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Influence of packaging geometry and material properties on the oxidation kinetic of bottled virgin olive oil
Journal of Food Engineering 57 (2003) 189–197 www.elsevier.com/locate/jfoodeng
Influence of packaging geometry and material properties on the oxidation kinetic of bottled virgin olive oil M.A. Del Nobile b
a,*
, S. Bove a, E. La Notte a, R. Sacchi
b
a Istituto di Produzioni e Preparazioni Alimentari, University of Foggia, Via Napoli, 25-71100 Foggia, Italy Dipartimento di Scienza degli Alimenti, University of Naples ‘‘Federico II’’, Via Universit a, 100-80055 Portici, Italy
Received 3 January 2002; accepted 24 June 2002
Abstract A two-dimensional mathematical model able to predict the time course of hydroperoxides and oxygen concentration profile inside bottled virgin olive oil during storage is presented. By simulating the behavior of the bottled virgin olive oil it was possible to assess the influence of the bottleÕs shape and size on the quality decay kinetics of virgin olive oil bottled in glass and plastic containers. In particular, five geometrically different containers were used to predict the storage behavior of bottled virgin olive oil. The obtained results show that the quality decay kinetics of bottled virgin olive oil greatly depends on container geometry. However, the extent to which the containerÕs geometrical factors affect the quality decay kinetics depends on the material used to make the bottle, and on the initial value of the oxygen partial pressure in the bottle headspace. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Modeling; Shelf life; Olive oil; Active packaging
1. Introduction The shelf life of a bottled vegetable oil is limited by the auto-oxidation of unsaturated fatty acids with the formation of hydroperoxides. The decomposition of hydroperoxides gives rise to different compounds, some of which are volatile and responsible for the sensory degradation of the oil (Frankel, 1998). It has been proved that mathematical models able to predict the shelf life of packed foods are a valuable tool in designing packaging systems (Del Nobile, Mensitieri, Nicolais, & Masi, 1997; Labuza & Contreras-Medellin, 1981; Tubert & Iglesias, 1985). In a previous paper, Del Nobile, Ambrosino, Sacchi, and Masi (in press) presented a mathematical model able to predict the evolution of oxygen and hydroperoxide concentrations in virgin olive oil bottled in plastic and glass containers. The developed model was used to assess the effect of the following upon the quality decay kinetics of bottled olive oil: oxygen diffusivity and the thickness of the
*
Corresponding author. Tel.: +39-881-589-233; fax: +39-881-740211. E-mail address: [email protected] (M.A. Del Nobile).
plastic container, the presence of an oxygen scavenger in the container wall and the concentration of oxygen in the oil prior to bottling. In particular, it was established that by increasing the barrier properties of the polymer used to manufacture the bottle it is possible to obtain a quality decay kinetic as slow as that obtained for olive oil bottled in glass containers. Oxidation kinetics slower than that found with glass bottles can be obtained by bottling olive oil in innovative materials containing an oxygen scavenger. However, the slowest decay kinetics were obtained by bottling the oil in poly(ethylene terephthalate) (PET) containers and reducing the oxygen concentration prior to bottling to 10% of the equilibrium value. Even though the above model was advantageously used to demonstrate several advantageous aspects related to the design of plastic bottles for packaging of virgin olive oil, it has some limitations. In fact, it can not be used to predict the quality decay kinetics of small containers (i.e., only for hc =rb > 10) and/or to assess the influence of the bottleÕs geometrical factors on the quality decay kinetics of the bottled oil. The above restrictions are a direct consequence of one of the hypotheses used to derive the model; i.e., oxygen diffusion takes place only in the radial direction (monodimensional model).
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 2 ) 0 0 2 9 7 - 2
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Nomenclature Av CROOH average hydroperoxide concentration
COOil2 COPolym 2 Polym COS
CROOH DOil O2 DPolym O2 DPET O2
oxygen concentration in virgin olive oil concentration of the oxygen dissolved in the container wall oxygen scavenger concentration in plastic container local hydroperoxide concentration in the bottled oil expressed as cm3 (STP)/cm3 (Oil) oxygen diffusivity through virgin olive oil diffusivity of oxygen through the plastic container wall oxygen diffusivity in PET
ðJOCap ÞInt D oxygen mass flux at the bottle headspace/ 2 aluminum cap interface ðJOOil2 ÞInt A oxygen mass flux at the oil/bottle wall interface (in the oil) ðJOOil2 ÞInt B oxygen mass flux at the bottle headspace/oil interface (in the oil) ðJOPolym Þ Int A oxygen mass flux at the oil/bottle wall 2 interface (in the container wall) ðJOPolym Þ Int C oxygen mass flux at the bottle headspace/ 2 bottle wall interface (in the container wall) Ki ’s constants, they have to be regarded as fitting parameters nHS number of oxygen moles present in the bottle O2 headspace nOil number of oxygen moles dissolved in the O2 virgin olive oil prior to bottling. pOOil2 oxygen partial pressure in virgin olive oil
In this work the mono-dimensional model was improved by taking into account also oxygen diffusion in the bottleÕs axial direction (two-dimensional model). The new model was then used to assess the influence of some of the bottleÕs geometrical factors on the quality decay kinetics of virgin olive oil bottled in glass and plastic containers.
2. Materials and methods In this study five geometrically different bottles were investigated. The first three differ in volumetric capacity (i.e., 1, 1/2 and 1/4 l), while the latter two contain the same amount of oil, 1 l, but differ in the capacity of the bottle headspace. Fig. 1 shows the axial section of the bottles used to run the simulations, while Table 1 lists the dimensions of the above bottles. The thickness of the bottles is equal to 350 lm.
pOHS2
oxygen partial pressure in the bottle headspace at time t pOHS2 ð0Þ oxygen partial pressure in the bottle headspace at time zero ðpOOil2 ÞInt A oxygen partial pressure at the oil/bottle wall interface (in the oil) ðpOOil2 ÞInt B oxygen partial pressure at the bottle headspace/oil interface (in the oil) ðpOPolym Þ Int A oxygen partial pressure at the oil/bottle 2 wall interface (in the plastic) ðpOPolym Þ Int C oxygen partial pressure at the bottle 2 headspace/bottle wall interface (in the plastic) r radial coordinate R universal gas constant RD rate at which hydroperoxides are decomposed expressed as cm3 (STP)/cm3 (Oil) s RF rate at which hydroperoxides are formed expressed as cm3 (STP)/cm3 (Oil) s ROS rate at which oxygen is consumed by the oxygen scavenger SBottle bottle surface SOOil2 oxygen solubility in virgin olive oil SOPET 2 t T VHS VOil z l
oxygen solubility in PET time absolute temperature volume of the bottle headspace volume of the bottled virgin olive oil axial coordinate liquid viscosity
2.1. Evaluation of the oil oxidation parameters The oxidation kinetics simulations were made using experimental data obtained from shelf-life tests made at 40 °C using extra virgin olive oils extracted from olives (Olea europaea sativa, cv Biancolilla) by the percolationcentrifugation system (Rapanelli, Foligno, Italy). The parameters characterizing extra virgin olive oil autooxidation at 40 °C were evaluated in a previous paper (Del Nobile et al., in press) and are summarized in Table 2. 2.2. Evaluation of the oxygen transport parameters 2.2.1. Oxygen/olive oil System There are no data reported in the literature on the solubility and diffusivity of oxygen in virgin olive oil. However, considering the chemical nature of virgin olive oil it is reasonable to assume that SOOil2 is enclosed in an
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Table 2 Parameters characterizing the lipid oxidation reaction of the investigated virgin olive oil 8:52 109 2:47 1010 7:32 103 1.02 3:28 108
K1 cm3 (STP)/cm3 s K2 K3 (atm) K4 K5 (s1 )
Eq. (1) was originally derived to correlate oxygen diffusivity through organic solvents to their viscosity. The viscosity of the virgin olive oil used in this investigation at 40 °C is 0.033 Pa s, having been evaluated using a Rheometrics RFS II viscometer. Substituting the above viscosity value in Eq. (1), the value obtained for DOil O2 is 2:72 106 cm2 /s. 2.2.2. Oxygen/PET system The values of oxygen diffusivity (DPET O2 ) and solubility PET (SO2 ) in PET were determined from the data reported in the literature on the diffusivity and solubility of oxygen in PET at 30 °C, which are 4:9 109 cm2 /s and 0.092 cm3 (STP)/cm3 atm respectively (Toi, 1973). The value for the diffusion activation energy and for the enthalpy of solubilization used to evaluate diffusivity and solubility at 40 °C are 11 and )3.1 kcal/mol respectively (Michaels, Vieth, & Barrie, 1963a,b). The data obtained for DPET and SOPET are 8:8 109 cm2 /s and 0.078 O2 2 3 3 cm (STP)/cm atm respectively. The oxygen transport parameters for the oxygen/oil and oxygen/PET systems used in the present investigation to run the simulations are listed in Table 3. Fig. 1. Axial section of the bottle.
