Mathematical modelling of diffusion channel length to maintain steady-state oxygen concentration for controlled atmosphere storage of tomato

Transcription

1 International Journal of Food Properties ISSN: (Print) (Online) Journal homepage: Mathematical modelling of diffusion channel length to maintain steady-state oxygen concentration for controlled atmosphere storage of tomato Palani Kandasamy To cite this article: Palani Kandasamy (2017) Mathematical modelling of diffusion channel length to maintain steady-state oxygen concentration for controlled atmosphere storage of tomato, International Journal of Food Properties, 20:sup2, , DOI: / To link to this article: Taylor & Francis Group, LLC Accepted author version posted online: 30 Jun Published online: 15 Dec Submit your article to this journal Article views: 38 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at

2 2017, VOL. 20, NO. S2, S1424 S Mathematical modelling of diffusion channel length to maintain steady-state oxygen concentration for controlled atmosphere storage of tomato Palani Kandasamy Department of Agricultural Engineering, Institute of Agriculture, Visva-Bharati University, Sriniketan, West Bengal, India ABSTRACT In this study, potential of the air-diffusion channels to maintain the desired controlled atmosphere condition in the storage chambers was evaluated. The diffusion channels of different combination in length (60, 120, 180, 240 mm) and diameter (3, 6, 9, 12 mm) were installed in the storage chambers of 2 L capacity. Tomato samples (0.805 kg) were taken in the chambers and stored at 10 C. Oxygen concentration in the chambers was measured periodically until the end of storage period. The tomatoes were stored upto 40 days under the channel length of 180 mm and diameter of 9 mm with harvest-fresh appearance, better texture and colour. The experimental results showed that the oxygen concentration ranging from 7% to 15% was maintained depending on the channel length and its tendency was found directly proportional to the channel diameter and inversely related to the channel length. Simultaneously, respiration rate of tomato was determined by closed respiration system to facilitate working with diffusion channel model. A model was developed based on Fick s first law of gas diffusion to predict the channel length. The model was fitted to the experimental data and channel lengths were calculated theoretically in the ranges between 30 and 320 mm. The predicted channel lengths maintained the oxygen concentration between 4% and 16% irrespective of the channel diameters. The predicted results were in accordance with the experimental results. The model was very useful in predicting the diffusion channel length and establishing the controlled atmosphere condition for storage of tomatoes. ARTICLE HISTORY Received 2 March 2017 Accepted 22 June 2017 KEYWORDS Tomato; Diffusion channel; Modelling; O 2 concentration; Respiration rate Introduction Tomato (Solanum lycopersicum) is one of the most consumed vegetables worldwide. It is a climacteric vegetable, so it is highly perishable in nature that encounters several problems in its transportation, storage, and marketing. [1] It has been estimated that the postharvest losses of tomato range from 20% to 50% in tropical countries. [2] Therefore, an increase in postharvest life of tomato is really desirable to reduce the losses during supply chain. One of the major physiological activities in the postharvest life of tomato is respiration. Fresh tomatoes generally have higher respiration rates that indicate more active metabolism and subsequently a faster deterioration rate in the normal course of time. [3] Respiration involves the consumption of oxygen (O 2 ) for oxidative breakdown of organic components into simple molecules such as carbon dioxide (CO 2 ) and water (H 2 O) with concurrent release of energy and other intermediates which can be used by the cell for synthetic reactions. [4] Respiration rates and deterioration rates can be minimized by storing the produce in controlled/ CONTACT Palani Kandasamy pkandasamy1973@gmail.com Department of Agricultural Engineering, Institute of Agriculture, Visva-Bharati University, Sriniketan, West Bengal , India. Colour versions of one or more of the figures in the article can be found online at Taylor & Francis Group, LLC

