Journal of Food Engineering 85 (2008) 94–104 www.elsevier.com/locate/jfoodeng

Development of a mathematical model for simulating gas and water vapor exchanges in modified atmosphere packaging with macroscopic perforations Nutakorn Techavises *, Yoshio Hikida Laboratory of Agricultural Process Engineering, Ehime University, Tarumi 3-5-7, Matsuyama 790-8566, Japan Received 22 June 2006; received in revised form 4 July 2007; accepted 4 July 2007 Available online 2 August 2007

Abstract A mathematical model based on Fick’s law for predicting O2, CO2, N2, and water vapor exchanges in modified atmosphere packaging (MAP) films with macroperforations was developed. The effective permeability of a perforation was measured for temperatures from 5 to 25 °C, perforation diameters from 2 to 15 mm and film thicknesses of 0.012 and 0.025 mm. The temperature and film thickness had no significant effect on the effective permeability (P > 0.05). For most conditions, the effective permeability did not differ between gas types (O2, CO2, N2, and water vapor). An empirical equation of the effective permeability of a macroperforation in a thin film as a function of perforation diameter was developed. The transmission rate of LDPE film was determined for temperatures between 5 and 25 °C. The effects of temperature on gas and water vapor transmission rates followed the Arrhenius model. The use of the proposed MAP model coupled with an effective permeability model was found to yield a good prediction of gas concentration and RH when compared to experimental results for MAP of ‘Kiyomi’ fruit. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: MAP; Perforation; Model; Permeability; Transmission rate; Fresh produce

1. Introduction Modified atmosphere packaging (MAP) is well known for storing fresh fruits and vegetables because it preserves the high quality of produce by reducing produce respiration, retarding ethylene production and sensitivity, delaying softening, and decreasing the incidence of postharvest rind disorders (Brody, 1989; Kader, Zagory, & Kerbel, 1989; Porat, Weiss, Cohen, Daus, & Aharoni, 2004; Zagory & Kader, 1988). MAP with either microscopic or macroscopic perforations in the packaging film was introduced to provide additional benefits, such as a decrease in the risk of anaerobic conditions, including excessive CO2, and reduced package condensation, particularly with temperature fluctuation, whilst maintaining a high CO2 level with *

Corresponding author. Tel.: +81 89 946 9828; fax: +81 89 946 9916. E-mail address: [email protected] (N. Techavises).

0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.07.014

a low O2 level for some products (Emond, Castaigne, Toupin, & Desilets, 1991; Fonseca, Oliveira, Lino, Brecht, & Chau, 2000; Hirata, Makino, Ishikawa, Katsuura, & Hasegawa, 1996; Lee & Renault, 1998; Paul & Clarke, 2002; Renault, Souty, & Chambroy, 1994; Silva, Chau, Brecht, & Sargent, 1999). Water vapor transfer rate can be increased using a perforated film, which may result in commodity spoilage reduction (Dirim, Ozden, Bayindirli, & Esin, 2004). Several mathematical models describing O2, CO2, and N2 exchanges in MAP with perforations have been developed. Some researchers employed macroperforations (Emond et al., 1991; Fonseca et al., 2000; Paul & Clarke, 2002; Silva et al., 1999), while others used microperforations (Hirata et al., 1996; Lee & Renault, 1998; Renault et al., 1994). However, few researchers have developed a model that includes atmospheric gas and water vapor exchanges in MAP with perforations (Merts, Cleland,

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Nomenclature surface area of the bag (m2) surface area of the film package (m2) ratio of CO2 to O2 permeability perforation diameter (mm) effective permeability of one perforation to gas i (106 m3/h kPa) Ki transmission rate of film to gas i (106 m3/ m2h kPa) Kfi permeability coefficient of film (106 m3 m/ m2h kPa) lf film thickness (m) M mass of produce (kg) np number of perforations Pi partial pressure of gas i outside the package (kPa) P in partial pressure of gas i inside the package (kPa) i PT total pressure inside the package (kPa), equal to 101.325 kPa P SAT ðT Þ saturation water vapor pressure at a given C H2 O temperature (kPa) RO 2 O2 consumption rate (106 kg/kg h) Ab Af b d Di

Banks, & Cleland, 2003). The water vapor exchange in the MAP system, which affects relative humidity (RH), is vital because RH plays an important role in the physiological responses influencing produce quality. For instance, a high RH helps reduce the rind breakdown of many varieties of citrus fruits (Porat et al., 2004). However, the maintenance of a very high RH can encourage moisture condensation on the commodity, creating conditions favorable for microbial growth. Alternatively, a low RH increases transpirational damage and leads to a high water loss and desiccation (Wills, McGlasson, Graham, & Joyce, 1998; Zagory & Kader, 1988). Some models have been developed for predicting the gas permeability of macroperforations for large film thicknesses (Emond et al., 1991; Fonseca et al., 2000; Silva et al., 1999). In this paper, ‘‘film thickness” means the diffusive path length of the perforation. Macroperforations in permeable polymeric films are used for packing various types of commodities. We found no published permeability model or data for the small film thicknesses used commercially with macroperforation. Gas permeability through perforation in thin films may differ significantly from that in thick films. This research aims to develop a mathematical model for simulating O2, CO2, N2, and water vapor exchanges in MAP with macroscopic perforations. To achieve this purpose, it was necessary to (1) determine the gas permeability of perforations (designated as effective permeability) (2) determine the gas permeability of polymeric film (designated as transmission rate), and (3) validate the proposed

CO2 evolution rate (106 kg/kg h) relative humidity (%) time (h) temperature in Celsius (°C) temperature in Kelvin (K) transpiration coefficient (106 kg/kg h kPa) transpiration rate (106 kg/kg h) test period duration (h) volume of an acrylic cylindrical box (106 m3) volume of gas i inside the package at time t (106 m3) VPD water vapor partial pressure difference between the fruit and the surrounding atmosphere (kPa) Dwb weight change of the bag (106 kg) Dwfl weight change of the flask (106 kg) in y i;0 concentration of gas i inside the box at t = 0 (%) y in concentration of gas i inside the box at t = t (%) i;t y out concentration of gas i outside the box (%) i;e di specific volume of gas i (106 m3/106 kg) (The subscript i is substituted with O, C, N, and H, to denote O2, CO2, N2, and water vapor, respectively.)