3. Results and discussions interval whose upper limit is the oxygen solubility in nhepthane (0.4 cm3 (STP)/cm3 atm) and the lower limit is oxygen solubility in polyethylene (0.08 cm3 (STP)/ cm3 atm) (Michaels & Bixler, 1961). Taking into account that the average molecular weight of virgin olive oil is closer to that of n-hepthane than to that of polyethylene, SOOil2 was set at 0.15 cm3 (STP)/cm3 atm. The values of DOil O2 were determined through the following expression (Schumpe & L€ uhring, 1990): D ¼ ð2:6 10
11
2=3
Þl
ð1Þ
During the storage of bottled virgin olive oil hydroperoxides are formed through the oxidation of Table 3 Transport parameters of the oil/oxygen and PET/oxygen systems SOOil2 (cm3 (STP)/cm3 atm)
0.15
2 DOil O2 (cm /s)
2:72 106
SOPET (cm3 (STP)/cm3 atm) 2
0.078
2 DPET Eff (cm /s)
8:8 109
Table 1 Dimensions of the investigated bottles Bottle A B C D E
Volume (cm3 ) 1000 480 251 1000 1000
SBottle =VOil (cm1 ) 1
6:1 10 7:9 101 9:8 101 6:2 101 6:3 101
VHS =VOil 2
1:8 10 2:5 102 2:8 102 3:3 102 4:6 102
Oil nHS O2 =nO2
rc (cm)
rb (cm)
hc (cm)
ho (cm)
hb (cm)
0.11 0.14 0.16 0.20 0.27
1.4 1.2 1.0 1.4 1.4
4.4 3.4 2.8 4.4 4.4
16.2 13.0 10.0 16.2 16.2
18.6 14.8 11.6 18.6 18.6
21.6 17.4 13.8 24.0 26.0
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unsaturated fatty acids and consumed by hydroperoxide breakdown reactions. In the first stage of oxidation, when the oxygen concentration is close to saturation, the rate at which hydroperoxides are consumed is lower than the rate at which they are produced through the autooxidation of unsaturated fatty acids, leading to an increase in hydroperoxide concentration during storage. As the lipid oxidation reaction proceeds, oxygen is consumed to form hydroperoxides. This causes: (a) the formation of an oxygen concentration gradient in the bottled oil, which in turn brings about the permeation of external oxygen through the wall of the plastic container; (b) an increase in the rate at which hydroperoxides break down. As a result of the above phenomena, concentrations of both local oxygen and hydroperoxides decrease. Given the above scenario during oil storage, to properly describe the oxidation kinetics of bottled virgin olive oil a mathematical model was developed to predict the time course of oxygen and hydroperoxide concentrations in bottled oil during storage. 3.1. Two-dimensional mathematical model The mathematical model was derived by assuming that: (a) the axial section of the bottle is that showed in Fig. 1; (b) the diffusive mass flux of hydroperoxides through both the olive oil and the container wall were considered negligible. Under the above restrictions the mass balance equation of the hydroperoxides dissolved in the bottled oil have the following expression: oCROOH ¼ RF RD ot
ð2Þ
Several models have been reported in the literature to describe the rate at which hydroperoxides are formed through the oxidation of unsaturated fatty acids (Quast & Karel, 1972; Quast, Karel, & Rand, 1972); the model proposed by Quast et al. (1972) to describe lipid oxidation in potato chips was used in the present investigation. Assuming that relative humidity is constant during storage, the model proposed by Quast et al. (1972) is further simplified to the following relationship: ! pOOil2 RF ¼ ðK1 þ K2 CROOH Þ ð3Þ K3 þ K4 pOOil2 Assuming that the solubilization process of oxygen into oil is governed by HenryÕs law, pOOil2 is related to the oxygen concentration in the oil through the following relationship: pOOil2 ¼ COOil2 =SOOil2 . As reported above, hydroperoxides break down, thereby giving rise to several secondary products (Labuza, 1971). Many reactions are involved in this process, each of which is characterized by a particular mechanism and should be described with a specific
equation. For the sake of simplicity, in the present investigation we assumed that at a given temperature the overall rate at which hydroperoxides decompose depends only on their concentration (Koelsch, Downes, & Labuza, 1991). Hexanal formation via lipid oxidation as a function of oxygen concentration (Koelsch et al., 1991) was obtained through the following expression: RD ¼ K5 CROOH
ð4Þ
Substituting Eqs. (3) and (4) in Eq. (2) the following expression is obtained: ! pOOil2 oCROOH K5 CROOH ¼ ðK1 þ K2 CROOH Þ ot K3 þ K4 pOOil2 ð5Þ The mass balance of the oxygen dissolved in the bottled oil was obtained by assuming that FickÕs first law and HenryÕs law govern oxygen diffusion and solubilization processes respectively. Starting from the above hypothesis, it can be easily demonstrated that oxygen mass balance has the following expression: # " ! Oil 2 Oil oCOOil2 oC o C 1 o O O 2 2 r ¼ DOil þ O2 r or ot or oz2 ! pOOil2 ðK1 þ K2 CROOH Þ ð6Þ K3 þ K4 pOOil2 The first term on the right side of the Eq. (6) is related to the oxygen diffusive mass flux, while the second term denotes the rate of oxygen consumption by the lipid oxidation reaction. To evaluate the amount of oxygen permeating through the container wall, it is necessary to write the mass balance equation for the oxygen dissolved in the container wall, which, in the case under investigation, has the following expression (Del Nobile et al., 1997; Masi & Paul, 1982; Paul & Koros, 1976): # " ! oCOPolym oCOPolym o2 COPolym Polym 1 o 2 2 2 r ð7Þ ¼ DO2 þ r or ot or oz2 In the presence of an oxygen scavenger uniformly dispersed in the container wall, Eq. (7) became: # " ! oCOPolym oCOPolym o2 COPolym Polym 1 o 2 2 2 r ¼ DO2 ROS þ r or ot or oz2 ð8Þ In principle, ROS depends on the following: the concentration of oxygen and the oxygen scavenger in the plastic, temperature and humidity. Since there are no data reported in the literature on the relationship between ROS and the above variables, we have proposed the following equation: Polym ROS ¼ K6 COPolym COS 2
ð9Þ
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K6 depends on the temperature and humidity. The valPolym ues for K6 and for the initial value of COS , are 5 3 3 3 1:58 10 cm /cm (STP) s and 14 cm (STP)/cm3 respectively. They were obtained assuming that a film 50 lm thick containing the oxygen scavenger consumes oxygen at a rate equal to 112 cm3 (STP)/m2 day at 40 °C, and that the maximum amount of oxygen consumed is equal to 700 cm3 (STP)/m2 . Interfacial conditions were imposed to ensure chemical and physical equilibrium at the interface between oil and container. Hence, both the mass flow and the oxygen partial pressure of the juxtaposed substances were required to be equal at the oil/bottle wall interface, i.e.: ( ðJOPolym ÞInt A ¼ ðJOOil2 ÞInt A 2 ð10Þ Polym ðpO2 ÞInt A ¼ ðpOOil2 ÞInt A At the bottle headspace/oil and bottle headspace/ bottle wall interfaces the following conditions were imposed: 8 HS pO2 ¼ ðpOOil2 ÞInt B > > > > HS Polym > < pO2 ¼ ðpO2 ÞInt C HS n RT ð11Þ > pOHS2 ¼ OV2HS > > > dnHS > : O2 ¼ ðJ Polym Þ Oil O2 Int C þ ðJO2 ÞInt B dt At the bottle headspace/aluminum cap interface the following condition was imposed: ðJOCap ÞInt D ¼ 0 2
