xan tho poulos 2012

Journal of Food Engineering 111 (2012) 326335

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Journal of Food Engineering

journal homepage: www.elsevier .com/locate / j foodeng

Mass transport analysis in perforation-mediated modified atmosphere packagingof strawberries

G. Xanthopoulos a,, E.D. Koronaki b, A.G. Boudouvis ba Agricultural University of Athens, Department of Natural Resources Management & Agricultural Engineering, 75 Iera Odos Str., 11855 Athens, Greeceb National Technical University of Athens, School of Chemical Engineering, 9 Heroon Polytechniou Str., 15780 Zografou, Greece

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 August 2011Received in revised form 2 February 2012Accepted 7 February 2012Available online 23 February 2012

Keywords:Modified atmosphere packaging (MAP)StrawberriesMathematical modellingFinite element methodMaxwellStefan equations

0260-8774/$ - see front matter 2012 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2012.02.016

Corresponding author. Tel.: +30 210 529 4031; faE-mail address: [email protected] (G. Xanthop

A space-and-time dependent mathematical model was developed to predict O2, CO2, N2 and H2O concen-tration in perforation-mediated polymeric packages during cold-storage of strawberries. The numericalsolution of the corresponding mathematical model was obtained by applying the finite element method(FEM). The problem was solved in a domain corresponding to the headspace of a package augmented bythe total void spaces of the contained bulk produce and for realistic boundary conditions. Transport of O2,CO2, N2 and H2O was modelled based on MaxwellStefan equations for gas transport through packagingsheadspace and on Ficks law for diffusion through the micro-perforated packaging. The model predictionswere tested against published experimental data of O2 and CO2 concentrations in modified atmospherepackaging storage of strawberries and the agreement is satisfactory. As for reaching the recommendedin the literature gases concentrations for strawberry storage, the model predictions revealed that thetested micro-perforated polypropylene packaging combined with the adopted storage conditions aremarginally adequate. To this end, the theoretical findings are suggestive of improvements, in terms ofmaterial properties, especially with regard to the permeability of the polymeric packaging film.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

Modified atmosphere packaging (MAP) is a technique for mod-ifying the in-package atmosphere using polymeric films with orwithout perforations to reduce quality deterioration and improveshelf-life of the packaged produce through water loss, metabolicand microbial activity reduction. The response of the packagedproduce to the generated atmosphere is affected by controllablefactors, such as packaging permeability, produce respiration, andstorage environment as well as uncontrollable factors, such as spe-cie, cultivar, cultural practices, stage of development, harvest tech-nique, tissue type, and postharvest handling. The permeability ofthe commercially used packagings depends on their type, areaand thickness. The mean permselectivity that is the CO2-to-O2 per-meability ratio, of the commercial packaging is close to 3.0 which,according to Exama et al. (1993), Smith et al. (2003) and Guillaumeet al. (2011), is inadequate to achieve the recommended O2 andCO2 concentrations when used with highly respired produce, un-less micro-/macro-perforations are employed. In the design of aMAP, produce mass/surface ratio, package dimensions and perme-ability should be considered. Significant design parameters are also

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x: +30 210 529 4032.oulos).

the time required for reaching gas equilibrium, the in-packagerelative humidity and the storage conditions.

Saltveit (2004) ranked strawberries, among others, perishablecommodities as highly respired produce with short storage-life.Therefore modelling their MAP response corresponds to a worstcase scenario. Strawberries are not chilling sensitive and the rec-ommended MA conditions are 05 C, 510% O2 and 1520% CO2as these have been sum up from different sources (Kader, 1992a;Thompson, 2003).

Respiration is a complex metabolic process affected by a range offactors such are storage temperature, gas concentrations, physicalstress, availability and type of consumed substrates and ripeningstage of the produce (Saltveit, 2004). The gas concentration depen-dent respiration rate models are based mainly on empirical equa-tions and enzyme kinetics theory (Peppelenbos and vant Leven,1996; Hertog et al., 1998, 1999; Fonseca et al., 2002; Saltveit,2004; Geysen et al., 2005). Transpiration is influenced by internalor commodity factors (morphological and anatomical characteris-tics, surface-to-volume ratio, surface injuries, and maturity stage)and environmental factors (temperature, relative humidity, airmovement, and atmospheric pressure; Kader, 1992b). Respirationand transpiration operate as source/sink mechanisms of O2, CO2and H2O and therefore their accurate mathematical descriptionplays an important role in the predictive capability of the overallmathematical model. Heat transport within the package can be
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Nomenclature

Ac produce surface (m2)Af packaging permeable area (m2)aw water activity of the packaged producedc equivalent produce diameter (m)Di/air binary diffusivity constant of i = O2, CO2, H2O in the air

