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Mass transferBeverage packagingComputational uid dynamics

sheer ilacr a

Residual carbonation histories are validated and presented for a variety of thermal regimes and for two

ntal faprodpackaed she

the adopted packaging material, anticipation of the carbon dioxideloss over time through the bottle walls has always been desirableand challenging at the same time. Several gas diffusion/permeationmechanisms take place: solubilization/absorption of molecules onthe inner surface of the bottle, diffusion through the polymer anddesorption in the environment (Brooks, 2002; Han and Scanlon,2005; Piringer and Baner, 2000). In case of a carbonic beverage,its organoleptic properties are strongly determined by the gas con-

ogy and utilization, to satisfy the new demands from the food andbeverage markets.

Del Nobile et al. (1997) have already shown that modeling of apackaged beverage is important, but their analysis was simpliedto a 1D geometry and limited to the keeping temperature. Instead,local and transient food features could help establish rmer knowl-edge grounds, and unfold the dependence on other parameterssuch as the bottle design and manufacture. To this end, Computa-tional Fluid Dynamics (CFD) models could help gaining knowledgeon such fundamental and critical processing variables, to describethe product evolution and help maintain its quality.

Corresponding author. Tel.: +39 3293606237; fax: +39 0971 205429.

Journal of Food Engineering 108 (2012) 570578

Contents lists available at

d

lsE-mail address: gianpaolo.ruocco@unibas.it (G. Ruocco).demands, in terms of packaging. In many cases the shelf life isstrongly dependent on the resistance offered by the containerwalls, through which the gas diffuses and escapes. An effectivepackage must prevent spoilage, and have gas, temperature, light,and watervapor barrier properties adequate to retard qualitydeterioration of packaged foods. Packaging must withstand pro-cessing conditions and distribution abuse (Singh and Singh, 2005).

Common examples of this condition are sparkling mineralwaters, and in general every carbonated drinks. Depending on

due to its own characteristics, such as barrier to gas and avorings,transparency and easy processing (Brooks and Giles, 2002). But theoverall planning of packaging is also affected by environmental andstorage conditions, and characteristics of the package (Del Nobileet al., 1997; Lewis et al., 2003; Chanda and Roy, 2007). In this pa-per, the storage temperature and package thickness uniformity arestudied, for their effect on the beverage shelf life, by means of agenerally applicable modeling tool. It is seen that a such a toolmay help the developments in polyethylene terephthalate technol-1. Introduction

It is well known that the fundamethe keeping characteristics of a foodthe conditioning treatments and thefore a dynamic systems with a limit0260-8774/$ - see front matter 2011 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2011.09.001different bottles carrying the same capacity. The paper highlights on the combination of bottle weight,initial carbonation and storage temperature, indicating the operational set for the longest shelf life withinthe explored cases. Lighter bottles can be used with no inference on shelf life, while the carbonic lossdepends non-linearly on initial carbonation and temperature increment. The associated concentrationmaps help infer on the importance of polyethylene terephthalate thickness uniformity.It is then demonstrated that the model carries the exibility of a general tool, applicable to any carbon-

ated beverage at any storage condition. 2011 Elsevier Ltd. All rights reserved.

ctors that contribute touct (shelf life) are bothging. The food is there-lf life and very specic

tent, in such a way that a carbon dioxide reduction of only 15% isgenerally enough for the drink to taste at (Swenson, 2002; Lewiset al., 2003; Profaizer, 2005; Syrett, 2006).

The choice of the packaging material is paramount to preservethe food features: in particular, the adoption of polythylene tere-phthalate for beverages helps pursue the food quality and safetyKeywords:

loss through the polyethylene terephthalate barrier has been computed by means of a multidimensionalnite element code, while actual measurements have been carried out to validate the computations.Modeling and experimental validation ofin polyethylene terephthalate bottles

Gabriella Carrieri, Maria Valeria De Bonis, GianpaoloCFDfood - DITEC, Universit degli Studi dalla Basilicata, Campus Macchia Romana, Pote

a r t i c l e i n f o

Article history:Received 6 February 2011Received in revised form 10 August 2011Accepted 6 September 2011Available online 12 September 2011

a b s t r a c t

Mass transfer and relatedchange due to mass transfCarbonation loss takes p

package itself. In this pape

Journal of Foo

journal homepage: www.ell rights reserved.ass transfer from carbonated beverages

uocco 85100, Italy

lf life assessment is an important issue in the beverage industry. Products at stake and, with it, its consumer value and consideration.e at the product/package interface, and to the environment through thejoint experimental/computational approach has been exploited: the CO2

SciVerse ScienceDirect

Engineering

evier .com/locate / j foodeng

sion caliper (Digital Caliper, Juwell Plus, Italy). The thickness d wasmeasured at every section as well with a precisionmicrometer (Mitu-toyo, Tokyo, Japan), having cut such sections along the bottle prole bya cutter (Coupe Bouteilles, Sidel, Luce, France). Bottle deformation dueto internal pressure build-up following polyethylene terephthalateblowing and bottle carbonation was therefore accounted for. Alllengths and thicknesses are summarized in Table 2 and 3.

