Modeling Gaseous Environment and Physiochemical Changes of

Chapter 15

Modeling Gaseous Environment and Physiochemical Changes of Fresh Fruits and Vegetables in Modified Atmospheric Storage Manjeet S. Chinnan

Downloaded by UNIV LAVAL on July 12, 2016 | http://pubs.acs.org Publication Date: September 7, 1989 | doi: 10.1021/bk-1989-0405.ch015

Georgia Experiment Station, Department of Food Science and Technology, The University of Georgia, Griffin, GA 30223-1797

There has been an increasing interest i n using polymeric films for packaging of fresh h o r t i c u l t u r a l commodities to provide several benefits such as protection against physical i n j u r i e s , improved sanitation, i n c l u s i o n of l i g h t , and more importantly modificaton of atmospheric composition. This a r t i c l e presents a review of empirical and non-empirical modeling approaches employed i n estimating the changing gaseous composition of the micro-atmosphere sorrounding respiring produce when packaged i n polymeric f i l m . In addition the work done i n our laboratory i s also discussed where ripening tomatoes at 'turning' stage were used as model commodity. The approach taken involved obtaining experimental data for r e s p i r a t i o n rate, and surface color change at twenty d i f f e r e n t but constant gas compositions. The experimental data obtained was used i n developing predictive models. The models were then validated against experimental conditions other than those used i n developing the models.

Modified atmosphere or controlled atmosphere storage are the terms used i n describing the storage environments where removal or addition of gases from the surroundings of the commodity i n storage r e s u l t s i n an atmospheric composition d i f f e r e n t from that of a i r (1-4). The term modified atmosphere i s used when the composition of the storage atmosphere i s not closely monitored and controlled, whereas controlled atmosphere generally indicates more precise gas compositional control. T y p i c a l l y , the modified atmosphere storage involves establishing or approaching to establish a desired gaseous environment around the product after a reasonably short transient period due to the interplay of the commodities' physiology and the physical environment. One p a r t i c u l a r technique i n creating modified atmospheres for storing h o r t i c u l t u r a l commodities deals with packaging the product i n a polymeric f i l m such that the 0097-6156/89/0405-0189$06.00/0 ο 1989 American Chemical Society

Jen; Quality Factors of Fruits and Vegetables ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

QUALITY FACTORS OF FRUITS AND


190

VEGETABLES

a c t i v e l y respiring and metabolizing product reduces O2 and increases CO2 l e v e l by r e s t r i c t i n g the exchange of a i r between the micro-atmosphere inside the package and the environment outside. With recent technical advances i n manufacturing polymeric films i t should be possible to produce a f i l m of desired physical and gas exchange c h a r a c t e r i s t i c s for packaging fresh produce. However, the l i m i t i n g factor i s i d e n t i f y i n g the appropriate packaging f i l m , which i s dependent upon the fundamental knowledge of the gas exchange c h a r a c t e r i s t i c s of both f i l m and commodity. Numerous researchers (5-7) i n the past have attempted to match the packaging needs to the commodity to be stored. The approaches taken have been largely empirical i n nature which involved testing of a large number of films produced by various f i l m manufacturing companies. Several other researchers have subsequently recognized the importance of using mathematical and computer modeling techniques i n developing p r e d i c t i v e equations for i d e n t i f y i n g polymeric films i n terms of permeability c h a r a c t e r i s t i c s such that desired modified atmospheres are obtained. This a r t i c l e reviews the modeling approaches reported by various investigators which have implications i n p r e d i c t i n g the appropriate c h a r a c t e r i s t i c s of packaging materials to maintain or create known and optimal l e v e l of gaseous atmosphere surrounding the commodity and within the commodity. Modeling of Gas Exchange i n F r u i t and Vegetable