(m2 h1)Di/eff effective diffusion coefficient of gas component i in the

air (m2 h1)Dij binary diffusion coefficient (m2 h1)dpac packaging width (m)Dv water vapour diffusion coefficient in the air (m2 h1)EaVmO2=CO2 activation energy of VmO2 or VmCO2 (J mol

1)ei error defined as the difference between the experimen-

tal and the predicted concentration of i = O2, CO2, H2Ohpac headspace height (m)Ka air-film mass transfer coefficient (kg m2 s1 Pa1)Kf ji packaging permeability in i = O2, CO2, H2O

(m3 m h1 m2 Pa1)KmO2 MichalisMenten constant for O2 consumption (kPa)KmO2f MichalisMenten constant for inhibition on the fermen-

tative metabolism by O2 (kPa)KmuCO2 MichalisMenten constant for non-competitive inhibi-

tion of CO2 (kPa)Ks skin mass transport coefficient (kg m2 s1 Pa1)lf thickness of the packaging film (m)mb mass of bulk produce (kg)Mi molecular weight of i = CO2, H2O, N2, O2 (kg mol1)_mtotalji flux rate of i = O2, CO2, H2O transport through the poly-

meric packaging and its micro-perforations(kg m2 h1)

_mw water vapour flux due to transpiration (kgH2O m2 h1)

n number of terms to sum upnp micro-perforation numberP total gas mixture pressure (Pa)

Pi partial pressure of i = O2, CO2, H2O, N2 (kPa)P0 atmospheric pressure (Pa)Ps saturation water vapour pressure (Pa)R ideal gas constant (J mol1 K1)Re Reynolds numberrespi respiration flux of O2 and CO2 (kg m2 h1)RH0 initial relative humidityRMSE root mean square errorRQox respiration quotient (dimensionless)RRi respiration rate of O2 consumption or CO2 production

(mol kg1 h1)Sc Schmidt numberSf film permselectivity without considering micro-

perforations (dimensionless)Sh Sherwood dimensionless numberSp micro-perforation area (m2)St film permselectivity considering and the micro

-perforations (dimensionless)T storage temperature (C g9 K)t storage time (h)Tref reference storage temperature (K)Vb bulk produce volume (m3)Vc packaging volume (m3)Vmi,ref reference maximum specific respiration rate of O2 or

CO2 (mol kg1 h1)VPD vapour pressure deficit (Pa)xiorj molecular fraction of i or j = CO2, H2O and O2x0ji initial molecular composition of i = O2, CO2, H2O (mol)Xm moisture ratio (kgH2O 100

1 kg1da)e porosity of the bulk produceq density of the air gasses components (kg m3)qb bulk density (kg m3)qi density of i = O2, CO2, H2O (kg m3)xi mass fraction of i = CO2, H2O, N2, O2 (%)

G. Xanthopoulos et al. / Journal of Food Engineering 111 (2012) 326335 327

assumed negligible for controlled environment storage. Moreover,temperature fluctuations during cold supply chain are ignoredbecause they are small and temporary; if accounted for, theywould increase the model complexity with negligible improve-ment of its predictive capability (Exama et al., 1993). Temperaturefluctuations modelling would be of interest if microbial prolifera-tion in the packaged produce is investigated which was beyondthe scope of this study.

Renault et al. (1994) developed a finite difference model forgas prediction using MaxwellStefan equation and Fickian diffu-sion through micro-perforations, in which transport resistanceat micro-perforations ends was neglected. Improving the previousmodel, Lee and Renault (1998) increased perforations length by10% of its diameter and solved their model employing finite dif-ferences. Paul and Clarke (2002) tested a series of mass transportmechanisms (Henrys, Ficks, Knudsens and Poiseuilles flow laws)through micro-perforations and calculated the theoretical lengthof a micro-perforation. The simulations were carried out with asteady-state model considering permeation and convective trans-port of atmospheric gases through the perforated packaging. Songet al. (2002) modelled the MAP of blueberry based on heat andmass balances accounting for the respiratory and transpiratoryresponse of the packaged produce and the transport phenomenaacross the package. Rennie and Tavoularis (2009) presented amass transport model, solved with a finite volume technique, ina cylindrical package with one perforation and found that the

in-package convective transport was 64% of the diffusive andthe most important mass transport mechanisms were respirationand transpiration while CO2 solubility was not significant for asteady state case.

In summary, the previous models, developed to predict the MAconcentrations in perforation-mediated packages, were based onunnecessary complicated assumptions related either with thetransport mechanisms or the physical responses of the packagedproduce under modified atmospheres. In few of them the resultinggoverning equations have been solved with a robust numericaltechnique like the finite element method. In some of them theproblem of gas transport was solved for non retail packaging do-mains to simplify the solution procedure. The main objective ofthis study is the development of an efficient space-and-timedependent model for perforation-mediated MAP, considering themost important mass transport mechanisms (respiration, transpi-ration and diffusive transport of O2, CO2, N2 and H2O) in a retailtype micro-perforated package.

