

studied in future research.

46

6 CONCLUSIONS

The oxygen transmission rate through a Gamma bottle and the effect of oxygen
consumption on the surface color of ketchup were studied separately. The relationship
between surface redness and the amount of oxygen consumed along with the separate
oxygen transmission and consumption rates for the bottle and ketchup were used to
predict the shelf life for ketchup packaged in a Gamma squeeze bottle. It was found that
browning was confined to a thin surface layer of ketchup and that the consumption of
0.072 moles of oxygen per square meter of exposed surface reduced the redness level of
fresh ketchup from 19.67 to 15.7 as measured by a Minolta chroma meter. This level was
found by a small test panel to be the color quality limit for consumer appeal. When
packaged in a Gamma bottle and stored at room temperature, the shelf life of ketchup,
defined as the time required to reach the brown color limit of 15.7, was calculated to be
320 days.

47

7 APPENDIX A

SOLUTION TO THE TRANSIENT DIFFUSION EQUATION

The transient diffusion equation in one direction is

32 a
”5,762 = 5% (A—1)

and the boundary and initial conditions for the problem in Figure 3 are

c (O,t) = c, = constant (A -2)
-a£(h,t) = 0 (A-3)
8x

c(x,0) = c,- = constant. (A—4)

Use of the separation of variables technique [Powers, 1979] with c(x,t)= X(x)T(t) in Eq
(A-l) leads to the following ordinary differential equations,

d’x

Zx—i-l-pzx = O (A-S)
dT 2 _ _
dt +p DT — 0 (A 6)

where the constant p is an eigenvalue to be determined from the boundary conditions.
Solving Eq (A-5) for X and Eq (A-6) for T and using a series of products to obtain
X(x)T(t) gives

c (x, x) = c, + 2 (A, sin (px) +B, cos (px)) exp (-p2Dt) (A -7)
P
where part of the zero eigenvalue solution c, has been added and the A, and B, are

arbitrary constants. The boundary condition in Eq (A-2) requires that B, = 0 and the
boundary condition in Eq (A-3) requires that cos (ph) = 0 which gives

48

 

p = n = 0,1,2... (A -8)

Therefore, the solution in Eq (A-7) can now be written as

c(x,t) = c,+iE,sin[zr_(_n..;_§).::lexp[“TBD(n+-;)zx] (A-9)

£80 h2

 

where the E, are arbitrary constants. Finally, the initial condition in Eq (A-4) leads to the

Fourierseries
l
c,-c, = XE,sin[M] (A—lO)
Ira-0 h
which requires that the E, be
h l __ c.—c.
E, = 2f (c,-c,)sin M dx = 33—,5 (A-ll)
h 0 ’1 1t n+3

Therefore, using these in Eq (A-9), the solution to Eqs. (A-l), (A-2), (A-3) and (A—4) is

 

c (x,t) = c,—-,-l-(c,—

 

At the bottom of the ketchup in Figure 3, x= h and Eq (A-12) reduces to

c0-ch,t 4 9 25 49
__<__2 = _[q_g_+9_-g_,m)

co-c, 1t 3 5 7 (A—13)

where

 

— D
q = exp[ if] (A-l4)

49

8 APPENDIX B

LIST OF PROGRAM TO CALCULATE REACTION RATE CONSTANTS

10
20
30
35
4o
50
60
70
80
90
100
1 10
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270

DIM T( 10),C( 10)

CO = 21.4

FOR I = 1 TO 10

READ T(I).C(I)

NEXT

INPUT Z

P = 0

Q = 0

R = 0

S = 0

FOR I = 1 TO 10

L1: LOG (C(I) / CO)
L2=LOG(1 -Z*T(I))

P = P + L1 * L2

Q=Q+T(I) *Ll/(l -Z*T(I))
R = R + L1 * L1

S=S+T(I) *L2/(1 -Z*T(I))
NEXT

E = P * S - R * Q

PWR = Q/ S

PRINT E

PRINT Z,PWR

FOR I = 1 TO 10
CP=CO*(1-Z*T(I))"PWR
PRINT CP,C(I)

NEXT

GO TO 50

DATA 3,21.lOZ,6,20.972,10,20.885,17,207.27,19.975,
30,19.9,33,19.81,36,19.803,52,19.65,55,19.6,
90,18.7

50

BAND MEASUREMENTS TAKEN FROM A TYPICAL GAMMA BOTTLE".

Band"

OO\IO\M#UJNr—I

\O

10
11
12
13
14
15
16
17
18

L... Luca...
11.89 12.01
12.06 13.50
13.49 14.61
14.61 15.24
15.24 15.88
15.88 17.15
17.15 18.42
18.42 18.73
18.73 25.40
25.40 26.03
26.04 27.31
27.31 27.62
27.62 27.62
27.62 27.31
27.31 26.04
26.04 25.88
25.88 25.88
25.88 0.0

9 APPENDIX C
SA 8., Sc
1.37 1.29 1.35
1.40 1.25 1.37
1.40 1.32 1.45
1.42 1.30 1.45
1.45 1.25 1.45
1.52 1.29 1.45
1.51 1.31 1.47
1.50 1.29 1.49
1.47 1.29 1.45
1.42 1.35 1.42
1.55 1.32 1.58
1.55 1.25 1.58
1.52 1.25 1.55
1.37 1.25 1.32
1.39 1.29 1.37
1.35 1.25 1.32
1.35 1.30 1.35
0.31 0.79 0.31