RCO2 RH t TC TK T0 T H2 O Dt Vb Vi(t)

model. An additional objective was to develop a simple, but precise, model for predicting the effective permeability of macroperforations in thin films when perforation dimensions and temperature are known. 2. Mathematical model for MAP with perforations The following key assumptions were made in developing the model: (1) the composition of the gas within the package and in the atmosphere outside the package is uniformly distributed; (2) polymeric film transmission rates are uniform and dependent on temperature only; (3) the molecular mass transfer through perforations is due to diffusion only; (4) gas exchange through one perforation is unaffected by the presence of other perforations; and (5) the total pressure inside the package is equal to the atmospheric pressure. Gas and water vapor exchanges through polymeric films follow Fick’s first law of diffusion (Dirim et al., 2004; Emond et al., 1991; Talasila & Cameron, 1997). Thus, the change in the volume of gas i inside a package is expressed as dV i ðtÞ Af K fi ¼ ðP i  P in i Þ dt lf Af K fi lf

ð1Þ

is designated as the overall mass transfer coefficient. Gas exchange through macroscopic perforations also follows Fick’s law (Emond et al., 1991; Paul & Clarke, 2002). It is suggested that water vapor exchange through macroperforations also follows Fick’s law. If so, the

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atmospheric gas and water vapor exchanges through macroperforations can be described by substituting the overall mass transfer coefficient of the film in Eq. (1) with the effective permeability of a perforation, Di: dV i ðtÞ ¼ Di ðP i  P in i Þ dt

ð2Þ

In the case of np perforations: dV i ðtÞ ¼ np Di ðP i  P in i Þ dt

ð3Þ

Gas and water vapor exchanges in a permeable package with perforations used to store fresh produce depend on the combination of the rates of respiration and transpiration by the produce and on the permeation of the permeable film and perforations to gas and water vapor. The differential equations for the volumetric changes of O2, CO2, N2, and water vapor inside a perforated MAP of respiring produce are   dV O ðtÞ V O ðtÞ ¼ ðnp DO þ Af K O Þ P O  P T dt V O ðtÞ þ V C ðtÞ þ V N ðtÞ þ V H ðtÞ

ð4Þ  dO MRO2   dV C ðtÞ V C ðtÞ ¼ ðnp DC þ Af K C Þ P C  P T dt V O ðtÞ þ V C ðtÞ þ V N ðtÞ þ V H ðtÞ ð5Þ þ dC MRCO2   dV N ðtÞ V N ðtÞ ¼ ðnp DN þ Af K N Þ P N  P T dt V O ðtÞ þ V C ðtÞ þ V N ðtÞ þ V H ðtÞ ð6Þ

  dV H ðtÞ V H ðtÞ ¼ ðnp DH þ Af K H Þ P H  P T dt V O ðtÞ þ V C ðtÞ þ V N ðtÞ þ V H ðtÞ þ dH MT H2 O

ð7Þ

where K i ¼ Klffi is known as the film transmission rate. The mole fraction of gas i inside a package is calculated as the volumetric fraction of gas i. The differential equations (4)–(7) were solved numerically using the fourth-order Runge–Kutta method with a step-size control algorithm (Chen & Yamamoto, 2002). The solution was programmed in Microsoft Quick BASIC Version 4.5 (Microsoft Corporation). The computer program computed O2, CO2, and N2 concentrations based on volumetric ratio, and RH based on the ratio of the partial pressure of water vapor to saturation water vapor pressure at the same temperature inside the package at any time. The model is also capable of estimating how long it would take to achieve steady-state point and the cumulative weight loss calculated from produce transpiration rate.

15 mm) using a 0.012 mm thick film. A set of three replicate experimental runs was conducted for each combination of temperature and perforation diameter. Further, three replicate experiments were conducted using a 0.025 mm thick film at 5 °C with a 5 mm diameter perforation to investigate the effect of film thickness on the effective permeability. For each trial, a sheet of gas-impermeable aluminum foil, at the center of which a perforation was made, was attached tightly on the open side of a gas-tight acrylic cylindrical box with three spring catches (1.991  103 m3) (Fig. 1). The box was placed in a controlled-temperature incubator and monitored by two thermocouples. A mixed gas of CO2 and N2 was first introduced through the left valve to mix with the ambient air inside the box while the right valve was open and the perforation was closed using masking tape. When the desired gas mixture containing 12% O2, 21% CO2, and 67% N2 inside the box was reached, both valves were closed and the tape was removed. The changes in gas concentration with time were determined by taking gas samples from inside the box through a silicon septum to analyze with a gas chromatograph (GC). The concentration of water vapor in the atmosphere was considered sufficiently low compared to O2, CO2, and N2 levels that it could be ignored in the analysis. By integrating Eq. (2), the change in concentration of gas i with time is given by ! out y in P Tt i;0  y i;e ln in ð8Þ ¼ Di out Vb y i;t  y i;e where i refers to O2, CO2, or N2 gases. The composition of the gas outside the box was normal atmospheric gas composition at 101.325 kPa. Effective permeability was out estimated from the slope of lnðy in i;t  y i;e Þ versus t as the plot was linear. An example comparing the measured and predicted changes in gas concentration inside the box with time (predicted using the estimated effective permeability and Eq. (2)) is given in Fig. 2. The agreement is good suggesting that the Di values were accurate. 3.1.2. Water vapor The effective permeability of a perforation to water vapor was measured for different temperatures (5, 15,

3. Materials and methods 3.1. Effective permeability through a perforation 3.1.1. O2, CO2, and N2 The effective permeability through a perforation was experimentally determined for different temperatures (5, 15, and 25 °C) and perforation diameters (2, 5, 10, and

Fig. 1. Schematic diagram of equipment for measuring effective permeability of a perforation for O2, CO2, and N2.