ð12Þ
Eqs. (5)–(7) (or (8) in the case of ‘‘active bottles’’), (10)–(12), form a set of differential equations, which, using the proper initial and boundary conditions, were solved simultaneously by numerical methods to predict the evolution of oxygen and hydroperoxides inside the bottled virgin olive oil during storage. The average hydroperoxide concentration was obtained by averaging CROOH over the volume of the bottled olive oil. In the following, the above model is used to assess the influence of some of the bottleÕs geometrical factors on the quality decay kinetics of virgin olive oil bottled in plastic and glass containers. The rate of hydroperoxide formation and breakdown was predicted by using the data listed in Table 2, while the data listed in Table 3 were used to describe the diffusion and solubilization processes of oxygen in olive oil and in PET. Unless otherwise specified, the oxygen partial pressure in the bottle headspace was set at 0.2 atm. 3.2. Influence of headspace and geometry of PET containers Av Fig. 2 shows the predicted CROOH plotted as a function of storage time for virgin olive oil bottled in containers A, B and C made of PET. In the above figure, two set of curves are shown: the first was obtained by
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Fig. 2. Predicted average hydroperoxide concentration versus time: (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2; ( ) bottle B, pOHS2 ð0Þ ¼ 0:2; (––) bottle C, pOHS2 ð0Þ ¼ 0:2; (– –) bottle A, pOHS2 ð0Þ ¼ 0; (- – -) bottle B, pOHS2 ð0Þ ¼ 0; (– – –) bottle C, pOHS2 ð0Þ ¼ 0.
setting pOHS2 ð0Þ equal to 0.2, while the second was obtained by setting pOHS2 ð0Þ equal to 0. As shown in Fig. 2, in the first stage of oxidation the six quality decay kinetics are identical; as the lipid oxidation reaction proceeds the six curves diverge. In fact, right after bottling the lipid oxidation reaction rate depends primarily on the oxygen dissolved in the oil prior to bottling. As the oxidation reaction proceeds, the oxygen present in the bottle prior to bottling is consumed and subsequently replaced by the oxygen permeating through the bottle wall. Thus, the lipid oxidation reaction rate will gradually depend less on the oxygen dissolved in the oil prior to bottling, and more on the oxygen permeating through the bottle wall, and thus on the bottle geometry. As shown in Fig. 2, by reducing either the bottleÕs volumetric capacity or the oxygen partial pressure in the bottle headspace, the quality decay kinetics slow down. In fact, bottles A, B and C differ in both the values of SBottle =VOil and VHS =VOil . To separate the effects that these two parameters have on the quality decay kinetics of bottled oil, let us first consider the curves obtained by setting pOHS2 ð0Þ equal to 0. As would be expected, as the ratio SBottle =VOil decreases the quality decay kinetics of the bottled virgin olive oil slow down. In fact, the amount of oxygen permeating the bottle per unit volume of the oil decreases as the ratio SBottle =VOil decreases, thus slowing down the oil quality decay kinetics. The curves obtained by setting pOHS2 ð0Þ equal to 0.2, show a trend similar to that obtained by removing the oxygen from the bottle headspace. As shown in Fig. 2, as the ratio VHS =VOil increases, the difference between the quality decay kinetics obtained by setting pOHS2 ð0Þ equal to 0.2 and that obtained by setting pOHS2 ð0Þ equal to 0 increase. In fact, as the ratio VHS =VOil increases, the oxygen present in the bottle headspace, which can freely diffuse into the bottled oil, increases, thus accelerating the time course during storage of the hydroperoxides.
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Fig. 3. Predicted average hydroperoxide concentration versus time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
Fig. 4. Predicted pOHS2 plotted as a function of storage time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
Fig. 3 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in PET containers A, D and E. As shown in Fig. 3, the influence of the ratio VHS =VOil on the oxidation kinetics is negligible. The above result is due to the fact that the amount of oxygen present in the bottle headspace does not change markedly during the investigated period (Fig. 4).
Fig. 5. Predicted average hydroperoxide concentration plotted as a function of storage time: (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2; ( ) bottle B, HS pOHS2 ð0Þ ¼ 0:2; (––) bottle C, pHS O2 ð0Þ ¼ 0:2; (– –) bottle A, pO2 ð0Þ ¼ 0; (- – -) bottle B, pOHS2 ð0Þ ¼ 0; (– – –) bottle C, pOHS2 ð0Þ ¼ 0.
expect, in the case of the curves obtained by setting pOHS2 ð0Þ equal to zero, by decreasing the ratio VHS =VOil the quality decay kinetics accelerate. In fact, in the latter case the bottle headspace acts as a empty reservoir that removes oxygen from the bottled oil. Therefore, the higher is the ratio VHS =VOil , the higher is the amount of oxygen that diffuses from the bottled oil into the bottle headspace. As an example, in Fig. 6 the time course during storage of the oxygen partial pressure in the bottle headspace is plotted. Similar to what was reported in Fig. 3, Fig. 7 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in glass containers A, D and E. As in the case of PET bottles (Fig. 3), the influence of the ratio VHS =VOil on the oxidation kinetics is negligible. Also in this case the observed behavior is due to the fact that the amount of oxygen present in the bottle headspace does not change markedly during the investigated period (Fig. 8).
3.3. Influence of headspace and geometry of glass containers Av Fig. 5 shows the predicted CROOH plotted as a function of storage time for virgin olive oil bottled in glass containers A, B and C. Two set of curves are shown: the first was obtained by setting pOHS2 ð0Þ equal to 0.2, the
other was obtained by setting pOHS2 ð0Þ equal to 0. Also in this case by decreasing the amount of oxygen that freely diffuses from the bottle headspace into the bottled oil (i.e., by decreasing the ratio VHS =VOil ) also the quality decay kinetics slow down. Contrary to what one would
Fig. 6. Predicted pOHS2 plotted as a function of storage time: (- -- -) bottle A; ( ) bottle B; (––) bottle C.
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Fig. 7. Predicted average hydroperoxide concentration versus time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
195
Fig. 9. Predicted average hydroperoxide concentration versus time: ¼ 8:8 1010 ; (- – -) bottle B, DPolym ¼ 8:8 (– –) bottle A, DPolym O2 O2 10 10 ; (– – –) bottle C, DPolym ¼ 8:8 1010 ; (- -- -) bottle A, DPolym ¼ O2 O2 8:8 109 ; ( ) bottle B, DPolym ¼ 8:8 109 ; (––) bottle C, O2 ¼ 8:8 109 ; (- - -) bottle A, DPolym ¼ 8:8 108 ; (- -) bottle B, DPolym O2 O2 DPolym ¼ 8:8 108 ; (- -) bottle C, DPolym ¼ 8:8 108 . O2 O2
of bottle, either because the oxygen mass flux is too high or too low.