3. Model formulation

A rendering of the package is shown in Fig. 1. A pure diffusiveproblem of CO2 is assumed to a 2D axial-symmetric model, exploit-ing the axi-symmetry. When the polyethylene terephthalatecontainer is stored at a given temperature, after thermal equilibrium

q density (kg/m3)

Subscripts0 initiala airh head spacep packagePET polyethylene terephthalatew water

Table 1

d Engineering 108 (2012) 570578 571In this paper, a general CFD tool has been employed for the rsttime to describe the diffusion and loss of CO2 through an actualpolyethylene terephthalate bottle, while experimental measure-ments have been performed to validate the model and establishits accuracy. The objectives of the study were to employ a generallyapplicable framework of transport phenomena to the assessmentof carbonation depletion and related product shelf life, by explor-ing the effects of thermal regimes, initial carbonation, and bottlethickness non-uniformity.

2. Experimental set-up and measurements

An experimental activity was rst set-up and performed in or-der to validate the model which will be presented later in the pa-per. The activity consisted in storing an adequate number ofbottles, containing sparkling water, in a variety of thermal condi-tions, for the necessary period of time. At given intervals, the per-meability of the bottles was assessed by sampling the residual gasin the stored product. Then the sampled bottles were disposed of.

All bottles were manufactured in polyethylene terephthalatewith a cap in HDPE (High-Density Polyethylene). Gas samplingand temperature measurements were carried out from six 0.5 lcapacity bottles, at each storage temperature, for water havingan initial carbonation range of 48005400 mg/l, depending onthe particular brand.

The following measurements were carried out at the initial timeand every 15 days:

1. The CO2 concentration measurements were carried out by anautomatic sampler (CarboQC, Anton Paar GmbH, Graz, Austria).Carbon dioxide measurement is performed by evaluating the

Nomenclature

c concentration (mg/l)D mass diffusivity (m2/s)J ow of gas (mol/m2s or kg/m2s)n normal versors curvilinear coordinate (m)t time (s)T temperature (K)V volume (m3)

Greekd thickness (mm)

G. Carrieri et al. / Journal of Foototal pressure of all gases dissolved in the sample upon multiplevolume expansions in a sealed chamber tted with absolutetemperature and pressure gases. The precision of the instru-ment was 0.05 g/l, with the accuracy of 0.01 bar.

2. The temperature was read by means of with a digital thermom-eter (HI9061, Hanna Instruments, Ronchi di Villafranca, Italy).The accuracy was 0.4 C.

Bottle tare W was 14.5 or 16.5 g, depending on the particularbrand and blowing procedure, and the product was stored in avariety of thermal conditions T. All conditions or modes are sum-marized in Table 1. In particular, the T1 condition correspondedto local daily and seasonal conditions, in the late-winter/early-spring period. All other temperature conditions were obtained bya controlled-temperature storage.

Furthermore, each bottle typewasmeasured to infer on the geom-etry non-uniformity (height, diameter, and specially the thickness).Each bottle type was divided in several sections of curvilinear lengthDs and scrutinized, on the lled bottle after carbonation, with a preci-Summary of experimental conditions.

Code Mode

W1 14.5 g, weight of bottleW2 16.5 g, weight of bottleT1 variable storage temperatureT2 10.0 C, constant storage temperatureT3 30.0 C, constant storage temperatureT4 40.0 C, constant storage temperature

Table 2Bottle thickness distribution d along the curvilinear coordinates along bottles edge (Fig. 2), for W1 bottle.

Section no. si si1 (mm) d (mm)Table 3Bottle thickness distribution d along the curvilinear coordinates along bottles edge (Fig. 2), for W2 bottle.