3 S1425 modified atmospheric condition at low temperature. Modified atmosphere can be achieved by maintaining the natural interplay between respiration rate of the commodity and transfer of gases through the storage that lead to an atmosphere richer in CO 2 and poorer in O 2. [5] Controlled atmosphere storage (CAS) has been defined as a form of storage where the concentration of gas is initially modified according to optimal conditions and then maintained during the period of storage. [6] Over ripening, senescence, ethylene production rates, and some physiological alterations such as mould growth, rotting, decay, butt discolouration can be minimized greatly in CAS condition. [7,8] The levels of both O 2 and CO 2 concentrations during storage affect the quality of the final product. Absence of O 2 results in development of off-flavours, and presence of high CO 2 concentration (more than 5% for tomato) may cause physiological injures. [9] There are different techniques such as O 2 control system, CO 2 control system, hypobaric system, membrane system, and diffusion channel system to provide the desired gas composition in the storage environment depending on the degree of control of the gases. [6,10] The final O 2 concentration in the storage chamber depends on the permeability of the membrane and area available for O 2 transfer. Moreover, for those commodities that need a high concentration of O 2 during storage, the use of polymeric membranes has not been successful due to their low O 2 permeability. [11] Among different techniques, the diffusion channel system is indeed a potential alternative for products that cannot be packed in polymeric films, and is capable of maintaining a specific steady-state gas composition in CAS systems over a longer period of time, relatively insensitive to changes in barometric pressure and fluctuations in the storage room temperature, provides great flexibility in the design of storage chamber, and materials used are considerably less expensive and are structurally simple. [12] Diffusion channel system works on the principle of Fick s first law of gas diffusion. Diffusion channel is a hollow tube fitted with an airtight storage chamber in which produce is stored and other end of the tube is exposed to the atmosphere. As a result of consumption of O 2 and liberation of CO 2 during respiratory process of the stored commodity, a great change in concentration of gases inside the storage chamber occurs. With respect to ambient condition, O 2 concentration decreases and that of CO 2 increases at rates depending on respiration rate of the produce. This creates a concentration gradient between inside and outside the chamber. Diffusion of gases takes place through the channel due to concentration gradient of gases between inside and outside the storage chamber, thus modified atmosphere is created inside the chamber which is beneficial for storage. The rate of diffusion of gases is dependent on length and cross-sectional area of the channel and gas concentration gradients between the chamber and ambient air. The gas composition in the storage chambers could easily be altered by varying the dimensions of diffusion channels. [12 16] There is not much research work on the concept of diffusion channel system to enhance the shelf life of fruits and vegetables. Some researchers have published their research work on diffusion channel system. Emond et al. [11] studied the gas exchanges through a perforation (considered as channel of zero length) and developed a model to predict the gas exchanges through the perforation. Baugerod [12] proved that the diffusion channel system is capable of maintaining the steady-state O 2 concentration from 1.5% to 18% depending on the mass of stored product, and length and crosssectional area of the diffusion channel. Ratti et al. [13] showed the influence of diffusion channel length on the concentration of O 2 in the storage chambers but no theoretical interpretation of the experimental data. Ratti et al. [14] developed mathematical model based on the molecular diffusion theory and this model includes the effect of mass of the produce, length and cross-sectional area of the diffusion channel on the final gas composition in the storage chamber. Different combinations of diffusion channel length (0.6, 3, 7, 12, 18, and 25 cm) and cross-sectional area (0.04, 0.18 and 1.15 cm 2 ) were tested for storage of broccoli at 0 C. [15] The length and cross-sectional area have a significant effect on the final O 2 steady-state concentration. Fick s first law of molecular diffusion theory was used to predict the required length of diffusion channel. Spinach was stored up to 30 days at 2 C under diffusion channel length of 0.18 m and cross-sectional area of m 2 with best colour and freshness. [16] CO 2 produced by the respiring spinach was completely scrubbed using calcium hydroxide, and O 2 was maintained in the range of 1 5%. The O 2 steady-state levels