2. Description of the mathematical model and computationalanalysis

In this section, are summed up the assumptions used in themathematical model and the sub-models that describe the biolog-ical activity (respiration and transpiration) and gas component

Table 1Properties of the packaged produce, package dimensions, and storage conditions usedin the model.

Property Value Reference

dc 0.03 m Rennie and Tavoularis (2009)e 0.27 Rennie and Tavoularis (2009)Ks 48.96 106 kg m2 h1 Pa1 ASHRAE (1997)qb 600 kg m3 Rennie and Tavoularis (2009)aw 0.99 Renault et al. (1994)mb 0.5 kg Renault et al. (1994)Af 0.1 m2 Renault et al. (1994)lf 50 lm Renault et al. (1994)Kf|H2O 4.5 1013 m3 m h1 m2 Pa1 Pauly (1996)Vc 0.0015 m3 Renault et al. (1994)Kf|O2 8.5 1014 m3 m h1 m2 Pa1 Renault et al. (1994)Kf|CO2 2.8 1013 m3 m h1 m2 Pa1 Renault et al. (1994)dp 80 lm Renault et al. (1994)RHo 0.6 AssumedEaVm;CO2 64 kJ mol

1 Geysen et al. (2005)EaVm;O2 64 kJ mol

1 Geysen et al. (2005)VmO2 ;ref 242 nmol kg

1 s1 Geysen et al. (2005)VmCO2 ;ref 175 nmol kg

1 s1 Geysen et al. (2005)Tref 10 C Geysen et al. (2005)RQox 0.7 Geysen et al. (2005)KmO2 1.2 kPa Geysen et al. (2005)KmuCO2 51 kPa Geysen et al. (2005)KmO2f 0.14 kPa Geysen et al. (2005)

R 8.314 J mol1 K1 Bird et al. (1960)dpac 0.12 m AssumedKfo jO2 230.4 10

7 m3 m h1 m1 Pa1 Pauly (1996)

Kfo jCO2 111.6 107 m3 m h1 m1 Pa1 Pauly (1996)

Kfo jH2O 288 107 m3 m h1 m1 Pa1 Pauly (1996)

Ef jO2 45.7 kJ mol1 Pauly (1996)

Ef jCO2 41.145.7 kJ mol1 Pauly (1996)

Ef jH2 O 42.345.7 kJ mol1 Pauly (1996)

Table 2Binary diffusion coefficients for low pressure (1 atm).

T (C) Dij 106 m2 s1 15 10 5 0

O2/CO2 14.15 13.69 13.25 12.81O2/H2O 19.48 18.82 18.17 17.53O2/N2 19.10 18.52 17.94 17.36CO2/H2O 13.73 13.25 12.79 12.33CO2/N2 14.13 13.68 13.24 12.81H2O/N2 19.13 18.48 17.84 17.22H2O/air 19.43 18.77 18.13 17.49O2/air 19.30 18.70 18.11 17.53CO2/air 14.25 13.80 13.35 12.91

Table 3Initial in package mass, volume and molecular gases fractions.

Gases Mass fraction (%) Volume fraction (%) Molecular fraction

N2 76.46a 78.49a 0.78a

O2 23.11 23.11 (28.89/32) = 20.87 0.21CO2 0.05 0.05 (28.89/44) = 0.033 0.00033H2O 0.38 0.38 (28.89/18) = 0.61 0.0061

qair = 1.25 kg m3; Mair = 28.89 g mol1; Xm = 0.0038 kgH2 O kg1

da,MO2 = 32 g mol

1; MCO2 = 44 g mol1; MH2 O = 18 g mol

1.a N2 is calculated from the balance of the gas components O2, H2O Kai CO2.

328 G. Xanthopoulos et al. / Journal of Food Engineering 111 (2012) 326335

transport taking place through the headspace and the tested perfo-ration-mediated modified atmosphere packaging.

2.1. Model assumptions

O2 consumption and CO2 production due to respiration dependon the O2 and CO2 partial pressures through a MichalisMententype of model.

CO2 production is a combined oxidative and fermentative pro-cess; the oxidative contribution is proportional to the O2 con-sumption and the fermentative follows a MichalisMententype of model.

O2 consumption and CO2 production are temperature depen-dent following an Arrhenius law.

O2, CO2, H2O and N2 are exchanged between headspace andpackaging surroundings through the packaging film and itsmicro-perforations.

S

MICRO-PERFORATED FILM

z x

y

Fig. 1. Schematic diagram of a perforation-mediated modified atmosphere package (conditions (S1, S2, S3, S4) are depicted on the right diagram.

Packaged produce has uniform porosity and bulk density andconsists of spherical elements of uniform diameter dc.

Package walls are impermeable to O2, CO2, H2O and N2. Packaged produce and the in-package gases are in thermal

equilibrium.