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that saturation water vapor pressure prevailed inside the flask. RH was the measured relative humidity of the air inside the chamber.

80

25

78 20 76

72 10

70 68

5 66 0 0

30

60

90

120

150 180 Time (min)

210

240

270

64 300

Fig. 2. Example of changes in gas concentration inside box with time under conditions of 5 °C and 15 mm diameter perforation (M, O2; h, CO2; s, N2; the line shows the predicted concentration calculated using an estimated effective permeability).

and 25 °C) and perforation diameters (2 and 5 mm) using 0.012 mm thick aluminum foil. The experimental apparatus used for O2, CO2, and N2 could not provide a sufficiently large water vapor concentration gradient. Therefore, the standard gravimetric method was employed (ASTM, 1993). Three glass Erlenmeyer flasks with a mouth area of 5.73 cm2 were filled with distilled water. The mouth of each flask was covered tightly with the perforated aluminum foil as above. The flasks were placed in a chamber with controlled temperature and RH and monitored by a temperature and humidity measurement system (model TRH-7X, Shinyei, Japan). A saturated LiCl solution was used to maintain a constant low RH of the air inside the chamber. The flasks were weighed daily until at least 3 days after steady state was reached. The effective permeability to water vapor was calculated using the following equation which is a variation on Eq. (2): ! Dwfl dH 1   DH ¼ ð9Þ RH Dt P SAT H2 O ðT C Þ 1  100 The weight change with time, (Dwfl/Dt) was calculated as the slope of the flask weight against time in the steady-state region. An example plot is shown in Fig. 3. It was assumed

3.2.1. O2, CO2, and N2 The transmission rates of LDPE films (0.019 mm thick) for O2, CO2, and N2 were determined at 5, 15, and 25 °C. The film, which has been commercially utilized for a variety of fruits and vegetables, was provided by the Japan Agricultural Cooperatives of Ehime, Japan. The method for determining film transmission rate was that proposed by Ishikawa, Hirata, and Hasegawa (1997) with slight modifications. Pure CO2 of known volume was initially introduced into a LDPE film package (size 18 cm  18 cm). The package was suspended in a gasimpermeable acrylic cylindrical box (2.209  103 m3) and stored in a controlled-temperature incubator monitored by two thermocouples. The initial gas composition inside the box was atmospheric. During the experiment, CO2 permeated out of the package (into the box), whereas O2 and N2 permeated into the package. Gas concentration inside the box was periodically measured by GC analysis of a sample. The transmission rates were estimated by choosing values that minimized the sum of the squares of the differences between the measured data and predictions simultaneously for all the gas species. The partial pressure of each gas inside the box can be calculated on the basic of the volumetric changes of the gases inside the box and film package. An example of the fit of the predicted partial pressure to the measured data is shown in Fig. 4. Good agreement was observed, suggesting that the gas transmission rates were accurate. 3.2.2. Water vapor The transmission rate of water vapor through the LDPE film was measured at 5, 15, and 25 °C using the whole-bag (water) method developed by Moyls (1998). For each temperature, two LDPE bags (size 20 cm  14 cm) containing 50 g of distilled water and some sheets of paper towel were sealed and suspended in a desiccator under controlled 0.25

332.00 331.98 331.96

-3

2

R = 1.00

331.94 331.92 331.90 331.88 331.86

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

2

w fl = -2.14×10 t + 3.32×10

O2 and CO2 partial pressure (atm)

Flask weight (g)

3.2. Transmission rate through polymeric film

331.84 331.82 331.80

0.20 0.15 0.10 0.05 0.00

0

24

48

72

Time (h)

Fig. 3. Typical example of change in flask weight (containing distilled water) against time at 15 °C with a 2 mm diameter perforation (}, flask weight; the line represents the curve fit).

N2 partial pressure (atm)

74

15

N2 concentration (%)

O 2 or CO2 concentration (%)

97

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time (h)

Fig. 4. Typical example of fit of predicted partial pressure of gases inside box to measured data at 5 °C (M, O2; h, CO2; s, N2; the line shows the predicted value).

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temperature and RH via a saturated LiCl solution. The paper towel, which covered the entire inside surface area of the film bag, ensured a uniform RH of 100% inside the bag throughout the experimental period. The bags were periodically weighed until 2 weeks after steady state was reached. The transmission rate of the film to water vapor was calculated using ! Dwb dH 1   KH ¼ ð10Þ RH Ab Dt P SAT H2 O ðT C Þ 1  100 The weight change with time, (Dwb/Dt) was calculated as the slope of the plot of weight change with time in the steady-state region. RH was the measured relative humidity of the air inside the desiccator. 3.3. Validation of the proposed model To validate the model, a series of experiments summarized in Table 1 was conducted. A 28.3 cm  28.3 cm LDPE film package was used in all treatments. For MAP without produce (with or without perforations), the package was sealed and then flushed with a gas mixture of 12% O2, 20% CO2, and 68% N2 as the initial gas composition. The initial composition was normal atmospheric gas composition for MAP with produce (with or without perforations). The package was stored in a controlled-temperature incubator. For all trials, gas samples inside the package were periodically taken and analyzed with GC. The measured and predicted concentrations of the gases inside the package (O2, CO2, and N2) were then compared. Additionally, another experiment was conducted to measure gas concentration and RH in MAP without produce at 5 and 15 °C using one 5 mm diameter perforation. The perforated package was sealed and flushed with a humidified gas mixture (the mixed gas was bubbled through water). This package was stored in a controlledtemperature and RH chamber, where the RH of the air inside the chamber was controlled by a saturated LiCl solution. The temperature and RH inside and outside the package were monitored by a temperature and humidity measurement system (model TRH-7X, Shinyei, Japan). The gas composition inside the package was periodically