3.5. Effect of an oxygen scavenger
Fig. 8. Predicted pOHS2 plotted as a function of storage time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
3.4. Influence of the container’s properties Fig. 9 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in plastic containers A, B and C. The figure shows three set of curves that refer to virgin olive oil bottled in plastic containers made of polymers differing in the value of the oxygen diffusion coefficient. As would be expected, regardless of the type of bottle used to pack the virgin olive oil, as DPolym decreases, the O2 bottled oil quality decay kinetics slow down. Interestingly, for DPolym higher and lower than that of PET, the O2 dependence of the quality decay kinetics on the bottle type is not as marked as that found for PET bottles. The above results suggest that, at least for the investigated bottles, the amount of oxygen permeating through the bottle wall per unit volume of bottled oil strongly depends on the shape and size of the bottle only for values of DPolym close to that of PET. For DPolym much higher or O2 O2 much lower than that of PET the oxygen permeating through the bottle wall depends only slightly on the type
It has been often reported in the literature (Vermeiren, Devlieghere, van Beest, de Kruijf, & Debevere, 1999) that oxygen scavengers can be successfully used to prolong the shelf life of foods whose quality decay kinetics depend on the oxygen concentration in the package. In the present paper, the two-dimensional model is used to assess the influence of the bottle geometrical factors on the quality decay kinetics of virgin olive oil bottled in an innovative PET container, the oxygen scavenger being uniformly dispersed in the container wall. Fig. 10 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in plastic containers A, B and C. The first refers to PET bottles, the second refers to the innovative PET containers mentioned above. As expected, by dispersing the oxygen scavenger into the container wall it is possible to slow down the oxidation kinetics of the bottled oil. Unlike what was observed in the case of virgin olive oil bottled in PET containers, the larger the bottle size, the slower is the quality decay rate of the bottled oil. In fact, the oxygen scavenger slows down the oxidation kinetics in part by reducing the amount of oxygen permeating into the bottle and in part by removing the oxygen dissolved in the oil prior to bottling. In fact, by reducing the size of the bottle, and consequently by increasing the ratio SBottle =VOil and the ratio VHS =VOil , both the amount of oxygen permeating into the bottle and that removed by the scavenger from the oil increase. The results obtained suggest that the effects related to the presence of an oxygen scavenger far
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Fig. 10. Predicted average hydroperoxide concentration versus time: (- -- -) bottle A, PET; ( ) bottle B, PET; (––) bottle C, PET; (- -) bottle A, PET þ oxygen scavenger; (- – -) bottle B, PET þ oxygen scavenger; (– – –) bottle C, PET þ oxygen scavenger.
outweigh those deriving from an increase in the permeated oxygen. 3.6. Predictive ability of mono- and two-dimensional models Fig. 11 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in PET containers. The three curves reported in the above figure refer to the quality decay kinetics predicted by the mono- and twodimensional model. A diffusive mono-dimensional model can be used in place of the more accurate diffusive two-dimensional model if the following relation is satisfied: hc =rb > 10. In the specific case of bottle A, the above ratio is equal to 3.7. However, as shown in Fig. 11 the difference between the quality decay kinetics predicted by the two models is not as marked as expected. In fact, in the first stage of storage the oxidation reaction rate does not depend much on the oxygen permeating
Fig. 12. Predicted average hydroperoxide concentration versus time: (––) mono-dimensional model; ( ) bottle A, pOHS2 ð0Þ ¼ 0; (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2.
through the bottle wall, thus accounting for the results shown in Fig. 11. The differences between the quality decay kinetics predicted by the two models have to be ascribed to the fact that the two-dimensional model takes into account the axial mass flux coming from the top and the bottom of the bottle as well as the presence of the oxygen in the bottle headspace. Referring to the latter point, it is worth noting that, as expected, if pOHS2 ð0Þ is equal to 0, the quality decay kinetics predicted by the two models are closer. Fig. 12 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in glass containers. The three curves reported in the above figure refer to the quality decay kinetics predicted by the mono- and two-dimensional model. In this case the difference between the predictions of the two models is less marked than that that observed in the case of the PET bottle. In fact, for glass bottles there is no mass flux from the bottom of the bottle as in the case of PET bottles.
4. Conclusions
Fig. 11. Predicted average hydroperoxide concentration versus time: (––) mono-dimensional model; ( ) bottle A, pOHS2 ð0Þ ¼ 0; (- -- -) bottle A, pOHS2 ¼ 0:2.
By means of the two-dimensional mathematical model presented it was possible to assess the influence of some of the bottle geometrical factor (VHS =VOil and SBottle =VOil ) on the quality decay kinetics of virgin olive oil bottled in polymer containers. The predictive ability of the mono- and two-dimensional models were also compared. In particular, it was observed that in the case of the bottle with a volumetric capacity of 1 l, the prediction of the mono-dimensional model is close to that of the more accurate two-dimensional model. This could be related to the fact that during the first stage of storage the oxidation reaction rate depends primarily on the oxygen dissolved into the oil prior to bottling.
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The results obtained in the case of PET bottles showed that when the ratio SBottle =VOil decreases, then the amount of oxygen permeating through the bottle wall decreases, thus slowing down the quality decay kinetics of the bottled oil. In the case of PET bottles with an oxygen scavenger uniformly dispersed in the bottle wall, the opposite is true. This is due to the fact that the oxygen scavenger consumes part of the oxygen dissolved in the oil prior to bottling. The ratio VHS =VOil also influences the evolution of the hydroperoxides during storage. In particular, it was observed that if pOHS2 ð0Þ is equal to 0.2 the quality decay kinetics slow down as the ratio VHS =VOil decreases. On the other hand, if pOHS2 ð0Þ is equal to 0, the quality decay kinetics slow down if VHS =VOil increases. These results suggest that, to control the oxidation kinetics during the storage of bottled oil, it may be useful to use well-designed plastic bottles, innovative plastic materials containing an oxygen scavenger and to perform the bottling operations under a nitrogen atmosphere (to reduce the oxygen pressure in the bottle headspace). These practices are often underestimated by the oil industry which defines empirically the period of shelf-life (date of recommended consumption) of bottled extra virgin olive oil, without carefully considering oil characteristics, packaging properties and the temperature conditions during product distribution. Acknowledgements The work was funded under the MURST ‘‘Piani di Potenziamento della Ricerca Scientifica e Tecnologica’’ and MURST-DIT3 Program grants. References Del Nobile, M. A., Ambrosino, M. L., Sacchi, R., & Masi, P. (in press). Design of plastic bottles for packaging of virgin olive oil. Journal of Food Science.
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Del Nobile, M. A., Mensitieri, G., Nicolais, L., & Masi, P. (1997). The influence of the thermal history on the shelf life of carbonated beverages bottled in plastic containers. Journal of Food Engineering, 34, 1–13. Frankel, E. N. (1998). Lipid oxidation (p. 303). Dundee: The Oily Press. Koelsch, C. M., Downes, T. W., & Labuza, T. P. (1991). Hexanal formation via lipid oxidation as a function of oxygen concentration: measurements and kinetics. Journal of Food Science, 56(3), 816–820. Labuza, T. P. (1971). Kinetics of lipid oxidation in foods. CRC Critical Reviews in Food Technology, 2, 355–405. Labuza, T. P., & Contreras-Medellin, R. (1981). Prediction of moisture protection requirements for foods. Cereal Foods World, 26, 335– 343. Masi, P., & Paul, D. R. (1982). Modelling gas transport in packaging applications. Journal of Membrane Science, 22, 137–151. Michaels, A. S., & Bixler, H. J. (1961). Solubility of gases in polyethylene. Journal of Polymer Science, 50, 393–412. Michaels, A. S., Vieth, W. R., & Barrie, J. A. (1963a). Diffusion of gases in polyethylene terephthalate. Journal of Applied Physics, 34(1), 13–20. Michaels, A. S., Vieth, W. R., & Barrie, J. A. (1963b). Solution of gases in polyethylene terephthalate. Journal of Applied Physics, 34(1), 1–12. Paul, D. R., & Koros, W. J. (1976). Effect of partially immobilizing sorption on permeability and diffusion time lag. Journal of Polymer Science, 14, 675–685. Quast, D. G., & Karel, M. (1972). Computer simulation of storage life of foods undergoing spoilage by two interacting mechanisms. Journal of Food Science, 37, 679–683. Quast, D. G., Karel, M., & Rand, M. (1972). Development of a mathematical model for oxidation of potato chips as a function of oxygen pressure, extent of oxidation and equilibrium relative humidity. Journal of Food Science, 37, 673–678. Schumpe, A., & L€ uhring, P. (1990). Oxygen diffusivities in organic liquids at 293.3. Journal of Chemical Engineering, 35, 24– 25. Toi, K. (1973). Diffusion and sorption of gases in poly(ethylene terephthalate). Journal of Polymer Science, 11, 1839–1929. Tubert, A. H., & Iglesias, H. A. (1985). Water sorption isotherms and prediction of moisture gain during storage of packaged cereal crackers. Lebensmittel-Wissenschaft und Technologie––Food Science and Technology, 19, 365–368. Vermeiren, L., Devlieghere, F., van Beest, M., de Kruijf, N., & Debevere, J. (1999). Developments in the active packaging. Trends in Food Science & Technology, 10, 77–86.
