-
mRnza
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: [email protected] (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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