4 S1426 P. KANDASAMY decreased with an increase in length and became more distinct as the cross-sectional area increased. A model was developed based on Fick s first law of molecular diffusion for predicting the length of diffusion channel. Stewart et al. [17] confirmed that the Cavendish bananas (also a climacteric fruit) can be stored for 42 days at 15 C under diffusion channel systems (4, 7, and 10 cm channel length). The shortest diffusion channel achieved 5% CO 2 and 3% O 2 in days. Karthiayani et al. [18] stored banana (Musa acuminate) under diffusion channel system (length: 5, 10, 15, and 20 cm and inner diameter: 3, 5, and 7 mm) at room temperature, 24 C and 14 C. They showed that the shelf life of banana can be increased 3 4 -folds as compared with control. They also developed a model using non-linear multiple regression to fit the observed data, and the model was found to be useful in determining the length of the diffusion channel for required steady-state O 2 concentration for banana. Since the polymeric membranes have low O 2 permeability, maintaining required O 2 concentration in the storage is not feasible. The use of diffusion channel system is theoretically able to handle the whole range of possible O 2 concentrations in the storage. The main objective of this work is to develop mathematical model to predict the optimal length of diffusion channel to maintain the steady-state O 2 concentration in the storage. Theory of modelling Fick s first law of gas diffusion CAS involves atmospheric gas mixtures and their diffusion characteristics. Gas diffusion describes the spread of particles through random motion from regions of higher concentration to regions of lower concentration. Diffusion occurs in response to a concentration gradient and is expressed as change in concentration due to a change in position. The gas diffusion generally obeys Fick s first law of gas diffusion, which states that the gas flux moves from region of higher concentration to region of lower concentration, with a magnitude that is proportional to the concentration gradient. The movement of gases is due to the random motion of the individual molecules caused by their kinetic energy. The molecular diffusion is typically described mathematically using Fick s first law of gas diffusion [19] as A N A ¼ D AB where N A is the rate of gas diffusion per unit area per unit time (mol m 2 s 1 ), D AB is the diffusion coefficient that describes the speed of gas that diffuses from region A to region B (m 2 s 1 ), C A is the concentration of gas in A, x is the distance between where the object started and ended after diffusion, ( ) sign indicates that N A is positive when movement is down the gradient. In steady-state conditions, diffusion rate of a gas is proportional to the concentration difference across the material and the area perpendicular to the diffusion. [20] Development of modelling The molecular diffusion theory on diffusion of O 2 through diffusion path was adopted in this study to develop a mathematical model to predict the optimal length of diffusion channel as described by Ratti et al. [14] for storage of cauliflower. This model takes into account the functionality between the mass of the produce, final O 2 concentration level in the storage chamber, diffusion channel length, and its cross-sectional area. While modelling process, the following key assumptions have been made. (i) total pressure in the chamber is 1 atm; (ii) the temperature is constant; (iii) the concentration of O 2 in the chamber is uniform at any time; (iv) the diffusion process is binary, since the CO 2 produced by the stored commodity is chemically scrubbed off, thus O 2 and N 2 are diffusing; (v) there is no concentration gradient for nitrogen (N 2 ) between the outside and the inside,

5 S1427 Figure 1. Diffusion of O 2 into a storage chamber through the diffusion path. thus O 2 will be diffusing in a stagnant N 2 gas; (vi) the diffusion coefficient of O 2 in N 2 is constant; and (vii) diffusion of gases in the chamber is one-dimensional. Figure 1 shows the diffusion of O 2 into a storage chamber through the diffusion path. The mass balance is written for a strip of the diffusion channel of length Δz. For a binary gas mixture, the general equation that describes the flux of the diffusing substance (O 2 ) into a stagnant gas (N 2 ) based on molecular diffusion can be stated as follows: n O2 ¼ cd O2 N 2 dy O2 dz þ y O 2 n O2 (2) where n O2 is the O 2 molar flux (mol cm 2 h 1 ), c is the total gas molar concentration (mol cm 3 ), D O2 N 2 is the diffusion coefficient of O 2 gas through diffusion channels (cm 2 h 1 ), y O2 is the O 2 mole fraction in sealed storage chamber (dimensionless), z is the spatial coordinate (cm). Under steadystate condition, the amount of O 2 utilized in the respiration process is equal to that diffusing into the chamber. Applying boundary conditions to the diffusion channel system z ¼ 0; y O2 z ¼ L; y O2 ¼ ðy O2 Þ chamber ¼ ðy O2 Þ air The mass flux of O 2 can be obtained by rearranging Eq. (2) and integrating with proper limits of boundary conditions. ð 0 ðð yo2 Þ air dy O2 n O2 dz ¼ cd O2 N 2 (3) L ðy O2 Þ 1 y O2 chamber