analyzed with GC. Consequently, the measured gas concentration and RH were compared with those predicted using the proposed model. The produce used was ‘Kiyomi’ Tangor (Citrus unshiu Marc.  C. sinensis Osb.). It is recognized as a high quality late-season citrus fruit. The fruit rind is orange-yellow and the flesh is orange, sweet, and delicious. The fruit is large (6.1–9.5 cm in diameter). The optimum atmospheric composition for ‘Kiyomi’ Tangor is probably in the range of 5–10% O2 and 0–5% CO2, similar to recommended conditions for most oranges and mandarins (http://postharvest.ucdavis.edu/). ‘Kiyomi’ fruit, size L (medium size, 7.3–8.0 cm in diameter), harvested during the period of March–April 2005, the normal commercial harvesting period, from Misaki, Ehime, Japan were transported to our laboratory and stored in LDPE film packages at 5 °C until use in the MAP with produce experiments. The respiration of the produce is greatly affected by temperature and this relation can often be described by the Arrhenius equation (Mannapperuma, Zagory, Singh, & Kader, 1989). The respiration of ‘Kiyomi’ fruit was measured using the closed system method. ‘Kiyomi’ fruit were placed in separate closed 7.8 l boxes and then stored in a controlled-temperature incubator (5, 10 or 20 °C). Two gas samples from inside the closed boxes were taken at a predetermined time, when the O2 and CO2 concentrations had changed by about 1% from their normal atmospheric concentrations, and analyzed with GC. By mass balance, the respiration rate at each temperature was calculated. The dependency of respiration rate on temperature and Arrhenius fits are shown in Fig. 5, providing the following equations:   1:061  104 17 RO2 ¼ 1:304  10 exp ð11Þ TK   1:029  104 RCO2 ¼ 5:440  1016 exp ð12Þ TK It should be noted that respiration rate is also affected by O2 and CO2 concentrations. In particular, low O2 and/or high CO2 generally decrease respiration rate. To get more precise model prediction, the respiration model as the function of temperature, O2 and CO2 concentrations should be developed. However, this is beyond the scope of the paper.

Table 1 Experimental conditions for validating proposed model (O2, CO2, and N2 exchanges were simulated) Experimental condition MAP without produce Without perforation With perforation

MAP with produce Without perforation With perforation a

Number of ‘Kiyomi’ fruit

Temperature (°C)

Perforation dimensions (number and diameter of perforation)

No No No No

5, 15, and 25 5a, 15, and 25 5 5

No One perforation of 5 mm diameter One perforation of 2, 5a, and 10 mm diameter 1a, 2, and 3 perforations of 5 mm diameter

6, 8, and 10 8

5 and 15 5 and 15

No One perforation of 2 and 5 mm diameter

All are the same experiment using one perforation of 5 mm diameter at 5 °C.

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3.4. Gas concentration analysis

5

ln (Respiration)

-6

Respiration rate (10 kg/kgh)

35 30 25 20

4 3

A 0.5 ml gas sample was taken using a 1 ml air-tight syringe via an equipped silicone septum in all the experiments and analyzed with a gas chromatograph (model GC-8A, Shimadzu, Japan) with a thermal conductivity detector for determining O2, CO2, N2, and CH4 gas concentrations. Helium gas at 1 kg/cm2 was used as the carrier gas. The temperatures of the injector, column and detector were 80 °C, 50 °C, and 80 °C, respectively.

2 1 0 0.0034 0.0035

15

0.0036 0.0037

1/ T K

10 5 0

0

5

10

15

20

Temperature (ºC)

Fig. 5. Effect of temperature on respiration rate of ‘Kiyomi’ fruit. Inset: Arrhenius plot of respiration (M, O2 consumption rate; h, CO2 evolution rate).

Talasila and Cameron (1997) reported that transpiration rate may be expressed in terms of a transpiration coefficient (T0) and the water vapor partial pressure difference between the fruit and the surrounding atmosphere (VPD) as T H2 O ¼ T 0 ðVPDÞ

ð13Þ

The transpiration rate of ‘Kiyomi’ fruit was estimated by measuring the rate of weight change when fruit was exposed to different VPDs in still air (the RH in the surrounding air was varied using various saturated salt solutions). Chau, Romero, Baird, and Gaffney (1988) reported that liquid in fruit contains solutes that lower the water activity (ratio of the actual partial pressure of water to the water vapor pressure). The water activity of the fruit was assumed to be 0.98 (Chau et al., 1988). The model described by Eq. (13) was fitted to the experimental data as shown in Fig. 6. The fitted value of T0 was 224.1  106 kg/ kg h kPa. The VPD was calculated using VPD ¼ 0:98P SAT H2 O ðT C Þ 

RH SAT P ðT C Þ 100 H2 O

ð14Þ

-6

Transpiration rate (10 kg/kgh)

For model predictions, the initial free volume of the film package was determined indirectly by dilution of a known quantity and concentration of a gas injected into the bag (Hagger, Lee, & Yam, 1992; Talasila & Cameron, 1997). Methane gas (CH4) was used due to its biological inactivity and detectability at low concentrations by GC (Talasila & Cameron, 1997). 300 250