2.2. Respiration model

The respiration model involves the partial pressures PO2 , PCO2(Pa) and the storage temperature T (K). The O2 consumption rate,RRO2 (mol kg

1 h1), is calculated from an enzyme kinetics modelwith uncompetitive type CO2 inhibition:

RRO2 PO2

KmO2 PO2 1PCO2=KmuCO2 VmO2 ;ref exp

EaVmO2R1=T1=Tref

" #( )

1

The maximum specific respiration rate of O2 is evaluated at areference temperature Tref = 283 K (10 C) and its temperaturedependence is given by an Arrhenius type equation-cf. inside thebrackets of Eq. (1) (Geysen et al., 2005). KmuCO2 and KmO2 (kPa)are MichalisMenten constants for uncompetitive inhibition ofCO2 and O2 consumption respectively; VmO2 ;ref (mol kg

1 h1) isthe reference maximum specific consumption rate of O2 at Tref;EaVmO2 (J mol

1) is an activation energy and R (J mol1 K1) is theideal gas constant-cf. Table 1.

A

PRODUCE AREA dpac

hpac

S1

3

S2

S4

left). The meshed computational domain (X) with 240 elements and boundary

c

0.0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120

Time (h)

b

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120

Time (h)

a

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120

Time (h)

O2 /

CO

2 Co

nce

ntr

atio

nO

2 / C

O2 C

on

cen

trat

ion

O2 /

CO

2 Co

nce

ntr

atio

n

ig. 2. The average headspace O2 and CO2 concentrations versus time forxperimental (Renault et al., 1994), (points) and predicted data (lines) for 5 (a),0 (b) and 20 (c) micro-perforations of the PP packaging.


The CO2 production rate, RRCO2 (mol kg1 h1) is a combination

of oxidative and fermentative processes and follows an Arrheniuslaw in temperature dependence (Geysen et al., 2005; Guillaumeet al., 2011):

RRCO2 RQoxRRO2

11 PO2=KmO2f

VmCO2 ;ref expEaVmCO2

R1=T 1=Tref

" #( )2

where RQox is the respiratory quotient (ratio of CO2 production andO2 consumption for oxidative respiration); KmO2f (kPa) is aMichalisMenten constant related to the inhibition of the fermenta-tive metabolism due to O2 presence; VmCO2 ;ref (mol kg

1 h1) is thereference maximum specific production rate of CO2 at Tref andEaVmCO2 (J mol

1) is an activation energy. The produce surface

area Ac (m2) is calculated assuming that the produce is sphericaland uniformly packed:

Ac 61 eVb=dc 3

where Vb (m3) and e are the volume and porosity of the bulk pro-duce, respectively; dc (m) is the equivalent produce diameter(Richardson et al., 2002). Porosity values for different bulk agri-cultural products can be found in literature. The quantities PO2 ,PCO2 , RRCO2 and RRO2 in Eqs. (1) and (2) are calculated in everytime step (see below) and the rest of the variables are taken fromTable 1.

2.3. Transpiration model

Transpiration is driven by the water vapour pressure deficit,VPD (Pa), between produce surface and its surroundings, givenby Eq. (4) (Diner, 2003). The saturation water vapour pressure-cf. in the polynomial equation in the second parenthesis of Eq.(4), is given by ASAE (1998).

VPD aw RH0:04T3 32:43T2 8;567T 757;070 4

The water activity, aw, of the packaged produce is takenslightly below saturation as 0.99 due to dissolved substrates(Becker et al., 1996). Transpiration sets in when the water vapourpressure at the produce surface (awPs) exceeds that in the head-space (RH Ps), i.e., when aw is higher than the relative humidity,RH; otherwise it is taken zero. The water vapour flux _mw(kgH2O m

2 h1), is given as:

_mw VPD=1=Ks 1=Ka 5

where 1=1=Ks 1=Ka (kg m2 s1 Pa1) is the transpiration coef-ficient and Ks (kg m2 s1 Pa1) the skin mass transport coefficient(ASHRAE, 1997; Diner, 2003)-cf. Table 1. Ka (kg m2 s1 Pa1) isthe air-film mass transport coefficient, calculated from Sher-woodReynoldsSchmidt correlation for a sphere (Becker et al.,1996):

Sh 2:0 0:55Re0:53Sc0:33 6

Re is the Reynolds number, Sc the Schmidt number and Dv(m2 h1) the diffusion coefficient of water vapour in the air. Con-sidering negligible flow around the packaged produce (i.e.,Re = 0), Ka is estimated by:

Ka 2Dv=T 273:15dcR=MH2O 7

where MH2O (kg mol1) is the water molecular weight and

Dv 9:1 109T2:5=T 245:18 (m2 h1) the diffusion coefficientof water in the air (Becker et al., 1996). The quantities VPD and_mw from Eqs. (4) and (5) are calculated in every time step and the

rest of the variables are taken from Table 1.