6 S1428 P. KANDASAMY n O2 ¼ cd O 2 N 2 1 ðy O2 ln L 1 ðy O2 Þ air Þ chamber where L is the length of the diffusion channel (cm), y O2air is the O 2 mole fraction in air (dimensionless), y O2chamber is the O 2 mole fraction in storage chambers installed in diffusion channel. Under steady-state conditions, the O 2 consumed by the commodity is equal to the O 2 diffusing through the channel into the chamber. The O 2 consumed in the respiration process can be expressed numerically as follows: M O2consumed ¼ R O2 M s t (5) where M O2consumed is the mass of O 2 consumed in the respiration process (mg O 2 ), R O2 is the respiration rate as a function of O 2 (mg O 2 kg 1 h 1 ), M s is the mass of the stored products (kg), t is the time (h). Under steady-state condition (z = 0), the mass flux of O 2 can be written as n O2 ¼ M O 2consumed t A C ω O2 (6) where A C is the cross-sectional area of the diffusion channel (cm 2 ), ω O2 is the O 2 molecular weight (kg mol 1 ), t is the time (h). Equating Eqs. (5) and (6) and simplifying, we get n O2 ¼ R O 2 M S A C ω O2 (7) The length of diffusion channel required to maintain a desired steady-state O 2 concentration inside the storage chamber can be obtained by equating Eqs. (4) and (7) L ¼ cd O 2 N 2 A c ω O2 1 y O2air ln (8) R O2 M s 1 y O2chamber The following model was adopted to predict the respiration rate of tomato as a function of O 2 and CO 2 concentration: [21] K 1 C O2 r ¼ (9) K 2 þ ð1 þ K 3 C CO2 ÞC O2 where r is the respiration rate (mg O 2 kg 1 h 1 or mg CO 2 kg 1 h 1 ), C O2 is the O 2 concentration (mol cm 3 ), C CO2 is the CO 2 concentration (mol cm 3 ), K 1 is the constant (mg kg 1 h 1 ), K 2 is the constant (mol O 2 mol total 1 ), K 3 is the inhibition constant (dimensionless). The inhibition constant (K 3 ) for CO 2 concentration was tended to zero as the rate of CO 2 evolution during the respiration process is not same as the rate of O 2 consumption. The constant K 3 was negligible in either case, which nullifies the effect of changing CO 2 concentration on the respiration rate. [21] Hence, the respiration rate was assumed only as a function of O 2 concentration as follows: R O2 ¼ K 1C O2 K 2 þc O2 (10) To facilitate working with the diffusion channel model, the concentration of O 2 is expressed as O 2 mole fraction and stated as follows: (4) R O2 ¼ K 1 y O2 K 2 þ y O2 (11) At steady-state condition, concentration of O 2 can be expressed as follows: Substituting Eqs. (11) and (12) in Eq. (8) can be written as: C O2 ¼ y O2 c (12)

7 h i " # L ¼ A D O2 N C 2 c ðk 2 =cþþy O2 1 y ω O2 ln O2air M S K 1 y O2 1 y O2chamber S1429 (13) Diffusion coefficient of oxygen The diffusion coefficient (D O2 N 2 )ofo 2 into N 2 can be determined with following key assumptions: (i) length of diffusion channel is unity, (ii) Fick s lawdefinesthistransportprocessclearly, (iii) O 2 concentration in the chamber is uniform at any time (steady state). Based on these assumptions, the diffusion coefficient of O 2 through diffusion channels can be calculated by following equation: [22] D O2 N 2 ¼ Q mδl (14) A C Δ c where Q m is the mass flow rate of O 2 through diffusion channel (mg h 1 ), Δl is the unit length of diffusion channel (cm), Δ c is the difference in gas concentration between inlet and outlet end of the diffusion channel (mg cm 3 ). D O2 N 2 c ¼a 1 (15) K 1 where a 1 and a 2 are constants. K 2 c ¼a 2 (16) Model for length of diffusion channel The model to predict the length of diffusion channel can be obtained by substituting Eqs. (15) and (16) in Eq. (13) and simplifying L ¼ A C a 1ða 2 þ y O2 Þ ð1 y O2air Þ ω O2 ln (17) M S y O2 ð1 y O2chamber Þ Materials and methods Sample preparation The popular tomato variety Roma in the West Bengal (India) was selected for this study. The matured tomatoes at breaker stage of ripeness (definite break in colour from green to tannishyellow, pink, or less than 10% red coloration [23] ) and uniform size were procured from a farmer field. The tomatoes were transported to the lab immediately after harvest. The harvested tomatoes were graded manually and washed in chlorinated water with the concentration of 100 mg L 1 to remove adhering dirt on their surface. [24] Thetomatosamplesof0.805kgwerechosensincethe selected storage chamber s capacity was 2 L and two-third of the headspace in the chambers was kept as free volume. Experimental design The experiments were designed with four levels of diffusion channel length (60, 120, 180, and 240 mm) and four levels of channel diameter (3, 6, 9, and 12 mm) as independent variables and gas concentration as dependent variable. The diffusion channels (fibre glass tubes) of different geometries were purchased from Hindusthan Industrial Syndicate, Kolkata, India. The geometries of