Influence of packaging geometry and material properties on the oxidation kinetic of bottled virgin olive oil M.A. Del Nobile b
a,*
, S. Bove a, E. La Notte a, R. Sacchi
b
a Istituto di Produzioni e Preparazioni Alimentari, University of Foggia, Via Napoli, 25-71100 Foggia, Italy Dipartimento di Scienza degli Alimenti, University of Naples ‘‘Federico II’’, Via Universit a, 100-80055 Portici, Italy
Received 3 January 2002; accepted 24 June 2002
Abstract A two-dimensional mathematical model able to predict the time course of hydroperoxides and oxygen concentration profile inside bottled virgin olive oil during storage is presented. By simulating the behavior of the bottled virgin olive oil it was possible to assess the influence of the bottleÕs shape and size on the quality decay kinetics of virgin olive oil bottled in glass and plastic containers. In particular, five geometrically different containers were used to predict the storage behavior of bottled virgin olive oil. The obtained results show that the quality decay kinetics of bottled virgin olive oil greatly depends on container geometry. However, the extent to which the containerÕs geometrical factors affect the quality decay kinetics depends on the material used to make the bottle, and on the initial value of the oxygen partial pressure in the bottle headspace. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Modeling; Shelf life; Olive oil; Active packaging
1. Introduction The shelf life of a bottled vegetable oil is limited by the auto-oxidation of unsaturated fatty acids with the formation of hydroperoxides. The decomposition of hydroperoxides gives rise to different compounds, some of which are volatile and responsible for the sensory degradation of the oil (Frankel, 1998). It has been proved that mathematical models able to predict the shelf life of packed foods are a valuable tool in designing packaging systems (Del Nobile, Mensitieri, Nicolais, & Masi, 1997; Labuza & Contreras-Medellin, 1981; Tubert & Iglesias, 1985). In a previous paper, Del Nobile, Ambrosino, Sacchi, and Masi (in press) presented a mathematical model able to predict the evolution of oxygen and hydroperoxide concentrations in virgin olive oil bottled in plastic and glass containers. The developed model was used to assess the effect of the following upon the quality decay kinetics of bottled olive oil: oxygen diffusivity and the thickness of the
*
Corresponding author. Tel.: +39-881-589-233; fax: +39-881-740211. E-mail address: [email protected] (M.A. Del Nobile).
plastic container, the presence of an oxygen scavenger in the container wall and the concentration of oxygen in the oil prior to bottling. In particular, it was established that by increasing the barrier properties of the polymer used to manufacture the bottle it is possible to obtain a quality decay kinetic as slow as that obtained for olive oil bottled in glass containers. Oxidation kinetics slower than that found with glass bottles can be obtained by bottling olive oil in innovative materials containing an oxygen scavenger. However, the slowest decay kinetics were obtained by bottling the oil in poly(ethylene terephthalate) (PET) containers and reducing the oxygen concentration prior to bottling to 10% of the equilibrium value. Even though the above model was advantageously used to demonstrate several advantageous aspects related to the design of plastic bottles for packaging of virgin olive oil, it has some limitations. In fact, it can not be used to predict the quality decay kinetics of small containers (i.e., only for hc =rb > 10) and/or to assess the influence of the bottleÕs geometrical factors on the quality decay kinetics of the bottled oil. The above restrictions are a direct consequence of one of the hypotheses used to derive the model; i.e., oxygen diffusion takes place only in the radial direction (monodimensional model).
0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 2 ) 0 0 2 9 7 - 2
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Nomenclature Av CROOH average hydroperoxide concentration
COOil2 COPolym 2 Polym COS
CROOH DOil O2 DPolym O2 DPET O2
oxygen concentration in virgin olive oil concentration of the oxygen dissolved in the container wall oxygen scavenger concentration in plastic container local hydroperoxide concentration in the bottled oil expressed as cm3 (STP)/cm3 (Oil) oxygen diffusivity through virgin olive oil diffusivity of oxygen through the plastic container wall oxygen diffusivity in PET
ðJOCap ÞInt D oxygen mass flux at the bottle headspace/ 2 aluminum cap interface ðJOOil2 ÞInt A oxygen mass flux at the oil/bottle wall interface (in the oil) ðJOOil2 ÞInt B oxygen mass flux at the bottle headspace/oil interface (in the oil) ðJOPolym Þ Int A oxygen mass flux at the oil/bottle wall 2 interface (in the container wall) ðJOPolym Þ Int C oxygen mass flux at the bottle headspace/ 2 bottle wall interface (in the container wall) Ki ’s constants, they have to be regarded as fitting parameters nHS number of oxygen moles present in the bottle O2 headspace nOil number of oxygen moles dissolved in the O2 virgin olive oil prior to bottling. pOOil2 oxygen partial pressure in virgin olive oil
In this work the mono-dimensional model was improved by taking into account also oxygen diffusion in the bottleÕs axial direction (two-dimensional model). The new model was then used to assess the influence of some of the bottleÕs geometrical factors on the quality decay kinetics of virgin olive oil bottled in glass and plastic containers.
2. Materials and methods In this study five geometrically different bottles were investigated. The first three differ in volumetric capacity (i.e., 1, 1/2 and 1/4 l), while the latter two contain the same amount of oil, 1 l, but differ in the capacity of the bottle headspace. Fig. 1 shows the axial section of the bottles used to run the simulations, while Table 1 lists the dimensions of the above bottles. The thickness of the bottles is equal to 350 lm.