Fe1

2.4. Modelling of O2, CO2, H2O and N2 transport in the headspace

MaxwellStefan equation relates flux and gradient concentra-tions among the diffusive gas components of a multicomponentgas system and is preferred due to its accuracy against the Fickslaw (Guillaume et al., 2011). The gas component mass fractions xi(i = O2, CO2, H2O) in the headspace are calculated by means of theMaxwellStefan diffusion formulation (Bird et al., 1960). Only gasdiffusion is considered, since inclusion of natural convection trans-port only marginally improves the theoretical prediction (Rennieand Tavoularis, 2009). The governing transport equations read as:

totalji Kf ji=lf qi npSpDi=air=lf Af R=MiT x0jiP0 xiR=MiqiT12

i

xiq Mi=X4i1

xiMi

!

13

0

20

40

60

80

100

0 20 40 60 80 100 120

Time (h)

Rel

ativ

e hu

mid

ity (%

)

Fig. 3. The average headspace RH with time at 10 C for 0.5 kg of strawberries.

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120

Time (h)

Vo

lum

e fr

acti

on

(%

)

O2 CO2

ig. 4. The average headspace O2 and CO2 concentrations when packaging has noicro-perforations.


q@xi@tr qxi

Xnj1

Dij rxj xj xjrPP

" # 0 8

where q (kg m3) is the gas mixture (O2, CO2, N2 and H2O) density:

q PRT 273:15

X4i1

XiMi

!9

In Eqs. (8) and (9), t (h) is the storage time, Dij (m2 h1) the (i, j)element of the multicomponent Fick diffusivity matrix D, xiorj themolecular fraction of component i or j = O2, CO2 and H2O and P(Pa) the total gas mixture pressure. The mass fraction of N2 iscalculated from the balance of the gas components mass fractions,xN2 1xO2 xCO2 xH2O. Renault et al. (1994) and Rennie andTavoularis (2009) found that accounting for CO2 solubility in theirmodels did not affect the final steady-state gas concentrations. Pre-dictions with and without CO2 solubility accounted for, differ byless than 2%. Based on the previous findings, the CO2 solubilitywas ignored. Estimation of the Dij coefficients was based on theChapmanEnskog kinetic theory analysis (Bird et al., 1960) andwas carried out for four storage temperatures (0, 5, 10 and 15 C)covering the cold supply chain-cf. Table 2. Mi (kg mol1) is themolecular weight of the component i.

For the initial (t = 0) in-package conditions, T = 10 C, P0 = 1 atmand RH0 = 60%, the model is fed with the initial mass fraction val-ues xi-cf. Table 3 and binary diffusivity coefficients Dij-cf. Table 2for i or j = O2, CO2, H2O and N2.

The initial xi values of O2, CO2 Kai H2O are calculated from Eqs.(10a)(10d), considering that gas components mass fractions inthe dry air are H2O < 1%; O2: 23.20%; CO2: 0.046% (ASAE, 1998).

X 100 0:62RH0PsP0 RH0Ps

;18 T 260C 10a

O2 23:20100 X 10b

CO2 0:046100 X 10c

N2 1 O2 CO2 X 10d

X (kgH2O 1001 kg1da) is the air moisture ratio (ASAE, 1998), P0

the atmospheric pressure (1 atm = 101,325 Pa), RH0 the initial rel-ative humidity and Ps (Pa) the saturation vapour pressure. At everytime step, the quantities q, xi, Dij, xj, P, in Eqs. (8) and (9) arecalculated.

2.5. Boundary conditions

The partial differential equations (Eq. (8)) are solved in a 2-Ddomain corresponding to a rectangular headspace of a packagingwith width dpac (m) of retail size and height hpac Vc 1 emb=qb=Af , augmented by the total void spaces of the containedbulk produce since this formulation improves significantly modelprediction; Af (m2) is the area of the permeable film, mb (kg) thebulk produce mass, Vc (m3) the packaging volume and qb (kg m3)the bulk density of the bulk produce, all tabulated in Table 1. As al-ready mentioned, the packaging walls are considered impermeableto gas transport. The bottom boundary conditions include thewater vapour production flux, _mw (cf. Eq. (5)) and the gas compo-nent i = O2, CO2 consumption and production fluxes, respi(kg m2 h1):

respi RRiMiqbAc 11

where RRi is calculated from Eqs. (1) and (2) and Ac from Eq. (3). Thetop boundary conditions include the gas component i = O2, CO2, H2Otransport through micro-perforated packaging film:

_m

q

Fm

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

0 20 40 60 80 100 120Time (h)

Res

pira

tion

flux

(kg

m-2

h-1 )

O2, 5-perforationsCO2, 5-perforations2, 10-perforationsCO2, 10-perforations2, 20-perforationsCO2, 20-perforationsO2, no-perforationsCO2, no-perforations

O2

O2

O2

O2

CO2

CO2

CO2

CO2

Fig. 5. Respiratory (O2 and CO2) fluxes for 0, 5, 10 and 20 micro-perforations.