Tissues

The work done i n t h i s area i s of significance both i n controlled and modified storage applications. I t deals with the rates at which metabolic gases d i f f u s e into and out of various commodities. Concentration of metabolic gases inside the tissue a f f e c t s i t s metabolic a c t i v i t y ( r e s p i r a t i o n r a t e ) . The metabolic a c t i v i t y along with the d i f f u s i o n c h a r a c t e r i s t i c s of the tissue has bearing on the gaseous concentration throughout the tissue. D i f f u s i o n Equations. Application of Fick's law of gas d i f f u s i o n i n f r u i t s was f i r s t investigated by Burg and Burg ( 8 ) . The Fick's f i r s t law of d i f f u s i o n (9) i s defined as:

J

=

A D

9c -sr

X

which states that the flux J (umoles/s · kg of f r u i t ) , of a gas, d i f f u s i n g normally through a b a r r i e r of area A (cm ) i s dependent on the d i f f u s i o n c o e f f i c i e n t D (cm /s), and the concentration gradient 9c/3x. In order to estimate the d i f f u s i o n c o e f f i c i e n t i t i s necessary to determine the concentration gradient of the gas i n the tissue. Further complicating the matter i s that one has to solve the equation of Fick's second law of d i f f u s i o n which i s needed not only i n knowing the change of the gas concentration at a given l o c a t i o n ( 9 c / 9 x ) i n the plant tissue but also to know how the concentration i s changing with time ( 9 c / 9 t ) . Such an equation for a metabolically active gas i n three dimensions (cartesion coordinates) i s given by Crank ( 9 ) : 2

2


15.

CHINNAN

Modeling Changes of Fresh Fruits and Vegetables 191 2

8c

8 c

8t

8x

82

2

2

8c

c

8y2

3z

2

where Ε i s the constant rate of gas consumption or evolution. The factor Ε i s zero for metabolically inactive or i n e r t gas. For one dimensional d i f f u s i o n i n x - d i r e c t i o n the Equation 2 s i m p l i f i e s to the following form:


8c/8t

2

= D 3 c/8x

2

±

Ε

(3)

The above equations are based on the assumption that the d i f f u s i o n c o e f f i c i e n t D i s independent of the gas concentration. However, that may not be necessarily true. Also, the d i f f u s i o n c o e f f i c i e n t i s usually dependent on temperature following an Arrhenius type r e l a t i o n s h i p . For a sphere, the Equation 2 can be represented i n terms of concentration gradient i n r a d i a l d i r e c t i o n (8c/8r) as follows: 3c — — 3t

2

=

3 c D(—— 8r

2 + 2

r

3c — ) 3r

±

Ε

(4)

General solutions of non-steady state problems (Equations 2 to 4) and of steady state problems when concentration i s independent of time, i . e . , 3c/8t = 0, are available i n the l i t e r a t u r e (9). For more complex problems, numerical solutions based on f i n i t e difference and f i n i t e element methods using high speed computers can be obtained (10-13). Solomos (14), i n a review of p r i n c i p l e s of gas exchange i n bulky plant tissues suggested that apart from the mathematical complexities, determining the resistance to d i f f u s i o n of the peel f r u i t s , roots, and tubers from the measurement of the e f f l u x of the inert gas introduces number of uncertainties due to d i f f e r e n t i a l d i f f u s i o n r e s i s t a n t between the skin, f r u i t surface and the f l e s h (15). Thus, i t cannot be always presumed that the concentration of the metabolically inert gas i s uniformly d i s t r i b u t e d throughout the fruit. Solomos (14) further i l l u s t r a t e d that the concentration gradient can be substantial i n non steady-state cases. For an example i t was assumed that a gas diffuses through an i n f i n i t e cylinder of unit cross-section area, with a d i f f u s i o n c o e f f i c i e n t s i m i l a r to that of the average f l e s h of 'Gala' apples (0.0014 cm /s). Then the d i s t r i b u t i o n of M molecules deposited at time t = 0 at one end ( o r i g i n , χ = 0) i s given by: 2

c(x,t)

=

l/(4irDt)

1 / 2

2

· exp(-x /4Dt)

(5)

Equation 5 i s solution of Equation 3 when Ε = 0 (9). From Equation 5 i t can be estimated that a f t e r t = 5 min % o f M a t x = 0 , 2.5 and 3.5 cm i s 42, 1.2 and 0.047, respectively. S i m i l a r l y , % of M after t = 20 min at χ = 0, 2.5 and 3.5 cm i s 24, 8.83 and 4.00, respectively (14). Solution of a governing d i f f u s i o n equation depends upon the assumptions made i n solving i t . As i l l u s t r a t e d i n an example above


192


VEGETABLES

numerical values of gas concentration at given time and location can be then estimated from the solution. However, the solution(s) i s only meaningful i f i t can be v e r i f i e d with experimental data.