99

T H 2 O = 224.1VPD

3.5. Statistical analysis All experiments were arranged as a factorial design or organized in a completely randomized design (CRD). All data were analyzed by factorial analysis or one-way analysis of variance (ANOVA), accordingly. The significance of differences between means was determined by the Tukey HSD test at P < 0.05. SPSS software for Windows version 11.5 (SPSS Inc., IL, USA) was used for all data analysis. 4. Results and discussion 4.1. Effective permeability through a perforation Table 2 summarizes the measured effective permeability through a perforation in a 0.012 mm thick film. As expected, an increase in perforation diameter significantly increased effective permeability (P < 0.05). For a range of film thicknesses, a similar result was reported by Emond et al. (1991), Fonseca et al. (2000), and Silva et al. (1999). If one considers the gas diffusion through still air of thickness equal to the film thickness (lf), the calculated effective permeability ranges from 1.68  104 to 94.2  104m3/ h kPa for perforation diameter from 2 to 15 mm, respectively, when assuming a mass diffusivity of 0.18  104 m2/s. The measured effective permeability is much smaller than the calculated value (77–628 times smaller) suggesting both that flow/convective effects through the Table 2 Effects of perforation diameter and temperature on effective permeability of a perforation to O2, CO2, and N2 gas using 0.012 mm thick film Effective permeability (106 m3/h kPa)a

2

200

R = 0.88

O2 Perforation diameter (mm) 2 1.89 a 5 4.21 b 10 8.68 c 15 15.17 d

150 100 50

CO2 2.04 4.23 9.14 15.62

N2 a b c d

2.14 4.32 9.69 15.99

a b c d

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Vapor pressure deficit (VPD ) (kPa)

Fig. 6. Fitting of transpiration model (Eq. (13)) to experimental data at different water vapor partial pressures of surrounding air (, average transpiration rate of two separate experiments, each containing 10 fruit per treatment; the line represents the curve fit).

Temperature (°C) 5 7.88 a 15 7.26 a 25 7.33 a

7.92 a 7.68 a 7.66 a

7.94 a 8.14 a 8.03 a

a Column means followed by different letters are significantly different at P < 0.05.

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perforation are low, and that end effects (entrance and exit effects) are significant. The effective permeability of the perforation did not vary linearly with perforation area which further suggests that end effects are important. The mass diffusion through the perforation can be considered as a series of three diffusions: (1) from the outside atmosphere to the perforation; (2) across the thickness; and (3) from the perforation to the inside of package (or vice versa). The series resistances of these three regions to mass diffusion can be treated by assigning an effective thickness (leff) that is greater than the actual film thickness (lf) (Nobel, 1983; Paul & Clarke, 2002). The effective thickness is taken as the sum of actual film thickness and end correction, which varies with the boundary conditions around the perforation and perforation geometry (Lee & Renault, 1998; Nobel, 1983; Renault et al., 1994). Paul and Clarke (2002) theoretically derived the overall mass transfer coefficient (H) which corresponds to our effective permeability (Di). Based on this theory, the effective thickness equals lf + (7/6)d when considering the series resistances of three zones. Our measured effective permeabilities were approximately 2.2-fold greater than the theoretical H values when assuming a mass diffusivity of 0.18  104 m2/s as proposed by Paul and Clarke (2002). The permeabilities measured by Emond et al. (1991), Fonseca et al. (2000) and Silva et al. (1999), were approximately 2.5-, 1.9-, and 1.8-fold greater than the theoretical H values, respectively. Therefore, the effective thickness proposed by Paul and Clarke (2002) was considered too large. Our measured effective permeabilities were very similar to the theoretical H values when the effective thickness was lf + 0.5d. The effective permeability (Di), which accounts for the effective thickness and area of the perfora-

Table 3 Effects of film thickness on effective permeability at 5 °C using one 5 mm diameter perforation Thickness (mm)

0.012 0.025

Effective permeability (106 m3/h kPa)a O2

CO2

N2

4.25 a 4.24 a

4.12 a 4.33 a

4.10 a 4.43 a

a Data are means of three separate experiments. Column means followed by different letters are significantly different at P < 0.05.

tion, is useful for describing the diffusive mass transfer through the macroscopic perforation in thin films. Table 3 shows that there is no significant difference between the effective permeabilities to gases for the film thicknesses used (0.012 and 0.025 mm) (P > 0.05). As previously described, the effective thickness for our effective permeabilities was about lf + 0.5d. In the case of macroperforations in thin films, the ratio of perforation diameter to film thickness is extremely large; therefore effective permeability will not be extremely sensitive to changes in the film thickness, again showing that end effects play an important role in gas exchange. A slight decrease in effective permeability due to an increase in film thickness was probably less than the variability of the experimental data. Therefore, film thickness does not seem to be a dominant factor on effective permeability of macroperforations in thin films. On the other hand, Emond et al. (1991), Fonseca et al. (2000), and Silva et al. (1999) using large film thickness ranges of 1.59–12.7 mm of a plexiglass cover, 6–30 mm of an inserted tube, and 5–40 mm of a fitted tube, respectively, reported that the increase in film thickness decreases the effective permeabilities to O2 and CO2. However, these thicknesses were not as small as the film thicknesses used commercially. Temperature had no significant effects on the effective permeabilities in that range tested (Table 2). Fonseca et al. (2000) and Silva et al. (1999) reported similar results; however, Emond et al. (1991) reported a positive effect of temperature. The diffusivity of gas in air increases by only 10% when temperature increases from 5 to 25 °C (Ozisik, 1985) so only a small effect that is probably smaller than the variability of the experimental data would be expected. To investigate the dependence of the effective permeability on gas type, the data obtained under the same experimental conditions (temperature and perforation dimensions) were statistically compared (Table 4). For most conditions, there is no significant difference in effective permeabilities between gas types (O2, CO2, N2, and water vapor). The average ratio of CO2 to O2 permeability, b ratio, was 1.04. This ratio did not depend on any factor tested. Emond et al. (1991) and Fonseca et al. (2000) reported average b ratios of 1.0 and 0.81, respectively, which was close to our b ratio. Paul and Clarke (2002) also reported that perforations serve the function of non-selective permeation of gases. In general, the b ratio for