Fig. 6. Contour maps of O2 and CO2 (%) concentrations for different micro-perforations number and diameters for 30 lm (a) and 60 film lm (b) thicknesses. Storagetemperature 5 C.


where _mtotalji (kg m2 h1) is the total flux (accounting for film and

micro-perforations) of i = O2, CO2, H2O; Kf ji (m3 m h1 m2 Pa1) isthe permeability of the packaging film (experimentally determined)for i = O2, CO2, H2O. Pauly (1999) described the temperature depen-dence of permeability for many polymeric films with an Arrheniustype equation, Kf ji Kf0 ji expEf ji=RT 273:15. The parametersof the previous equation (cf. Table 1) for i = O2, CO2, H2O, were takenfrom Pauly (1999) for a PP film and used for strawberry MAP stor-age at 5 C to consider in this way, the temperature dependence ofpermeability. At 10 C storage, the O2 and CO2 permeability values

were taken from Renault et al. (1994) study for their tested PP film.lf (m) is the thickness of the packaging film-cf. Table 1, qi (kg m3)the density of the gas component i and x0|i the initial molecularfraction of i = O2, CO2, N2, H2O in the headspace-cf. in Table 3. Sp(m2) is the area of a cylindrical micro-perforation of diameter dp(m2), np the number of packaging micro-perforations and lf (m)the micro-perforation length taken equal to the thickness of thepackaging film-cf. Table 1. Di=air (m2 h1) is the diffusion coefficientof component i in the air (cf. Table 2) taken at 10 C. Di/air can also becalculated in terms of an effective diffusion coefficient:

0

2

4

6

8

10

12

14

16

18

20

22

0 20 40 60 80 100 120

Time (h)

Vo

lum

e fr

actio

n (%

)

O2 CO2

Fig. 7. Average O2 and CO2 concentration for PP packaging of 30 lm thickness; 6 micro-perforations; 50 lm diameter of micro-perforation. Storage temperature 5 C.


1=Di=eff Xj1

nxj=Dij 14

The previous approach is justified when the diffusive compo-nent i moves with velocity close to the rest of the diffusive gascomponents (Bird et al., 1960). In preliminary computations, theDi/air and Di/eff formulations yield almost identical values (differ-ence 6 1%) and thus a simpler approach of a constant diffusioncoefficient, Di=air was used in Eq. (12), for the tested cases. The_mtotalji is calculated from Eq. (12) at each time step, since the in-

package partial pressure of component i = O2, CO2, H2O,Pi = xiR=MiqiT, changes with storage time.

2.6. Computational domain and numerical solution procedure

The computational domain geometry and the applied condi-tions correspond to a retail package and have been chosen to im-prove computational efficiency and facilitate comparison withthe experimental data of Renault et al. (1994). The chosen compu-tational domain (cf. Fig. 1) corresponds to a rectangular retail plas-tic container. Due to the uniform ambient conditions applied, a 2-Dformulation of the gas transport in a perforation-mediated MApackaging is feasible. The set of the governing equations along withtheir boundary and initial conditions was discretized numericallyby the FEM using COMSOL Multiphysics 3.4 (Comsol Inc., 2007,USA). The mesh was unstructured and composed of triangular ele-ments and Langrange quadratic shape functions. The choice forsolving the resulting linearised equation system was the General-ized Minimal Residual Method (GMRES) with the incompleteLU-factorization as preconditioner (Pashos et al., 2009), due to itsreduced memory requirements and low computational cost.Mesh-independence of the solutions was tested by solving theproblem for three meshes composed of 60, 240 and 960 elements.In each case, the maximum time step taken was 3600 s, as dictatedby the solver. From the trials, small differences (>1%) were de-tected among the calculated concentrations of O2, CO2, and H2O.Finally, the mesh of 240 elements (cf. Fig. 1) was selected and usedfor obtaining the results presented below.

3. Results and discussion

The case studied here was so chosen as to enable comparison ofmodel predictions with the experimental data in Renault et al.