Measurement of Internal Concentration of Gases. Several techniques have been reported i n the l i t e r a t u r e (15, 16) for determining i n t e r c e l l u l a r gas concentration i n h o r t i c u l t u r a l commodities. These techniques include evacuation, manometric procedures, gas (oxygen) microelectrodes, and removal of plugs of tissues followed by sealing i n a i r tight v i a l s . None of these methods are r e a l l y non-destructive to the extent they do not a l t e r the conditions the investigator may be interested i n measuring. Uncertainties associated with measuring true internal concentration of gases makes v e r i f i c a t i o n of mathematical models a d i f f i c u l t task. D i f f u s i o n B a r r i e r s . Another degree of complexity i n modeling gas d i f f u s i o n i n f r u i t s may come from the non-uniformity of resistance to d i f f u s i o n form one part of the f r u i t to the other. For example i n case of apples the d i f f u s i o n c o e f f i c i e n t at the center may be d i f f e r e n t from that of the fleshy part which may be then d i f f e r e n t from that of the skin. Nature of the d i f f u s i o n b a r r i e r i s another variable which can play a s i g n i f i c a n t role i n exchange of gases i n f r u i t s and other bulky organs as the d i f f u s i o n of gases can occur through gaseous pores, l e n t i c e l s , or stomata, or through aqueous or waxy layers of the epidermis. Water diffuses through d i f f e r e n t channels than gases (8, 17, 18). Gases d i f f u s e mainly through channels f i l l e d with a i r whereas water vapor transport takes place through aqueous medium. Modeling of Gaseous Composition of H o r t i c u l t u r a l Commodities Stored i n Polymeric Films Produce packaged i n a polymeric f i l m i s a dynamic system involving r e s p i r a t i o n and permeation. Permeation, P Q (ml/hr), of a gas G i n the f i l m package can be expressed as follows: P

G

(6)

= k AAG G

2

In Equation 6, k i s f i l m gas permeance constant (ml/hr•m «atm), A i s f i l m area (m ) and AG i s concentration (atm) difference of the gas G across the f i l m thickness ( f r a c t i o n ) . Respiration, R Q (ml of gas G/hr · kg of f r u i t ) , of a r e s p i r i n g product depends on number of factors such as gaseous composition surrounding the products, c h a r a c t e r i s t i c s of the product (gas d i f f u s i o n c h a r a c t e r i s t i c s discussed e a r l i e r ) , storage period and temperature, etc. Thus, R Q may be represented as a function f of those factors as given by: G

2

R

G

= f ( c ( 0 ) , c ( C 0 ) , c(E), t, T, M, CV, 2

2

X)

(7)

where subscript G refers to gas associated with r e s p i r a t i o n (oxygen, carbon dioxide or ethylene e t c . ) . In the above equation c(Û2) i s oxygen concentration, c(CÛ2) i s carbon dioxide concentration,


15. CHINNAN

Modeling Changes ofFresh Fruits andVegetables 193

c(E) i s ethylene concentration, Τ i s temperature, t i s storage time, M i s product maturity, CV i s c u l t i v a r type, and X i s any other f a c t o r ( s ) not e x p l i c i t l y expressed. By mass balance the rate of change of concentration of a p a r t i c u l a r gas of r e s p i r a t i o n i n the package i s given as: Ac(G)/At

=

P /V G

where, V i s t o t a l free volume i n the of the product i n the package (kg). the following d i f f e r e n t i a l forms for carbon dioxide concentrations i n the

R W/V

(8)