8 S1430 P. KANDASAMY Table 1. Treatment details of the experiments. Diffusion channel dimensions Treatments (T) Diameter of channel, D (mm) Length of channel, L (mm) Cross-sectional area of channel, A C (cm 2 ) T T T T T T T T T T T T T T T T diffusion channel were selected based on the information available in the previous studies. [14 17] Different symbols (Table 1) were used to denote different treatments with three replicates. Factorial completely randomized design using AGRESS software package (P 0.05) was used for analysis of the effect of different lengths and diameters of the diffusion channel on gas concentration in the storage chambers. The storage temperature of 10 C was selected as recommended by the previous research (fresh tomatoes stored at around 10 C were more favourable as compared with high temperature (24 30 C) for prolonged shelf life and to retain fresh tomato quality, [25] and postharvest recommendations indicate that tomatoes, including cherry and grape tomatoes, should be stored at 10 C or higher to avoid chilling injury [26] ). Fabrication of experimental setup The storage chambers of 2 L capacity made up of polyethylene tetrachloride (PET) were used for conducting the experiments. The experimental setup (Fig. 2) was fabricated in such a way that four holes were provided on the lid. A silicone septum was fitted in the first hole to facilitate the withdrawal of gas sample from the chamber for analysis. Brass nipples with rubber gaskets were connected in second and third holes and tightened with nuts. Rubber tubes of length 200 mm were connected to these nipples and closed by pinch clips after purging gas. In the fourth hole, a conicalshaped hallow rubber cork was fitted. The diffusion channel of required size was rigidly fixed in the rubber cork. The joints were crammed by melted paraffin wax to secure air tightness. The absence of air bubble ensured the air tightness of diffusion chambers. Experimental procedure The experimental chambers were washed with chlorinated water of concentration 500 mg L 1 and wiped completely by cotton cloth. Calcium hydroxide (50 g kg 1 ) with tomato wrapped in a tissue paper was placed at the bottom of the each storage chamber to prevent any accumulation of CO 2 and absorb condensed moisture within the storage chambers. [14 16] The tomato samples (M s = kg) were taken in the storage chambers. About two-third of headspace was left in the chambers as free volume. The chambers were provided perfect air tightness by top lid and wrapped with Teflon tape. To achieve a fast pull-down O 2 level inside the chamber, the storage chamber with tomato sample was flushed with N 2 until O 2 level is brought down to required level (6%). The selected gas mixture

9 S1431 Figure 2. Experimental setup of diffusion channel system for storage of tomato. was flushed from one sampling port, and the other sampling port was opened as gas outlet to atmosphere. The gas was flushed for about 3 5 min. During flushing, diffusion channels were closed with a thin wax plate. At the end of flushing, both inlet and outlet ports were closed with pinch clips. The storage chambers were transferred to the cold room where the temperature of 10 C was maintained throughout the storage period. The chambers were kept in vertical position until end of the storage period. Measurement of respiratory gases The storage chambers were allowed to sit for about 30 min for their temperature to come to equilibrium with room temperature. The first gas samples were drawn without breaking the wax cover of channel opening. The readings indicated that gas concentrations in the chamber were uniform. The wax plate was then removed from the diffusion channels and the gases were allowed to diffuse. Gas samples of 0.5 ml were drawn periodically from each chamber through the silicone septum using syringes. The gas samples were analysed for CO 2 and O 2 concentration (%) using gas chromatograph (SRI 8610A model, SRI Instruments, USA) equipped with thermal conductivity detector and operating at an oven temperature of 45 C and detector temperature of 100 C using helium as the carrier gas. Calculation of concentration of the gases was made with the Peak Simple software. The standard gas mixture (purchased from Span Gas Equipments Ltd., Mumbai) was analysed, and calibration curves were developed for determining the amount of components in experimental gas mixture quantitatively.