(1994) for strawberries stored at 10 C in a PP packaging. Theparameter values used in the model are summarized in Table 1.Renault et al. (1994) provided values only for the packaging per-meable area 0.1 m2 and the container volume 1.5 L. In this case,the container geometry was of a retail type, following a generalrule which associates container and produce volumes by a factorof 4/3 (Vc = 4/3Vb) (Exama et al., 1993). In the proposed model,the gas diffusion is computed only in the augmented packagingheadspace and this is of interest in the model. Therefore, assuminga width of the micro-perforated film, dpac = 0.12 m, the headspaceheight (hpac = 0.009 m) is estimated as previously explained (cf.in Section 2.5) based on the container volume, produce mass, bulkdensity and porosity, and the micro-perforated film area (cf. Table1). In Renault et al. (1994), the film thickness, lf, is not specified andthe length of the micro-perforations was taken 50 lm; here lf wastaken 50 lm too. Lee and Renault (1998) and Paul and Clarke(2002) used in their calculations an effective micro-perforationlength assuming transport resistance at micro-perforations endsbut this approach needs further analysis and experimental verifica-tion and therefore it was not taken in account. The aspect ratio ofthe previous container, defined as hpac/dpac is 0.075. The corre-sponding ratio from Rennie and Tavoularis (2009) simulationswas 0.28, which was higher since their tested domain did not cor-respond to a retail type container and the headspace height washigher than the respective commodity layer height. The effectiveproduce area for 0.5 kg strawberries is 0.12 m2 and the ratio ofthe produce area to permeable area is 1.2. The initial in-packagegases concentrations are estimated (cf. Eqs. (10a)(10d)) assumingthat the temperature within the package stays constant and equalto the storage temperature throughout the simulation period. Theambient gas concentrations were calculated based on Eqs. (10a)(10d) and the simulation period extended up to 5 days. Rennieand Tavoularis (2009) report that equithermal conditions lead toover-prediction of O2 concentration and under-prediction of CO2,but their conclusions were based on long-term simulations(4 days) rather to short-term which actually correspond to afluctuation case. The estimated root mean square error,RMSE n1

Pni1e

2i

0:5 between predicted and experimental datafor CO2 and O2 mass fractions (cf. Fig. 2) ranged between 1.0%and 2.2%.

Although no data were given from Renault et al. (1994) aboutwater vapour concentration, the estimated in-package relativehumidity varied in a similar way as in the case of Fishman et al.

2

0.0E+00

1.0E-05

2.0E-05

3.0E-05

4.0E-05

5.0E-05

6.0E-05

0 20 40 60 80 100 120

Time (h)

Flux

(kg

m-2 h

-1)

Total Flux "Flux through microperforations" Flux through film

0%

20%

40%

60%

80%

100%

0 20 40 60 80 100 120

Time (h)

Mas

s flu

x %

flux through film flux through microperforations

O2

C2

-6.0E-05

-5.0E-05

-4.0E-05

-3.0E-05

-2.0E-05

-1.0E-05

0.0E+00

0 20 40 60 80 100 120

Time (h)

Flux

(kg

m-2

-1)

Total flux "Flux through microperforations" Flux through film

0%

20%

40%

60%

80%

100%

0 20 40 60 80 100 120

Time (h)

Mas

s flu

x %


CO2

H2

-6.0E-07-5.0E-07-4.0E-07-3.0E-07-2.0E-07-1.0E-070.0E+001.0E-072.0E-073.0E-074.0E-075.0E-07

0 20 40 60 80 100 120 140Time (h)

Flux

(kg/

m 2 h

)

Total flux Flux through microperforations Flux through film

0%

20%

40%

60%

80%

100%

0 8 16 24 32 40 48 56 64 72 80 88 96 104

112

120

Time (h)

Mas

s flu

x %


H2

h

Fig. 8. O2, CO2 and H2O fluxes through PP packaging with micro-perforations and film (left) and the % mass flux (right).


(1996) and Song et al. (2002). According to these, the packageswere saturated (100% RH) few hours after the produce had beensealed-cf. Fig. 3. An average value for the skin mass transport coef-ficient (cf. Eq. (5)) was taken as 48.96 106 kg m2 h1 Pa1 fromASHRAE (1997).

The PP packaging tested by Renault et al. (1994) had permeabil-ity for O2 8.5 1014 m3 m h1 m2 Pa1 and for CO22.8 1013 m3 m h1 m2 Pa1 at 10 C. The permselectivity ofthe non-perforated area of the PP packaging was 3.3 and CO2accumulation (>30%) and O2 exhaustion, shown in Fig. 4, occurredinducing anaerobiosis after 38 h of storage. The fermentativemetabolism (Geysen et al., 2005) increased CO2 production(Fig. 5) before it reached an equilibrium value (1.0 1041.2 104 kg m2 h1) while the O2 consumption became zero.