Section no. si si1 (mm) d (mm)1 12.3 1.92 9.95 0.263 76.6 0.234 57.0 0.245 51.9 0.216 26.0 0.367 10.0 1.5

1 9.5 1.4452 1.25 0.1353 74.7 0.184 58.0 0.185 50.7 0.196 26.9 0.397 11.1 1.6

d En572 G. Carrieri et al. / Journal of Foowith the environment, mass transfer of gas to the outside is estab-lished causing the reduction in shelf life. But since the actualpackagethickness varies along the bottle height, the mass transfer is non-uniform along its surface.

The actual ll level (liquid/head space interface) is also repre-sented in Fig. 2. Therefore, two domains are congured and ana-lyzed in the model, the Vh (head space) and the Vw domain(packed water).

3.1. Assumptions

1. Initially, the gas is distributed uniformly in each domain(Fig. 2); in Vw the gas concentration is set at the desired initialcarbonation, while in Vh an atmospheric concentration isassumed.

2. A diffusive ux through the polyethylene terephthalate matrixis attributed locally depending on the actual local thickness ofthe package (Tables 2 and 3).

3. The diffusion coefcient depends on storage temperature andpolyethylene terephthalate density (determined by the bottleweight and blowing procedure), only. The adoption of actualvalues for these coefcients will be discussed later in Section 4.

Fig. 1. A rendering of the package under scrutiny, with its dimensions.gineering 108 (2012) 5705784. All cases are computed by assuming the same surface masstransfer mechanism. The driving mechanism is then the diffu-sion in the polyethylene terephthalate matrix, and the externalconvection is not discussed in this paper.

5. Equilibrium exists at all times between head space and packedwater.

6. In case of variable environmental temperatures, the thermaluxes are considered to be small enough to ensure that no ther-mal gradients are formed, then no buoyancy effects are consid-ered in the packaging.

7. No signicant swelling of the polymer occurs when CO2 perme-ates through the polymer self.

8. The effects of competition on the sorption by other possiblespecies (e.g. N2) are neglected.

Fig. 2. Domains under scrutiny, with indication of the curvilinear coordinate s (notin scale, Table 2).

subject Vh or Vw subdomain, respectively.

atm

the In

At

2009), even for the T1 mode (Table 1).

4. Results and discussion

4.1. Diffusion optimization and material properties

It is acknowledged in this work that the diffusion coefcientplays an important role, as the process at hand is diffusion-driven.In order to allow preventive model validation, the integration ofthe governing Eq. (1) has been complemented by using the designenvironment modeFRONTIER (modeFRONTIER, 2008) in which aSIMPLEX (Edgar et al., 2001) multi-object optimization routine isexploited to form the desired diffusion coefcient value. Practi-cally, n design constraints can be analyzed by calculating the fol-lowing error function f x; e:

f x; e x0 e02 x1 e12 x2 e22 . . . xn en2 6with xi the i-th constraint variable (the calculated carbonic concen-tration) and ei the corresponding i-th experimental validating da-tum. In the present case, n = 15. By this routine, the CFD kernel(COMSOL Multiphysics Users Guide, 2008) is iteratively run, untilconvergence for a minimized error function f.

With this procedure, the optimal Dp value has been found foreach constant temperature and bottle weight modes.

Fig. 3. Close-up of adopted grid.

Table 4Diffusion coefcients of CO2 in package, air and water (m2/s) employed, for theconstant temperature modes.

Mode Dp at W1 Dp at W2 Dh Dw14 14 5 9

d Engineering 108 (2012) 570578 5733.4. Discretization of domains and run durations

A computational grid, whose close-up is shown in Fig. 3, isadopted. Both subdomains are discretized by Lagrange-quadraticelements. Several grids were tried, from a total of 5800 triangularelements up to more than 18,000. The nal grid, yielding for grid-independency results, had some 10,000 elements, and more than37,000 degrees of freedom.

The UMFPACK direct solver is used. The BDF method for timedependent problems is used for the time stepping setting. The timen rc 0 5

The model requires the denition of the properties of water andbottles walls, the initial concentration of gas and the diffusivecoefcients. For every storage condition, all constants depend onstorage temperature (Massman, 1998; Singh and Heldman,n Dprc 0 3 At bottles boundaries, an outward ux condition is applieddepending on the diffusion coefcient in the polyethylene tere-phthalate material and boundary section thickness:

J n Dprc 4

At the subdomain interface Vh Vw, the gas ux continuity isimposed;

At the symmetry boundary, the proper condition is imposed asfollows:step icuteda Supebottles cap an insulation condition is applied:concentration carbonation level, for the product at hand.