G

package (ml), and W i s weight Equation 8 can be written i n rate of change of oxygen and package:

dc(0 ) Downloaded by UNIV LAVAL on July 12, 2016 | http://pubs.acs.org Publication Date: September 7, 1989 | doi: 10.1021/bk-1989-0405.ch015

2

k A(0.21-c(0 ))/V o

dt

-

2

R W/V

(9)

0

dc(C0 ) 2

k Ac(C0 )/V c

dt

+

2

R W/V

(10)

C

The solutions of the above two equations w i l l y i e l d 0 and C0 concentrations within a produce package at any time between the s t a r t of the experiment and the time steady state conditions are achieved. The knowledge of r e s p i r a t i o n functions R and R (Equation 7) i s essential to solving Equations 9 and 10 and degree of complexity of obtaining those solutions depends upon the mathematical form of the r e s p i r a t i o n functions. Equation 8 i s expressed into Equations 9 and 10 for only oxygen and carbon dioxide, a s i m i l a r equation can be written for any other b i o l o g i c a l l y active gas ( f o r example ethylene); but again s o l u t i o n of that equation can be obtained only i f the corresponding rate of production or u t i l i z a t i o n function i s known. For steady-state conditions, that i s when permeation equals r e s p i r a t i o n , Equations 8-10 take a simpler form: 2

0

P

P

0

G

= RG

2

c

= k A(0.21 - c ( 0 ) ) = R W

(12)

P

(13)

o

C

2

0

= k Ac(C0 ) = R W c

2

C

However, solutions of the above equations can be obtained only i f the r e s p i r a t i o n functions are known. Work published by various investigators i n handling equations r e s u l t i n g from Equations 7 and 8 i s reviewed below. They have taken d i f f e r e n t approaches and made d i f f e r e n t assumptions i n modeling modified atmosphere packaging. Some of the e a r l i e r work was done at the Massachusetts I n s t i t u t e of Technology. J u r i n and Karel (19) investigated optimum packaging conditions for apples, and Karel and Go (20) for bananas. They assumed R to be a function of oxygen concentration only and obtained oxygen consumption rate curves from experimental data. They also found that r e s p i r a t i o n quotient, R /R , was equal to one for oxygen l e v e l greater than 3%. They 0

c

0


194


VEGETABLES

dealt with steady state conditions only and solved the respiration-permeation equation graphically. Graphical solution for 350 gm of bananas packaged i n polyethylene f i l m (package area = 0.095 m ) i s presented i n Figure 1, which shows steady-state oxygen concentration of 6.9%. Steady-state concentration of carbon dioxide was e a s i l y calculated from Equation 13, where R = R and R was obtained from Figure 1. Changes i n the package c h a r a c t e r i s t i c s w i l l r e f l e c t on the l o c a t i o n of the d i f f u s i o n (permeation) curve i n Figure 1, thus a desired gas composition i n the package, at steady-state conditions, can be obtained by appropriate s e l e c t i o n of package c h a r a c t e r i s t i c s . Karel and Go (20) also investigated the effect of temperature on the rate of r e s p i r a t i o n and assumed Equation 7 to be R = f ( c ( 0 ) , T). They found that at a given oxygen concentration l e v e l , temperature dependence of r e s p i r a t i o n rate conformed to the Arrhenius type equation. Veeraju and Karel (21) followed up on an e a r l i e r work of (19) and t r i e d to use two films of d i f f e r e n t permeabilities for c o n t r o l l i n g oxygen and carbon dioxide l e v e l s i n a package and met with reasonable success. They worked with apples and focussed on steady-state concentration values. They simultaneously solved the following two equations, while using the r e s p i r a t i o n rates, as needed, from the experimental curves for R and R : 2

c

0

0

0


2

0

RW 0

c

= (k A! + k A )(0.21 - c(0 ))

(14)