Table 4 Dependences of effective permeability on gas type under various experimental conditions using 0.012 mm thick film Type of gas

Effective permeability (106 m3/h kPa)a 5 °C

O2 CO2 N2 H2O a

15 °C

25 °C

2 mm diameter

5 mm diameter

2 mm diameter

5 mm diameter

2 mm diameter

5 mm diameter

1.93 1.97 2.02 1.94

4.25 4.12 4.10 4.02

1.94 2.30 2.48 1.96

4.15 4.20 4.30 4.25

1.80 1.86 1.92 2.01

4.24 4.36 4.55 4.38

a a a a

a a a a

a b b a

a a a a

a a a a

Data are means of three separate experiments. Column means followed by different letters are significantly different at P < 0.05.

a a a a

N. Techavises, Y. Hikida / Journal of Food Engineering 85 (2008) 94–104

polymeric films used for packing agricultural products is usually in the range of 3–6 (Hanlon, Kelsey, & Forcinio, 1998). Perforations in polymeric films can change the ratio of gas transport, generally reducing b ratio, thereby making it possible to adjust gas composition. From the aforementioned results, perforation diameter showed a marked effect on effective permeability (Fig. 7). All experimental data were empirically fitted, leading to the development of the following model of effective permeability as a function of perforation diameter (R2 = 0.97):

20 -2

2

-1

-1

D i = 2.98×10 d + 5.37×10 d + 8.22×10

16

2

R = 0.97

14

(10-6m3/hkPa)

Effective permeability (Di )

18

12 10 8 6 4 2 0 0

1

2

3

4

101

5 6 7 8 9 10 11 12 13 14 15 16 Perforation diameter (d ) (mm)

Fig. 7. Effect of perforation diameter on effective permeability under overall experimental conditions in a temperature range of 5–25 °C and a film thickness range of 0.012–0.025 mm (M, O2; h, CO2; s, N2; }, water vapor; the line represents the average curve for the model development).

Di ¼ 2:98  102 d 2 þ 5:37  101 d þ 8:22  101

ð15Þ

This equation can be applied for atmospheric gases and water in a temperature range of 5–25 °C, and film thicknesses of less than 0.025 mm (1 mil). 4.2. Transmission rate through polymeric film

Table 5 Transmission rates of 0.019 mm thick LDPE film to atmospheric gases and water vapor and b ratios at different temperatures Temperature (°C)

Transmission rate (106 m3/m2h kPa) O2

CO2

N2

H2O

5 15 25

2.71 4.49 5.87

7.92 14.92 21.82

1.64 3.03 4.89

49.76 83.24 122.03

b ratio

2.92 3.32 3.71

6 3

2

R = 0.99

4 3

1

y = -4.21×10 x + 1.72×10 2

4.3. Validation of the proposed model

3

1

y = -3.22×10 x + 1.26×10 2

1

R = 0.98 3

1

y = -4.55×10 x + 1.69×10 2

0 0.0033

R = 1.00 0.0034

0.0035 Inverse temperature (K-1)

0.0036

0.0037

Fig. 8. Arrhenius plot of transmission rates of LDPE films to atmospheric gases and water vapor (M, O2; h, CO2; s, N2; }, water vapor).

MAP without produce and perforations at 5ºC

MAP without produce and perforations at 15ºC

82

25

For MAP without produce, the model was found to yield good predictions of the gas concentration changes inside the package at different temperatures (Fig. 9), perforation diameters (Fig. 10), and the number of perforations (Fig. 11). Gas concentration reached equilibrium faster at higher temperatures than at lower temperatures owing to the dependence of the film gas transmission rate on the temperature (Fig. 9). At the same temperature, the use of

76

15

74 10

72 70

5

O2 or CO2 concentration (%)

O2 or CO2 concentration (%)

78

N2 concentration (%)

80 20

20

78 15

76

10

74 72

5

70

66 0 2 4 6 8 10 12 14 16 18 20 22 24 Time (h)

0

68 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Time (h)

82 80

80

68 0

MAP without produce and perforations at 25ºC

25

82

25

20

O2 or CO 2 concentration (%)

2

78 76

15

74 10

72 70

5

N2 concentration (%)

R = 0.99

3

N2 concentration (%)

ln (Transmission rate)

1

y = -3.72×10 x + 1.73×10

5

All the transmission rates of the LDPE film to atmospheric gases and water vapor are shown in Table 5. The effect of temperature on the transmission rates of O2, CO2, N2, and water vapor was accurately fitted by the Arrhenius equation as shown in Fig. 8 (R2 of 0.98– 1.00). Activation energies of permeation for the LDPE film were 26.8, 35.0, 37.8, and 31.0 kJ/mol for O2, CO2, N2, and water vapor, respectively. A similar result was reported by Beaudry, Cameron, Shirazi, and DostalLange (1992) and Hasbullah, Gardjito, Syarief, and Akinaga (2000). Therefore, the transmission rate data were considered sufficiently reliable for use in the proposed MAP model.

68 0

66 0

1

2

3

4 5 6 Time (h)

7

8

9 10

Fig. 9. Changes in gas concentrations inside LDPE film packages without produce and perforations at different temperatures (M, O2; h, CO2; s, N2; the line represents the predicted value).