Boundary conditions:environment).the Vw subdomain the gas concentration is due to the givenc0 0:03%qa 2

This concentration is constant at T2, T3 and T4modes, while it isvariable at T1 mode (due to the inherent thermal oscillation ofospheric concentration, depending on its partial pressure:3.3. Initial and boundary conditions

Initial conditions:

In the Vh subdomain the gas concentration is initially set at the3.2. Governing equations

With reference to the previous statements, the governing equa-tion for the diffusion of CO2 is applied to yield for the gas concen-tration c in both domains (Bird et al., 2002):

@c@t

r Dirc 1

where i denotes the head space h or the water w, depending on the

G. Carrieri et al. / Journal of Foos taken by the solver itself in free mode. The run was exe-for a total period of 7 months, taking less than a minute onrmicro PC carrying a Xeon (3 GHz) CPU, under Windows XP.T2 4.32 10 3.71 10 1.47 10 1.44 10T3 2.51 1013 2.16 1013 1.667 105 2.16 109T4 4.3 013 3.39 1013 1.768 105 2.52 109

As proposed for example by Del Nobile et al., 1997, Dp varieswith temperature. Therefore, for the variable temperature T1mode, based on the above optimized values, a tting polynomialwas found, with the coefcients of Dp aT2 bT c determinedby means of Matlab (MATLAB, 2009). For W1 we found:

Dp 0:0025 1013T2 0:0038 1013T 0:1440 1013 7while for W2 we assumed, for the same temperatures but varyingwith bottle weight:

Dp 0:0021 1013T2 0:0047 1013T 0:1120 1013 8

The employed diffusion coefcients for package, air and waterare summarized in Table 4. Dp values are consistent with those re-ported in the available literature (e.g. in Lewis et al., 2003 andMcGonigle et al., 2001), considered that Dp is generally inuencedby the crystallinity degree upon bottle formation also.

4.2. Comparison of computations with experiments

In order to validate the model, preliminary measurements wereperformed for W1T1 and W2T1 bottles (Figs. 4 and 5), and thencompared with the corresponding simulations. It is shown that

Fig. 4. Comparison between experimental data and predicted data for W1T1.

574 G. Carrieri et al. / Journal of Food Engineering 108 (2012) 570578Fig. 5. Comparison between experimental data and predicted data for W2T1.

the comparison with the experiments holds well enough, evenwith the variable storage temperature. The computations slightlyoverestimates the loss history for the lighter W1 bottle, while forthe heavier W2 bottle the optimized diffusivity yields a certainunderestimation, its maximum value being some 23% at the nalstorage time of 210 days. The experiments also show that thereis no appreciable effect on the carbonic loss due to the bulk weightW1 or W2. In both cases, however, the average CO2 reduction rangesfrom 5300 mg/l to about 2700 mg/l (almost 50%) after the entirestorage period.

Then modelling was also conducted and validated for the W1T3, W2T3, W1T2 and W1T4 bottles (Figs. 69). At all mode com-

binations, it is conrmed that the model is fairly able to simulatethe evolution at stake.

A rst interesting issue is the yield obtained by a given initialcarbonic content. For example, the W1T3 (Fig. 6) bottle has aslightly higher initial concentration (5100 mg/l) that the W2T3(Fig. 7) one (4860 mg/l): nevertheless, in the former case the nalconcentration is only about 1000 mg/l while in the latter it reachesalmost 1300 mg/l. In other words, a mere 5% decrement in the ini-tial concentration helps extend the shelf life by 45 days. This differ-ence cannot be attributed to the bottle weight, as speculatedabove, but to a higher driving force (the concentration gradientwith the environment) that induces a greater carbonic depletion.

Fig. 6. Comparison between experimental data and predicted data for W1T3.

G. Carrieri et al. / Journal of Food Engineering 108 (2012) 570578 575Fig. 7. Comparison between experimental data and predicted data for W2T3.

d En576 G. Carrieri et al. / Journal of FooA second evident effect is the increment of carbonic loss withtemperature, as expected. It is indeed instructive to compare, fora given bottle weight, the concentration history with varying tem-perature mode: that is, the variable temperature W1T1 (Fig. 4)with the one kept at constant temperature W1T3 (Fig. 6), and sim-ilarly the W2T1 results (Fig. 5) with the W2T3 ones (Fig. 7). It isevident that at the warm T3 temperature the carbonic loss is muchhigher: after 150 days, for example, the W1T3 (Fig. 6) and W2T3(Fig. 7) bottles loose about 2000 mg/l (some 50%) more than thecorresponding variable temperature storage W1T1 (Fig. 4) and

Fig. 8. Comparison between experimenta

Fig. 9. Comparison between experimentagineering 108 (2012) 570578W2T1 (Fig. 5). At the same storage time, the loss is even higherand up to 3000 mg/l (almost 83%) when comparing the cold tem-perature W1T2 case (Fig. 8) with the hotter one W1T4 (Fig. 9).