Strawberries are not chilling sensitive fruits and are normallystored at low temperatures (05 C), where respiratory metabo-

lism is reduced. Based on this storage practice, simulations werecarried out at 5 C for two PP thicknesses, namely 30 and 60 lm,for 5 micro-perforation diameters, 30, 40, 50, 60 and 70 lm andfor various micro-perforation numbers ranging from 0 up to 10(cf. Fig. 6). The recommended MA conditions ranged between 510% for O2 and 1520% for CO2 (Kader, 1992a; Thompson, 2003).The O2 and CO2 concentrations range widely due to the differentpostharvest response among strawberries from different varieties.From the plotted contour maps in Fig. 6, it was found that theclosest to the recommended O2 and CO2 volume fraction combina-tion was 8.1% and 9.7% (average values) respectively, and it wasachieved with a packaging of 30 lm thick, with 6 micro-perfora-tions of 50 lm diameter each (cf. Fig. 7). The total micro-perfora-tions area, assuming them as cylindrical, was 1.18 108 m2 andthe calculated permselectivity values were Sf = 3.4 without mi-cro-perforations and St = 0.78 with micro-perforations. From the


same contour maps can be seen that the desired accumulation ofCO2 (1520%) is achieved for less than 2 micro-perforations regard-less diameter size while the suggested reduced O2 level (510%) isachieved for more than 4 micro-perforations and more than 50 lmin diameter. Based on the previous findings, for the specific PPpackaging and storage conditions, the recommended O2 and CO2concentrations are marginally achieved. Exama et al. (1993) men-tioned that a packaging permselectivity close to 1.1, under certainstorage conditions, is required for reaching the recommended O2and CO2 concentrations, a value higher than the one estimated here(0.78).

Based on Eq. (12), the O2 and CO2 contribution to the overall gasflux through the micro-perforated packaging was quantified usingthe previous MAP case. In Fig. 8 are presented the O2 influx(positive) and CO2 and H2O efflux (negative). It can be seen thatthe largest gas exchange is taking place through the packaging mi-cro-perforations, as it was expected. Mannapperuma et al. (1989)noted that O2 diffusion in air is about 8.5 106 times than in LDPEfilms while the corresponding ratio for CO2 is 1.5 106. This differ-ence in gas diffusion means that the gas exchange through amicroperforated material occurs almost entirely through themicro-perforations. The effect of very small holes on the O2 con-centration in the package atmosphere is greater than its effect onCO2 concentration. Kader (1992a) reported that the permselectivi-ty of commonly used packaging films for fresh produce is for LDPE2.05.9, for PVC 3.66.9 and for PP 3.35.9. The adoption of micro-perforation with these films as referred by Mannapperuma et al.(1989) changes considerably their permselectivity. The previousbehaviour was noted in the present study, as the permselectivityof the continuous PP film reduces from close to 3.0 down to 0.74with the inclusion of micro-perforations, regardless of the storagetemperature, the pores number and their diameter.

From the present simulation, 7.3% of O2 exchange is taking placethrough the continuous part of the packaging and 92.7% throughthe micro-perforations. For CO2, 20.5% through the continuous partand 79.5% through the micro-perforations and for water, 3.6%through the continuous and 96.4% through the micro-perforations.Among the three gas components, CO2 transport through the non-perforated part of the packaging is comparable with the transportthrough the packaging micro-perforations (20.5% against 79.5%).This calls for further investigation with regard to the mechanicalor chemical modification of the material properties so as to en-hance accumulation of CO2 in the packaging, which is desirablein most of the MAP cases.

4. Conclusions

A computational model was developed for the prediction of O2,CO2, H2O (and N2) transport in perforation-mediated polymericpackages during MAP of strawberries. The model incorporatesthe most important mass transport mechanisms, namely respira-tion, transpiration and diffusive transport of O2, CO2, N2 and H2O.The problem of formulating the usually randomly packaged com-modity is tackled by treating it as a porous medium and solvingthe simplified problem only for the headspace in a 2-D arrange-ment. The comparison of models predictions with publishedexperimental data was satisfactory with discrepancy P 2.2%. Thecomputations showed that with the PP micro-perforated packag-ing, the recommended gas concentrations were marginallyachieved at 5 C. The predictions suggest as most advantageouspackaging choice the one with 30 lm thickness and 6 micro-perfo-rations of 50 lm diameter each; the in-package atmospherereached, had 8.2% O2 and 9.7% CO2. In this particular case, the ratioof the exchanged CO2 through the continuous packaging andthrough the micro-perforations is approximately 1:4, while forthe other gas components is about 1:9.

In overall, the model can be used for fruits and vegetables of anyshape, whole or fresh-cut. Based on the adopted boundary condi-tions, the model can easily be adjusted to different types of pack-aging (permeable or not) given that the appropriate propertyvalues are available. Moreover, calculations can be performed fordifferent storage temperature regimes, relative humidity and gasconcentrations met in the fresh cold chain, providing, in thisway, useful predictions about the appropriateness of the usedpackaging film and/or the applied storage conditions.

Acknowledgments

The authors would like to thank the reviewers for their insight-ful and helpful comments.

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Mass transport analysis in perforation-mediated modified atmosphere packaging of strawberries1 Introduction2 Description of the mathematical model and computational analysis2.1 Model assumptions2.2 Respiration model2.3 Transpiration model2.4 Modelling of O2, CO2, H2O and N2 transport in the headspace2.5 Boundary conditions2.6 Computational domain and numerical solution procedure3 Results and discussion4 ConclusionsAcknowledgmentsReferences

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