*See Fig 8. L: cm, S: cm, and x= mil.
“Band 1 is at the top; band 18 is at the bottom.

so

1.25
1.25
1.25
1.25
1.25
1.25
1.32
1.32
1.25
1.27
1.29
1.58
1.25
1 .25
1.37
1 .25
1.30
0.79

X1

54
57
57
56
52
45
34
29
32
32
30
30
29
30
27
27
25
27

X3

53
62
54
53
46
45
39
38
52
59
56
56
56
53
50
38
28
27

xc

59
62
58
60
47
47
39
34
27
29
30
32
30
30
28
29
26
27

X6

48
55
46
44
41
41
32
30
36
46
43
46
45
43
4o
29
19
27

51

10 REFERENCES

Clulow, F.W. 1972. Colour: Its Principles and Their Applications. Fountain Press,
London.

Dow Chemical Co. 1984. Introduction to Banier Polymer Performance. Report #
190-333-1084.

Eckerle, J .R., Harvey, CD, and Chen, T. 1984. Life Cycle of Canned Tomato Paste:
Egrrelationgléetween Sensory and Instrumental Testing Methods. J. Food Science.
:1 188-11 .

Clulow, F.W. 1972. Colour: Its Principles and Their Applications. Fountain Press,
London.

Dow Chemical Co. 1984. Introduction to Banier Polymer Performance.

Eckerle, J .R., Harvey, CD, and Chen, T. 1984. Life Cycle of Canned Tomato Paste:
Correlation Between Sensory and Instrumental Testing Methods. J. Food Science.
49:1188-1193.

Evans, RM. 1948. An Introduction To Color. John Wiley and Sons, Inc., New York,
London, Sydney.

Frost, A.A. and Pearson, RG. 1961. Kinetics and Mechanisms 2nd Ed John Wiley and
Sons, Inc., New York, London.

Geankoplis, C.J. 1983. Transport Processes and Unit Operations 2nd Ed. Allyn and
Bacon Inc., Boston, London, Sydney, Toronto.

Gould, W.A. 1974. Tomato Production, Processing and Quality Evaluation. The AVI
Publishing Co. Inc., Westport, Connecticut.

Hand, D.B., Robinson, W.B., Wishnetsky, T., and Ransford, J .R. 1953. Application to
Food Quality Grades. J. Agr. Food Chem. 1:1209-1212.

Heinz Company, 1988. Private communication with R & D department

Hodge, LE. 1953. Dehydrated Foods: Chemistry of Browning Reactions in Model
Systems. J. Agr. Food Chem. 1:928.

Holman, JP. 1986. Heat Transfer, 6th Ed. McGraw-Hill Book Co., New York.

KarelisM8 19674. Packaging Protection for Oxygen-Sensitive Products. Food Technology.
( ):5 .

Kramer, A., Twigg, B.A., and Clark, B.W. 1959. Procedures for Determining Grades of
Raw Tomatoes for Processing. Food Technology. 13:62-65.

 

52

Labuza, TR and Riboh, D. 1982. Theory and Application of Arrhenius Kinetics to the
Prediction of Nutrient Losses in Foods. Food Technology. 36(10):66.

Lamb, EC. 1977. Tomato Products. National Canners Association Research
Laboratories. Bulletin 27-L, 5th Edition.

Latham, J .L. 1964. Elementary Reaction Kinetics. Butterworth and Co., London.
Little, A.C. 1975. Off on a Tangent. J. Food Science. 40:410-413.

Masterton, WL. and Slowinski, E.J. 1973. Chemical Principles 3rd Ed. W.B. Saunders
Co., Philadelphia, London, Toronto.

Minolta Camera Company. 1988 Chroma Meter Owners Manual.
Packaging Encyclopedia and Yearbook. 1985. Films, Properties Chart. 30(4):92-93.

Powers, BL. 1979. Boundary Value Problems, 2nd Ed. Academic Press, New York, San
Francisco, London.

Robinson, W.B., Ransford, J .R., and Hand, DB. 1951. Measurement and Control of
Color in the Canning of Tomato Juice. Food Technology. 6:314-319

Tobolsky, A.V., Mark, HF. 1971. Polymer Science and Materials. Wiley-Interscience
Inc, New York, London, Sydney, Toronto.

Vilece, R.J., Fagerson, 1.8., and Esselen Jr., W.B. 1955. Darkening of Food Purees and
Concurrent Changes in Composition of Head—Space Gas. Agr. and Food Chemistry.
3(5):433-435.

Williams, J .E., Trinklein, F.E., Metcalfe, HQ, and Lefler, R.W. 1972. Modern Physics.
Holt, Rhinehart and Winston, Inc., New York, Toronto, London, Sydney.

Wright, W.D. 1969. The Measurement of Colour. Adam Hilger LTD, London.

Yeatman, J .N., Sidwell, AP, and Norris, K.H. 1960. Derivation of a New Formula for
Computing Raw Tomato Juice Color from Objective Color Measurement. Food
Technology. 14(1):]6.

Yeatman, J.N. 1969. Tomato Products: Read Tomato Red? Food Technology.
23:618-627.

 

"Illlllllllllllllllllls