pOHS2
oxygen partial pressure in the bottle headspace at time t pOHS2 ð0Þ oxygen partial pressure in the bottle headspace at time zero ðpOOil2 ÞInt A oxygen partial pressure at the oil/bottle wall interface (in the oil) ðpOOil2 ÞInt B oxygen partial pressure at the bottle headspace/oil interface (in the oil) ðpOPolym Þ Int A oxygen partial pressure at the oil/bottle 2 wall interface (in the plastic) ðpOPolym Þ Int C oxygen partial pressure at the bottle 2 headspace/bottle wall interface (in the plastic) r radial coordinate R universal gas constant RD rate at which hydroperoxides are decomposed expressed as cm3 (STP)/cm3 (Oil) s RF rate at which hydroperoxides are formed expressed as cm3 (STP)/cm3 (Oil) s ROS rate at which oxygen is consumed by the oxygen scavenger SBottle bottle surface SOOil2 oxygen solubility in virgin olive oil SOPET 2 t T VHS VOil z l
oxygen solubility in PET time absolute temperature volume of the bottle headspace volume of the bottled virgin olive oil axial coordinate liquid viscosity
2.1. Evaluation of the oil oxidation parameters The oxidation kinetics simulations were made using experimental data obtained from shelf-life tests made at 40 °C using extra virgin olive oils extracted from olives (Olea europaea sativa, cv Biancolilla) by the percolationcentrifugation system (Rapanelli, Foligno, Italy). The parameters characterizing extra virgin olive oil autooxidation at 40 °C were evaluated in a previous paper (Del Nobile et al., in press) and are summarized in Table 2. 2.2. Evaluation of the oxygen transport parameters 2.2.1. Oxygen/olive oil System There are no data reported in the literature on the solubility and diffusivity of oxygen in virgin olive oil. However, considering the chemical nature of virgin olive oil it is reasonable to assume that SOOil2 is enclosed in an
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Table 2 Parameters characterizing the lipid oxidation reaction of the investigated virgin olive oil 8:52 109 2:47 1010 7:32 103 1.02 3:28 108
K1 cm3 (STP)/cm3 s K2 K3 (atm) K4 K5 (s1 )
Eq. (1) was originally derived to correlate oxygen diffusivity through organic solvents to their viscosity. The viscosity of the virgin olive oil used in this investigation at 40 °C is 0.033 Pa s, having been evaluated using a Rheometrics RFS II viscometer. Substituting the above viscosity value in Eq. (1), the value obtained for DOil O2 is 2:72 106 cm2 /s. 2.2.2. Oxygen/PET system The values of oxygen diffusivity (DPET O2 ) and solubility PET (SO2 ) in PET were determined from the data reported in the literature on the diffusivity and solubility of oxygen in PET at 30 °C, which are 4:9 109 cm2 /s and 0.092 cm3 (STP)/cm3 atm respectively (Toi, 1973). The value for the diffusion activation energy and for the enthalpy of solubilization used to evaluate diffusivity and solubility at 40 °C are 11 and )3.1 kcal/mol respectively (Michaels, Vieth, & Barrie, 1963a,b). The data obtained for DPET and SOPET are 8:8 109 cm2 /s and 0.078 O2 2 3 3 cm (STP)/cm atm respectively. The oxygen transport parameters for the oxygen/oil and oxygen/PET systems used in the present investigation to run the simulations are listed in Table 3. Fig. 1. Axial section of the bottle.
3. Results and discussions interval whose upper limit is the oxygen solubility in nhepthane (0.4 cm3 (STP)/cm3 atm) and the lower limit is oxygen solubility in polyethylene (0.08 cm3 (STP)/ cm3 atm) (Michaels & Bixler, 1961). Taking into account that the average molecular weight of virgin olive oil is closer to that of n-hepthane than to that of polyethylene, SOOil2 was set at 0.15 cm3 (STP)/cm3 atm. The values of DOil O2 were determined through the following expression (Schumpe & L€ uhring, 1990): D ¼ ð2:6 10
11
2=3
Þl
ð1Þ
During the storage of bottled virgin olive oil hydroperoxides are formed through the oxidation of Table 3 Transport parameters of the oil/oxygen and PET/oxygen systems SOOil2 (cm3 (STP)/cm3 atm)
0.15
2 DOil O2 (cm /s)
2:72 106
SOPET (cm3 (STP)/cm3 atm) 2
0.078
2 DPET Eff (cm /s)
8:8 109
Table 1 Dimensions of the investigated bottles Bottle A B C D E
Volume (cm3 ) 1000 480 251 1000 1000
SBottle =VOil (cm1 ) 1
6:1 10 7:9 101 9:8 101 6:2 101 6:3 101
VHS =VOil 2
1:8 10 2:5 102 2:8 102 3:3 102 4:6 102
Oil nHS O2 =nO2
rc (cm)
rb (cm)
hc (cm)
ho (cm)
hb (cm)
0.11 0.14 0.16 0.20 0.27
1.4 1.2 1.0 1.4 1.4
4.4 3.4 2.8 4.4 4.4
16.2 13.0 10.0 16.2 16.2
18.6 14.8 11.6 18.6 18.6
21.6 17.4 13.8 24.0 26.0
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unsaturated fatty acids and consumed by hydroperoxide breakdown reactions. In the first stage of oxidation, when the oxygen concentration is close to saturation, the rate at which hydroperoxides are consumed is lower than the rate at which they are produced through the autooxidation of unsaturated fatty acids, leading to an increase in hydroperoxide concentration during storage. As the lipid oxidation reaction proceeds, oxygen is consumed to form hydroperoxides. This causes: (a) the formation of an oxygen concentration gradient in the bottled oil, which in turn brings about the permeation of external oxygen through the wall of the plastic container; (b) an increase in the rate at which hydroperoxides break down. As a result of the above phenomena, concentrations of both local oxygen and hydroperoxides decrease. Given the above scenario during oil storage, to properly describe the oxidation kinetics of bottled virgin olive oil a mathematical model was developed to predict the time course of oxygen and hydroperoxide concentrations in bottled oil during storage. 3.1. Two-dimensional mathematical model The mathematical model was derived by assuming that: (a) the axial section of the bottle is that showed in Fig. 1; (b) the diffusive mass flux of hydroperoxides through both the olive oil and the container wall were considered negligible. Under the above restrictions the mass balance equation of the hydroperoxides dissolved in the bottled oil have the following expression: oCROOH ¼ RF RD ot
ð2Þ
Several models have been reported in the literature to describe the rate at which hydroperoxides are formed through the oxidation of unsaturated fatty acids (Quast & Karel, 1972; Quast, Karel, & Rand, 1972); the model proposed by Quast et al. (1972) to describe lipid oxidation in potato chips was used in the present investigation. Assuming that relative humidity is constant during storage, the model proposed by Quast et al. (1972) is further simplified to the following relationship: ! pOOil2 RF ¼ ðK1 þ K2 CROOH Þ ð3Þ K3 þ K4 pOOil2 Assuming that the solubilization process of oxygen into oil is governed by HenryÕs law, pOOil2 is related to the oxygen concentration in the oil through the following relationship: pOOil2 ¼ COOil2 =SOOil2 . As reported above, hydroperoxides break down, thereby giving rise to several secondary products (Labuza, 1971). Many reactions are involved in this process, each of which is characterized by a particular mechanism and should be described with a specific
equation. For the sake of simplicity, in the present investigation we assumed that at a given temperature the overall rate at which hydroperoxides decompose depends only on their concentration (Koelsch, Downes, & Labuza, 1991). Hexanal formation via lipid oxidation as a function of oxygen concentration (Koelsch et al., 1991) was obtained through the following expression: RD ¼ K5 CROOH
ð4Þ