RW

(15)

o l

C

o2

2

2

= (k Ai + k A )c(C0 ) c l

c 2

2

2

Equations 14 and 15 are manifestations of Equations 12 and 13, where additional subscripts 1 and 2 refer to two d i f f e r e n t packaging films. Henig and G i l b e r t (22) used f i n i t e difference method i n numerically solving the two f i r s t - o r d e r d i f f e r e n t i a l equations (Equations 9 and 10). They assumed R and R to be functions, f and g, of both oxygen and carbon dioxide concentrations, R = f ( c ( 0 ) , c(G0 )) and R = g ( c ( 0 ) , c ( C 0 ) ) , and obtained experimental r e s p i r a t i o n curves for tomatoes (Figure 2) to a t t a i n the solutions. Accuracy of computer predictions were tested against experimental data (Figure 3). A good agreement was found. Hayakawa and h i s colleagues (23) reported complex a n a l y t i c a l solutions using Laplace transformations for transient and steady state conditions simulating the gas exchange of a fresh product package. Although they assumed R and R to be functions of oxygen and carbon dioxide as done by (22), they expressed r e s p i r a t i o n rates as combination of l i n e a r equations of the following form: 0

c

0

2

2

c

2

2

0

R

c

(16)

o i = Pi + Qic(0 ) + r c(C0 ) 2

R

ci

i

2

(17)

= l i + m c(0 ) + n ( C 0 ) i

2

i C

2

where, c ( 0 ) < c ( 0 ) < c ( 0 ) ; c ( C 0 ) i < c(C0 ) < c ( C 0 ) ; ( i = 0, 1, 2, n); and l i , mi, n p q r i are constants of the i t h segment. Respiration rate data obtained by 2

i + 1

2

2

i

2

it

2

if

2

if


i + 1

Modeling Changes of Fresh Fruits and Vegetables 195


CHINNAN

2

4 6 8 10 12 Oxygen Concentration (%)

Figure 1. Graphical estimate of steady state concentrations of 0 and C0 i n polyethylene bags containing bananas. (Reproduced with permission from Ref. 20. Copyright 1964 Modern Packaging.) 2

2

LEGEND:

- CO

10

12

14

ABSORBED ACCUMULATED EVOLUTION RATE

16 18 2021

CONCENTRATION, PER CENT C0

2

CONCENTRATION,PERCENT

Figure 2. E f f e c t of 0 and C0 concentrations on 0 consumption rate and C0 evolution rate of tomatoes. (Reproduced with permission from Ref. 22. Copyright 1975 I n s t i t u t e of Food Technologists.) 2

2

2

2


Jen; Quality Factors of Fruits and Vegetables ACS Symposium Series; American Chemical Society: Washington, DC, 1989. ·

+ ^•COMPUTER

TIME, HR.

2

(C0 )

2

2

(0 )

60

CALCULATION (C0 )

+ EXPERIMENTAL

12 16 20 24 28 32 36 40 44 48 52 56

»

(O2)

CALCULATION

EXPERIMENTAL

Figure 3. A comparison between computer c a l c u l a t i o n and experimental results of the atmosphere change i n RMF-61 package. (Reproduced with permission from Ref. 22. Copyright 1975 I n s t i t u t e of Food Technologists.)

8

·

-ο-ο--ο- C O M P U T E R

•


15.

Modeling Changes of Fresh Fruits and Vegetables 197

CHINNAN

(22) was used by (23) i n constructing appropriate l i n e a r equations. A f a i r agreement has been reported between the estimated gas composition values of (23) and the experimental values of (22). They (23) also proposed solutions for two f i l m packages, d e t a i l s of which are not presented here. Deily and R i z v i (24) derived a n a l y t i c a l solutions, s i m i l a r to (23) , solutions of Equations 9 and 10 to optimize packaging parameters or to estimate transient and equilibrium gas concentrations i n polymeric packages containing peaches. The r e s p i r a t i o n rate functions based on experimental data were of the following form, which were used i n obtaining the a n a l y t i c a l solutions:


R

0

= constant for c ( 0 ) > 5% 2

= -a exp(-bt) for c ( 0 ) < 5%

(18)

= constant for 1 < c(C0 ) < 27%

(19)