N. Techavises, Y. Hikida / Journal of Food Engineering 85 (2008) 94–104 MAP without produce, 1 perforation of 5 mm at 5ºC

82

25

15

74 10

72 70

5

20

78 76

15

74 10

72 70

5

68 0

82 80

O2 or CO2 concentration (%)

76

O2 or CO2 concentration (%)

78

25

80 N2 concentration (%)

O2 or CO2 concentration (%)

80 20

MAP without produce, 1 perforation of 10 mm at 5ºC

82

20

78 76

15

74 10

72 70

5

68

66

0

0 1 2 3 4 5 6 7 8 9 10 11 12 Time (h)

68

66 0.0

1.0

2.0

3.0 4.0 Time (h)

5.0

N2 concentration (%)

MAP without produce, 1 perforation of 2 mm at 5ºC

25

N2 concentration (%)

102

0

6.0

66 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (h)

Fig. 10. Changes in gas concentrations inside LDPE film packages without produce, but with a perforation of different perforation diameters at 5 °C (M, O2; h, CO2; s, N2; the line represents the predicted value).

25

72 70

5

76

15

74 10

72 70

5 68

0 0.0

1.0

2.0

3.0 4.0 Time (h)

5.0

66 6.0

80 O2 or CO2 concentration (%)

74 10

78

N2 concentration (%)

15

20 O2 or CO2 concentration (%)

76

82

80 N2 concentration (%)

O2 or CO2 concentration (%)

78

25

82

80 20

MAP without produce, 3 perforations of 5 mm at 5ºC

MAP without produce, 2 perforations of 5 mm at 5ºC

82

20

78 76

15

74 10

72 70

5

68

68 0

66 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time (h)

N2 concentration (%)

MAP without produce, 1 perforation of 5 mm at 5ºC

25

0

66 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Time (h)

Fig. 11. Changes in gas concentrations inside LDPE film packages without produce, but with different numbers of 5 mm diameter perforations at 5 °C (M, O2; h, CO2; s, N2; the line represents the predicted value).

a higher total area of perforations (higher perforation diameter or the number of perforations) needed less time to reach equilibrium than that with lower total area of perforations (Figs. 10 and 11). The good agreement for varying number of perforations confirmed that the assumption that gas exchange through one perforation is unaffected by the presence of other perforations was reasonable. The model also gave good prediction of the relative humidity change inside the package (Fig. 12). For the MAP storage of ‘Kiyomi’ Tangor fruit without and with perforation, reasonable agreement between the

measured and predicted gas concentrations was achieved (Figs. 13 and 14). A higher produce weight gave a lower O2 concentration and a higher CO2 concentration (Fig. 13). The introduction of a small perforation in the film package markedly changed the package atmospheres because of the high relative magnitude of the permeability of the perforation than the LDPE film. For instance, in the case of 8 ‘Kiyomi’ fruit stored in MAP at 5 °C, the steadystate O2 and CO2 concentrations were 13.2% and 2.8% for no perforations (Fig. 13) and 20.2% and 0.7% for one 5 mm diameter perforation (Fig. 14).

MAP without produce, 1 perforation of 5 mm at 15ºC

RH (%)

RH (%)

MAP without produce, 1 perforation of 5 mm at 5ºC

100 90 80 70 60 50 40 30 20 10 0 0.0

1.0

2.0

3.0 4.0 5.0 Time (h)

6.0

7.0

8.0

100 90 80 70 60 50 40 30 20 10 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time (h)

Fig. 12. Changes in relative humidity inside LDPE film packages without produce, but with one 5 mm diameter perforation at 5 and 15 °C (}, relative humidity; the line represents the predicted value).

5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (day)

MAP with 10 'Kiyomi' fruit, no perforations at 5ºC

25

90 88 86 84 82 80 78 76 74 72 70

20 15 10 5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (day)

90 88 86 84 82 80 78 76 74 72 70

20 O2 or CO2 concentration (%)

10

MAP with 8 'Kiyomi' fruit, no perforations at 5ºC

25

N2 concentration (%)

15

O2 or CO2 concentration (%)

O2 or CO2 concentration (%)

20

90 88 86 84 82 80 78 76 74 72 70

N2 concentration (%)

MAP with 6 'Kiyomi' fruit, no perforations at 5ºC

25

103

15 10 5 0

N2 concentration (%)

N. Techavises, Y. Hikida / Journal of Food Engineering 85 (2008) 94–104

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (day)

MAP with 8 'Kiyomi' fruit, 1 perforation of 5 mm at 5ºC 90 25 88 20 86 84 15 82 80 78 10 76 5 74 72 70 0 0 6 12 18 24 30 36 42 48 Time (h)

N2 concentration (%)

O2 or CO2 concentration (%)

MAP with 8 'Kiyomi' fruit, 1 perforation of 2 mm at 5ºC 25 90 88 20 86 84 15 82 80 78 10 76 74 5 72 70 0 0 6 12 18 24 30 36 42 48 Time (h)

N2 concentration (%)

O2 or CO2 concentration (%)

Fig. 13. Changes in gas concentrations inside LDPE film packages without perforations, but with different numbers of ‘Kiyomi’ Tangor fruit at 5 °C (M, O2; h, CO2; s, N2; the line represents the predicted value).

Fig. 14. Changes in gas concentrations inside LDPE film packages, but with one perforation of 2 and 5 mm diameter storing 8 ‘Kiyomi’ Tangor fruit at 5 °C (M, O2; h, CO2; s, N2; the line represents the predicted value).

All these results confirm the predictive ability of the MAP with macroperforations model combined with the effective permeability model. As shown by the prediction results, the assumption that the effective permeability of the perforation is the same regardless of the gas species and temperature is valid. 5. Conclusions A mathematical model for simulating O2, CO2, N2, and water vapor exchanges in MAP with macroperforations was successfully established and yielded good prediction results. Atmospheric gas and water vapor exchanges through a polymeric film and macroscopic perforations could be described by Fick’s law. Temperature, film thickness, and gas type had no significant effects on the effective permeability of a perforation for the ranges tested. A simple empirical equation for predicting the effective permeability of a thin macroscopic perforation was developed as a function of perforation diameter. References ASTM (1993). Standard test methods for water vapor transmission of materials. Annual Book of ASTM Standards. E96-93. Philadelphia: American Society for Testing and Materials.