Substituting Eqs. (3) and (4) in Eq. (2) the following expression is obtained: ! pOOil2 oCROOH K5 CROOH ¼ ðK1 þ K2 CROOH Þ ot K3 þ K4 pOOil2 ð5Þ The mass balance of the oxygen dissolved in the bottled oil was obtained by assuming that FickÕs first law and HenryÕs law govern oxygen diffusion and solubilization processes respectively. Starting from the above hypothesis, it can be easily demonstrated that oxygen mass balance has the following expression: # " ! Oil 2 Oil oCOOil2 oC o C 1 o O O 2 2 r ¼ DOil þ O2 r or ot or oz2 ! pOOil2 ðK1 þ K2 CROOH Þ ð6Þ K3 þ K4 pOOil2 The first term on the right side of the Eq. (6) is related to the oxygen diffusive mass flux, while the second term denotes the rate of oxygen consumption by the lipid oxidation reaction. To evaluate the amount of oxygen permeating through the container wall, it is necessary to write the mass balance equation for the oxygen dissolved in the container wall, which, in the case under investigation, has the following expression (Del Nobile et al., 1997; Masi & Paul, 1982; Paul & Koros, 1976): # " ! oCOPolym oCOPolym o2 COPolym Polym 1 o 2 2 2 r ð7Þ ¼ DO2 þ r or ot or oz2 In the presence of an oxygen scavenger uniformly dispersed in the container wall, Eq. (7) became: # " ! oCOPolym oCOPolym o2 COPolym Polym 1 o 2 2 2 r ¼ DO2 ROS þ r or ot or oz2 ð8Þ In principle, ROS depends on the following: the concentration of oxygen and the oxygen scavenger in the plastic, temperature and humidity. Since there are no data reported in the literature on the relationship between ROS and the above variables, we have proposed the following equation: Polym ROS ¼ K6 COPolym COS 2
ð9Þ
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K6 depends on the temperature and humidity. The valPolym ues for K6 and for the initial value of COS , are 5 3 3 3 1:58 10 cm /cm (STP) s and 14 cm (STP)/cm3 respectively. They were obtained assuming that a film 50 lm thick containing the oxygen scavenger consumes oxygen at a rate equal to 112 cm3 (STP)/m2 day at 40 °C, and that the maximum amount of oxygen consumed is equal to 700 cm3 (STP)/m2 . Interfacial conditions were imposed to ensure chemical and physical equilibrium at the interface between oil and container. Hence, both the mass flow and the oxygen partial pressure of the juxtaposed substances were required to be equal at the oil/bottle wall interface, i.e.: ( ðJOPolym ÞInt A ¼ ðJOOil2 ÞInt A 2 ð10Þ Polym ðpO2 ÞInt A ¼ ðpOOil2 ÞInt A At the bottle headspace/oil and bottle headspace/ bottle wall interfaces the following conditions were imposed: 8 HS pO2 ¼ ðpOOil2 ÞInt B > > > > HS Polym > < pO2 ¼ ðpO2 ÞInt C HS n RT ð11Þ > pOHS2 ¼ OV2HS > > > dnHS > : O2 ¼ ðJ Polym Þ Oil O2 Int C þ ðJO2 ÞInt B dt At the bottle headspace/aluminum cap interface the following condition was imposed: ðJOCap ÞInt D ¼ 0 2
ð12Þ
Eqs. (5)–(7) (or (8) in the case of ‘‘active bottles’’), (10)–(12), form a set of differential equations, which, using the proper initial and boundary conditions, were solved simultaneously by numerical methods to predict the evolution of oxygen and hydroperoxides inside the bottled virgin olive oil during storage. The average hydroperoxide concentration was obtained by averaging CROOH over the volume of the bottled olive oil. In the following, the above model is used to assess the influence of some of the bottleÕs geometrical factors on the quality decay kinetics of virgin olive oil bottled in plastic and glass containers. The rate of hydroperoxide formation and breakdown was predicted by using the data listed in Table 2, while the data listed in Table 3 were used to describe the diffusion and solubilization processes of oxygen in olive oil and in PET. Unless otherwise specified, the oxygen partial pressure in the bottle headspace was set at 0.2 atm. 3.2. Influence of headspace and geometry of PET containers Av Fig. 2 shows the predicted CROOH plotted as a function of storage time for virgin olive oil bottled in containers A, B and C made of PET. In the above figure, two set of curves are shown: the first was obtained by
193
Fig. 2. Predicted average hydroperoxide concentration versus time: (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2; ( ) bottle B, pOHS2 ð0Þ ¼ 0:2; (––) bottle C, pOHS2 ð0Þ ¼ 0:2; (– –) bottle A, pOHS2 ð0Þ ¼ 0; (- – -) bottle B, pOHS2 ð0Þ ¼ 0; (– – –) bottle C, pOHS2 ð0Þ ¼ 0.
setting pOHS2 ð0Þ equal to 0.2, while the second was obtained by setting pOHS2 ð0Þ equal to 0. As shown in Fig. 2, in the first stage of oxidation the six quality decay kinetics are identical; as the lipid oxidation reaction proceeds the six curves diverge. In fact, right after bottling the lipid oxidation reaction rate depends primarily on the oxygen dissolved in the oil prior to bottling. As the oxidation reaction proceeds, the oxygen present in the bottle prior to bottling is consumed and subsequently replaced by the oxygen permeating through the bottle wall. Thus, the lipid oxidation reaction rate will gradually depend less on the oxygen dissolved in the oil prior to bottling, and more on the oxygen permeating through the bottle wall, and thus on the bottle geometry. As shown in Fig. 2, by reducing either the bottleÕs volumetric capacity or the oxygen partial pressure in the bottle headspace, the quality decay kinetics slow down. In fact, bottles A, B and C differ in both the values of SBottle =VOil and VHS =VOil . To separate the effects that these two parameters have on the quality decay kinetics of bottled oil, let us first consider the curves obtained by setting pOHS2 ð0Þ equal to 0. As would be expected, as the ratio SBottle =VOil decreases the quality decay kinetics of the bottled virgin olive oil slow down. In fact, the amount of oxygen permeating the bottle per unit volume of the oil decreases as the ratio SBottle =VOil decreases, thus slowing down the oil quality decay kinetics. The curves obtained by setting pOHS2 ð0Þ equal to 0.2, show a trend similar to that obtained by removing the oxygen from the bottle headspace. As shown in Fig. 2, as the ratio VHS =VOil increases, the difference between the quality decay kinetics obtained by setting pOHS2 ð0Þ equal to 0.2 and that obtained by setting pOHS2 ð0Þ equal to 0 increase. In fact, as the ratio VHS =VOil increases, the oxygen present in the bottle headspace, which can freely diffuse into the bottled oil, increases, thus accelerating the time course during storage of the hydroperoxides.
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Fig. 3. Predicted average hydroperoxide concentration versus time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
Fig. 4. Predicted pOHS2 plotted as a function of storage time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
Fig. 3 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in PET containers A, D and E. As shown in Fig. 3, the influence of the ratio VHS =VOil on the oxidation kinetics is negligible. The above result is due to the fact that the amount of oxygen present in the bottle headspace does not change markedly during the investigated period (Fig. 4).
Fig. 5. Predicted average hydroperoxide concentration plotted as a function of storage time: (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2; ( ) bottle B, HS pOHS2 ð0Þ ¼ 0:2; (––) bottle C, pHS O2 ð0Þ ¼ 0:2; (– –) bottle A, pO2 ð0Þ ¼ 0; (- – -) bottle B, pOHS2 ð0Þ ¼ 0; (– – –) bottle C, pOHS2 ð0Þ ¼ 0.
expect, in the case of the curves obtained by setting pOHS2 ð0Þ equal to zero, by decreasing the ratio VHS =VOil the quality decay kinetics accelerate. In fact, in the latter case the bottle headspace acts as a empty reservoir that removes oxygen from the bottled oil. Therefore, the higher is the ratio VHS =VOil , the higher is the amount of oxygen that diffuses from the bottled oil into the bottle headspace. As an example, in Fig. 6 the time course during storage of the oxygen partial pressure in the bottle headspace is plotted. Similar to what was reported in Fig. 3, Fig. 7 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in glass containers A, D and E. As in the case of PET bottles (Fig. 3), the influence of the ratio VHS =VOil on the oxidation kinetics is negligible. Also in this case the observed behavior is due to the fact that the amount of oxygen present in the bottle headspace does not change markedly during the investigated period (Fig. 8).
3.3. Influence of headspace and geometry of glass containers Av Fig. 5 shows the predicted CROOH plotted as a function of storage time for virgin olive oil bottled in glass containers A, B and C. Two set of curves are shown: the first was obtained by setting pOHS2 ð0Þ equal to 0.2, the
other was obtained by setting pOHS2 ð0Þ equal to 0. Also in this case by decreasing the amount of oxygen that freely diffuses from the bottle headspace into the bottled oil (i.e., by decreasing the ratio VHS =VOil ) also the quality decay kinetics slow down. Contrary to what one would
Fig. 6. Predicted pOHS2 plotted as a function of storage time: (- -- -) bottle A; ( ) bottle B; (––) bottle C.