2

R

c

2

Cameron and h i s colleagues (Cameron, H. C ; Boylan-Pett, W.; Lee, J . , Michigan State University, unpublished data) obtained r e s p i r a t i o n data for tomatoes at three d i f f e r e n t stages of maturity, breaker, pink and red. For each stage they f i r s t obtained oxygen depletion curve with storage time and f i t t e d a function of the following form: c(0 ) = 2

They calculated R relationship:

0

a

a i

{l-exp[-(a + a t> 4]} 2

3

(20)

from Equation 20 using the following

dc(0 ) 2

V

where, V i s free space volume of experimental container used i n obtaining oxygen depletion data (ml), and W i s weight of f r u i t (kg). They were not concerned with the transient stage of gas exchange and developed only the prediction models for oxygen concentrations within sealed packages of tomato f r u i t . To achieve that goal they obtained the solution of Equations 12, 20 and 21 for various combinations of W, c ( 0 ) and f i l m permeability parameters. Details of methodology i n designing a packaging system i s given i n (25). Yang and Chinnan (26) developed an integrated model to predict gas composition and color development of tomatoes stored i n polymeric f i l m packages. They conducted t h e i r investigation i n several phases (26-28). F i r s t they obtained models to describe the effects of gas composition, oxygen and carbon dioxide, and storage period on r e s p i r a t i o n rate (oxygen consumption rate and carbon dioxide evolution r a t e ) . To obtain the mathematical expression of the following equation (Equation 7): 2

R

G

= f ( c ( 0 ) , c ( C 0 ) , t) 2

2


(22)

198

QUALITY FACTORS OF FRUITS AND VEGETABLES

they experimentally observed the r e s p i r a t i o n rates at 20 d i f f e r e n t but constant gas compositions involving four l e v e l s of oxygen (5, 10, 15 and 20%) and f i v e l e v e l s of carbon dioxide (0, 5, 10, 15 and 20%) and f i t t e d polynomial equations (28)· V a l i d a t i o n of models was done by testing the adequacy of predictions against the experimental data of two a r b i t r a r i l y selected constant gas compositions (28). The next step taken was to predict steady-state oxygen and carbon dioxide concentration of the environment of ripening tomatoes packaged i n f i l m . The method used i s summarized below. It was assumed that for a short time period, At, the net amount of 0 and C0 change i n the package, based on Equations 12 and 13, can be expressed as follows: Downloaded by UNIV LAVAL on July 12, 2016 | http://pubs.acs.org Publication Date: September 7, 1989 | doi: 10.1021/bk-1989-0405.ch015

2

2

a = R WAt - k A(0.21 - c ( 0 ) ) A t 0

o

(23)

2

b = R WAt - k Ac(C0 )At c

c

(24)

2

I t i s obvious that at steady-state conditions a and b w i l l be t h e o r e t i c a l l y zero, but i t i s d i f f i c u l t to obtain an e x p l i c i t s o l u t i o n for c ( 0 ) and c(C0 ) from Equations 23 and 24 when R and R are polynomial functions of c ( 0 ) , c(C0 ) and t . As a r e s u l t , Yang and Chinnan (26) employed an i t e r a t i v e method to determine c ( 0 ) and c(C0 ) values at any given time, t , such that a + b had the smallest possible value. Algorithm and further d e t a i l s are given i n (26)· Experimental and predicted values of the atmosphere changes i n four scenarios are i l l u s t r a t e d i n Figure 4, which showed a good agreement between estimated and observed values. In modeling physio-chemical changes i n tomatoes stored i n modified atmosphere storage, Yang and Chinnan (27) went one step further than predicting r e s p i r a t i o n rates. They used tomato surface color development as an indicator of physiological changes affected by environmental gas composition. Tomatoes were held at 20 constant gaseous compositions, as mentioned above f o r the r e s p i r a t i o n rate data, and the surface color development was p e r i o d i c a l l y monitored with a Hunter color instrument. Color data were presented i n terms of a/b r a t i o , where 'a' and 'b' are Hunter color parameters. A mathematical equation of the following form was proposed based on a study reported by (29). 2

0

2

c

2

2

2

2

2

2

(a/b)

Modeling Gaseous Environment and Physiochemical Changes of

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