Beaudry, R. M., Cameron, A. C., Shirazi, A., & Dostal-Lange, D. L. (1992). Modified-atmosphere packaging of blueberry fruit: Effect of temperature on package O2 and CO2. Journal of the American Society for Horticultural Science, 117(3), 436–441. Brody, A. L. (1989). Controlled/ modified atmosphere/vacuum packaging of foods. CT, USA: Food and Nutrition Press. Chau, K. V., Romero, R. A., Baird, C. C., & Gaffney, J. J. (1988). Transpiration coefficients for certain fruits and vegetables. Transactions of the American Society of Heating, Refrigerating and AirConditioning Engineers, 94(1), 1553–1562. Chen, X., & Yamamoto, T. (2002). Numerical analysis (pp. 101–114). Tokyo, Japan: Corona Publishing. Dirim, S. N., Ozden, H. O., Bayindirli, A., & Esin, A. (2004). Modification of water vapour transfer rate of low density polyethylene films for food packaging. Journal of Food Engineering, 63, 9–13. Emond, J. P., Castaigne, F., Toupin, C. J., & Desilets, D. (1991). Mathematical modeling of gas exchange in modified atmosphere packaging. Transactions of the American Society of Agricultural Engineers, 34(1), 239–245. Fonseca, S. C., Oliveira, F. A. R., Lino, I. B. M., Brecht, J. K., & Chau, K. V. (2000). Modelling O2 and CO2 exchange for development of perforation-mediated modified atmosphere packaging. Journal of Food Engineering, 43, 9–15. Hagger, P. E., Lee, D. S., & Yam, K. L. (1992). Application of an enzyme kinetics based respiration model to closed system experiments for fresh produce. Journal of Food Process Engineering, 15, 143–157. Hanlon, J. F., Kelsey, R. J., & Forcinio, H. E. (1998). Handbook of package engineering (3rd ed., pp. 207–262). Boca Raton, USA: CRC Press. Hasbullah, R., Gardjito Syarief, A. M., & Akinaga, T. (2000). Gas permeability characteristics of plastic films for packaging of fresh

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N. Techavises, Y. Hikida / Journal of Food Engineering 85 (2008) 94–104

produce. Journal of the Society of Agricultural Structures, Japan, 31(2), 5–11. Hirata, T., Makino, Y., Ishikawa, Y., Katsuura, S., & Hasegawa, Y. (1996). A theoretical model for designing modified atmosphere packaging with a perforation. Transactions of the American Society of Agricultural Engineers, 39(4), 1499–1504. Ishikawa, Y., Hirata, T., & Hasegawa, Y. (1997). Development of simple gas permeability measurement for polymeric films - on high gas permeability films for MA packaging of fresh produce. Journal of Packaging Science and Technology, 6(4), 213–220 (in Japanese with the summary in English). Kader, A. A., Zagory, D., & Kerbel, E. L. (1989). Modified atmosphere packaging of fruits and vegetables. Critical Reviews in Food Science and Nutrition, 28, 1–30. Lee, D. S., & Renault, P. (1998). Using pinholes as tools to attain optimum modified atmospheres in packages of fresh produce. Packaging Technology and Science, 11, 119–130. Mannapperuma, J. D., Zagory, D., Singh, R. P., & Kader, A. A. (1989). Design of polymeric packages for modified atmosphere storage of fresh produce. In Fifth international controlled atmosphere research conference, 14–16 June, Wenatchee, Washington, USA. Merts, I., Cleland, D. J., Banks, N. H., & Cleland, A. C. (2003) Development of a mathematical model of modified atmosphere packaging systems for apples. In Proceedings of the 21st international congress of refrigeration, Washington, DC (paper 382). Moyls, A. L. (1998). Whole-bag (water) method for determining water vapor transmission rate of polyethylene films. Transactions of the American Society of Agricultural Engineers, 41(5), 1447–1451.

Nobel, P. S. (1983). Biophysical plant physiology and ecology (pp. 387– 460). NY, USA: W.H. Freeman and Company. Ozisik, M. N. (1985). Heat transfer (Int. ed., pp. 702–731). Singapore: McGraw-Hill Book Company. Paul, D. R., & Clarke, R. (2002). Modeling of modified atmosphere packaging based on designs with a membrane and perforations. Journal of Membrane Science, 208, 269–283. Porat, R., Weiss, B., Cohen, L., Daus, A., & Aharoni, N. (2004). Reduction of postharvest rind disorders in citrus fruit by modified atmosphere packaging. Postharvest Biology and Technology, 33, 35–43. Renault, P., Souty, M., & Chambroy, Y. (1994). Gas exchange in modified atmosphere packaging. 1: A new theoretical approach for microperforated packs. International Journal of Food Science and Technology, 29, 365–378. Silva, F. M., Chau, K. V., Brecht, J. K., & Sargent, S. A. (1999). Tubes for modified atmosphere packaging of fresh fruits and vegetables: Effective permeability measurement. Applied Engineering in Agriculture, 15(4), 313–318. Talasila, P. C., & Cameron, A. C. (1997). Free-volume changes in flexible, hermetic packages containing respiring produce. Journal of Food Science, 62(4), 659–664. Wills, R., McGlasson, B., Graham, D., & Joyce, D. (1998). Postharvest: An introduction to the physiology and handling of fruit, vegetable and ornamentals (4th ed., pp. 77–96). Adelaide, South Australia: Hyde Park Press. Zagory, D., & Kader, A. A. (1988). Modified atmosphere packaging of fresh produce. Food Technology, 42(5), 70–77.