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Fig. 7. Predicted average hydroperoxide concentration versus time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
195
Fig. 9. Predicted average hydroperoxide concentration versus time: ¼ 8:8 1010 ; (- – -) bottle B, DPolym ¼ 8:8 (– –) bottle A, DPolym O2 O2 10 10 ; (– – –) bottle C, DPolym ¼ 8:8 1010 ; (- -- -) bottle A, DPolym ¼ O2 O2 8:8 109 ; ( ) bottle B, DPolym ¼ 8:8 109 ; (––) bottle C, O2 ¼ 8:8 109 ; (- - -) bottle A, DPolym ¼ 8:8 108 ; (- -) bottle B, DPolym O2 O2 DPolym ¼ 8:8 108 ; (- -) bottle C, DPolym ¼ 8:8 108 . O2 O2
of bottle, either because the oxygen mass flux is too high or too low.
3.5. Effect of an oxygen scavenger
Fig. 8. Predicted pOHS2 plotted as a function of storage time: (––) bottle A; ( ) bottle D; (- -- -) bottle E.
3.4. Influence of the container’s properties Fig. 9 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in plastic containers A, B and C. The figure shows three set of curves that refer to virgin olive oil bottled in plastic containers made of polymers differing in the value of the oxygen diffusion coefficient. As would be expected, regardless of the type of bottle used to pack the virgin olive oil, as DPolym decreases, the O2 bottled oil quality decay kinetics slow down. Interestingly, for DPolym higher and lower than that of PET, the O2 dependence of the quality decay kinetics on the bottle type is not as marked as that found for PET bottles. The above results suggest that, at least for the investigated bottles, the amount of oxygen permeating through the bottle wall per unit volume of bottled oil strongly depends on the shape and size of the bottle only for values of DPolym close to that of PET. For DPolym much higher or O2 O2 much lower than that of PET the oxygen permeating through the bottle wall depends only slightly on the type
It has been often reported in the literature (Vermeiren, Devlieghere, van Beest, de Kruijf, & Debevere, 1999) that oxygen scavengers can be successfully used to prolong the shelf life of foods whose quality decay kinetics depend on the oxygen concentration in the package. In the present paper, the two-dimensional model is used to assess the influence of the bottle geometrical factors on the quality decay kinetics of virgin olive oil bottled in an innovative PET container, the oxygen scavenger being uniformly dispersed in the container wall. Fig. 10 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in plastic containers A, B and C. The first refers to PET bottles, the second refers to the innovative PET containers mentioned above. As expected, by dispersing the oxygen scavenger into the container wall it is possible to slow down the oxidation kinetics of the bottled oil. Unlike what was observed in the case of virgin olive oil bottled in PET containers, the larger the bottle size, the slower is the quality decay rate of the bottled oil. In fact, the oxygen scavenger slows down the oxidation kinetics in part by reducing the amount of oxygen permeating into the bottle and in part by removing the oxygen dissolved in the oil prior to bottling. In fact, by reducing the size of the bottle, and consequently by increasing the ratio SBottle =VOil and the ratio VHS =VOil , both the amount of oxygen permeating into the bottle and that removed by the scavenger from the oil increase. The results obtained suggest that the effects related to the presence of an oxygen scavenger far
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Fig. 10. Predicted average hydroperoxide concentration versus time: (- -- -) bottle A, PET; ( ) bottle B, PET; (––) bottle C, PET; (- -) bottle A, PET þ oxygen scavenger; (- – -) bottle B, PET þ oxygen scavenger; (– – –) bottle C, PET þ oxygen scavenger.
outweigh those deriving from an increase in the permeated oxygen. 3.6. Predictive ability of mono- and two-dimensional models Fig. 11 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in PET containers. The three curves reported in the above figure refer to the quality decay kinetics predicted by the mono- and twodimensional model. A diffusive mono-dimensional model can be used in place of the more accurate diffusive two-dimensional model if the following relation is satisfied: hc =rb > 10. In the specific case of bottle A, the above ratio is equal to 3.7. However, as shown in Fig. 11 the difference between the quality decay kinetics predicted by the two models is not as marked as expected. In fact, in the first stage of storage the oxidation reaction rate does not depend much on the oxygen permeating
Fig. 12. Predicted average hydroperoxide concentration versus time: (––) mono-dimensional model; ( ) bottle A, pOHS2 ð0Þ ¼ 0; (- -- -) bottle A, pOHS2 ð0Þ ¼ 0:2.
through the bottle wall, thus accounting for the results shown in Fig. 11. The differences between the quality decay kinetics predicted by the two models have to be ascribed to the fact that the two-dimensional model takes into account the axial mass flux coming from the top and the bottom of the bottle as well as the presence of the oxygen in the bottle headspace. Referring to the latter point, it is worth noting that, as expected, if pOHS2 ð0Þ is equal to 0, the quality decay kinetics predicted by the two models are closer. Fig. 12 shows the predicted average hydroperoxide concentration plotted as a function of storage time for virgin olive oil bottled in glass containers. The three curves reported in the above figure refer to the quality decay kinetics predicted by the mono- and two-dimensional model. In this case the difference between the predictions of the two models is less marked than that that observed in the case of the PET bottle. In fact, for glass bottles there is no mass flux from the bottom of the bottle as in the case of PET bottles.
4. Conclusions
Fig. 11. Predicted average hydroperoxide concentration versus time: (––) mono-dimensional model; ( ) bottle A, pOHS2 ð0Þ ¼ 0; (- -- -) bottle A, pOHS2 ¼ 0:2.
By means of the two-dimensional mathematical model presented it was possible to assess the influence of some of the bottle geometrical factor (VHS =VOil and SBottle =VOil ) on the quality decay kinetics of virgin olive oil bottled in polymer containers. The predictive ability of the mono- and two-dimensional models were also compared. In particular, it was observed that in the case of the bottle with a volumetric capacity of 1 l, the prediction of the mono-dimensional model is close to that of the more accurate two-dimensional model. This could be related to the fact that during the first stage of storage the oxidation reaction rate depends primarily on the oxygen dissolved into the oil prior to bottling.
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The results obtained in the case of PET bottles showed that when the ratio SBottle =VOil decreases, then the amount of oxygen permeating through the bottle wall decreases, thus slowing down the quality decay kinetics of the bottled oil. In the case of PET bottles with an oxygen scavenger uniformly dispersed in the bottle wall, the opposite is true. This is due to the fact that the oxygen scavenger consumes part of the oxygen dissolved in the oil prior to bottling. The ratio VHS =VOil also influences the evolution of the hydroperoxides during storage. In particular, it was observed that if pOHS2 ð0Þ is equal to 0.2 the quality decay kinetics slow down as the ratio VHS =VOil decreases. On the other hand, if pOHS2 ð0Þ is equal to 0, the quality decay kinetics slow down if VHS =VOil increases. These results suggest that, to control the oxidation kinetics during the storage of bottled oil, it may be useful to use well-designed plastic bottles, innovative plastic materials containing an oxygen scavenger and to perform the bottling operations under a nitrogen atmosphere (to reduce the oxygen pressure in the bottle headspace). These practices are often underestimated by the oil industry which defines empirically the period of shelf-life (date of recommended consumption) of bottled extra virgin olive oil, without carefully considering oil characteristics, packaging properties and the temperature conditions during product distribution. Acknowledgements The work was funded under the MURST ‘‘Piani di Potenziamento della Ricerca Scientifica e Tecnologica’’ and MURST-DIT3 Program grants. References Del Nobile, M. A., Ambrosino, M. L., Sacchi, R., & Masi, P. (in press). Design of plastic bottles for packaging of virgin olive oil. Journal of Food Science.
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