Finally, it can be observed that the computed concentration his-tory at the warmer T3 and T4 modes (Figs. 6, 7 and 9) are nicelysuperimposed with the corresponding experimental progress. In-stead, at the beginning of the T1 and T2 modes (Figs. 4, 5 and 8),when the storage temperature is low, a discrepancy of maximum10% is found with measurements. It is speculated that in these con-ditions the model cannot compensate with the additional retention

l data and predicted data for W1T2.

l data and predicted data for W1T4.

Fig. 10. Local evolution of carbonic concentration, ranging from 1.26 to 108 mol/m3, at W1T2 modes and for six times: from left to right, at t = 0 (bottling), and at day 1, 15,30, 90 and 210, respectively.

Fig. 11. Local carbonic concentration, ranging from 1.26 to 108 mol/m3, at W1 mode, after 15 and 210 days: for T2 (rst and second from left) and T4 (third and fourth fromleft) modes, with indication of intensity and direction of diffusive ux.

G. Carrieri et al. / Journal of Food Engineering 108 (2012) 570578 577

effect by the water, as CO2 features a higher solubility at low tem-peratures (Steen, 2006), and therefore is poorly available to trans-fer through polyethylene terephthalate.

4.3. Maps of carbonation evolution

In Fig. 10 the local evolution of carbonic concentration, at W1T2 modes and for several times is shown. A similar evolution isfound for all other explored modes. It is evident that an equilib-rium is soon reached between the head space and the water (whichis evident comparing the rst two maps from left in Fig. 10). Theconcentration gradient disappears completely after 3 months. At

The carbonation decrement does not appear to depend on bottleweight, although diffusive non-uniformity is observed depending

Author contributions

G.C. conceived the study that was then designed by G.R. in con-junction with M.V.D.B. G.C. carried out the experiments. Allauthors participated in developing the model. G.C. carried out thecomputations, set up the model validation and wrote the rst draftof the manuscript. G.C. and M.V.D.B. participated in manuscriptrevisions and discussion, coordinated and critiqued by G.R.

Acknowledgments

578 G. Carrieri et al. / Journal of Food Engineering 108 (2012) 570578on polyethylene terephthalate thickness distribution, given bythe bottle manufacture. An adequate initial carbonation favorsthe extension of shelf life up to 20%, in the explored case. Theimportance of a controlled storage temperature is conrmed, asthe diffusion of gas through polyethylene terephthalate is acceler-ated with temperature: a fourfold increase of temperature from10 C yields a 83% higher gas loss.

The model created in this work can be used as a design and ver-ication tool for predicting shelf life in any carbonic beverage, andcan be easily supplemented with the dependence on lling levelamong other product and storage parameters. Its results can beemployed to rapidly establish the best used by date variation,depending of some manufacturing practice change, so that the de-sired features can be ensured.the end of the observed storage period, the polyethylene tere-phthalate bottle will lose about 35% of its initial carbonation.

Finally, in Fig. 11 the effect of storage temperature on the localconcentration is inspected, for the W1 bottle at the T2 and T4modes. From the beginning of the process (15 days), a warmerT4 storage yields for a greater carbonic loss (third map from left)with respect to the a cooler T2 condition (rst map from left).The uneven pattern of ux arrows (in their intensity and direction)also evidences that the polyethylene terephthalate thickness dis-tributions (Table 2) and arrangement diffusivities (Table 4), makesthe carbonic loss non-uniform along the bottle height. The net car-bonic loss is then accelerated at the end of the period (210 days)for T4 (last map), rather than with T2 (second map from left), con-rming what speculated earlier when examining Figs. 8 and 9.

5. Conclusions

In this work a model of shelf life of carbonated drinks has beenproposed and validated by experimental results. The model takesinto consideration the weight of bottle and storage temperature,allowing for a good agreement with the explored two parameters.The authors gratefully acknowledge Dr. A. Libutti and Dr. A.V.Lotito of Fonti del Vulture S.r.l., in Rionero in Vulture (Italy).

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