10 S1432 P. KANDASAMY Determination of respiration rate Respiration rate of tomato was measured using the closed respiration system, which involves monitoring the O 2 and CO 2 concentrations as a function of time inside a closed chamber containing the tomatoes. The respiration rate can be measured by observing the concentration of O 2 consumption or CO 2 evolution per unit time per unit weight of the produce [27,28] (it can be expressed by mg O 2 kg 1 h 1 or mg CO 2 kg 1 h 1 ). The experimental respiration rate was calculated periodically using the data such as difference in gas concentration per time, weight of the stored produce, and free volume of the chamber. The mass concentration of O 2 and CO 2 inside the closed experimental chamber were determined and plotted as a function of time. Curve fitting was done using secondorder polynomial regression equation. [29] The fitted polynomial was differentiated to determine the change of rate of gas concentrations. The first derivative of the regression functions were used to obtain the experimental respiration rates as a function of O 2 consumption (R O2 ) and CO 2 evolution (R CO2 ) [30] R O2 ¼ d O ½ 2Š PM a V f (18) dt 100RTW p R CO2 ¼ d CO ½ 2Š PM a V f (19) dt 100RTW p where [O 2 ] is the oxygen concentration (%), [CO 2 ] is the carbon dioxide concentration (%), d[o 2 ]is the change in concentration of O 2 with time, d[co 2 ] is the change in concentration of CO 2 with time, dt is the difference in time between two gas measurements (h), P is the gas pressure (1 atm), M a is the mean molecular mass of air (g mol 1 ), V f is the free volume of the chamber (L), R is the gas constant in the ideal gas equation ( L atm mol 1 K 1 ), T is the temperature of the gas (K), W p is the weight of the stored tomatoes (kg). The negative sign in Eq. (18) signifies that the O 2 concentration in the chamber decreases with time. Results and discussion The respiration rate of tomato was obtained through the closed respiration system experiments at 10 C. Kandasamy et al. [21] reported detailed experiment as well as calculation procedures. The experimental respiration data were used to estimate the respiration rate model constants in Eq. (9). The respiration rates were plotted as a function of O 2 and CO 2 concentration (Fig. 3). The model was then fitted to the experimental data. The respiration rate model constants K 1, K 2, and K 3 in Eq. (9) were determined by non-linear regression with experimental data using Gauss Newton procedure for non-linear least squares. The regression described that the experimental data, that is, O 2 concentration was very well (R 2 = 0.970), whereas CO 2 concentration was fair (R 2 = 0.812) for tomato. The results of fitting for K 1, K 2, and K 3 were , , and 0.007, respectively. Constant K 3 is quite close to zero and nullifies the influence of CO 2 concentration on respiration rate. Therefore, the respiration rate of tomato was considered mainly as a function of O 2 concentration. [21] The inhibition parameter K 3, calculated as the rate of CO 2 evolution, was inversely related to temperature, whereas the one calculated as the rate of O 2 consumption was directly proportional to the temperature. This is because the rate of CO 2 evolution during the respiration process is not same as the rate of O 2 consumption. The parameter K 3 wasnegligibleineithercasewhich nullifies the effect of changing CO 2 concentration on the respiration rate. [21] As the inhibition constant K 3 for CO 2 concentration in Eq. (9) was negligible, the model was modified mainly as afunctionofo 2 concentration (Eq. 10). To facilitate working with the diffusion channel model, the concentration of O 2 was expressed as O 2 mole fraction (Eq. 11). The respiration rate of tomato in sealed storage chambers was calculated

11 S1433 (a) RR (mg O 2 kg -1 h -1 ) (b) RR (mg CO 2 kg -1 h -1 ) Time (h) Time (h) Figure 3. Respiration rate of tomato: (a) function of O 2, (b) function of CO 2 concentration at 10 C. as a function of O 2 molar fraction. The respiration rate was plotted against the O 2 molar fraction. Curve fitting was done using non-linear regression equation as shown in Fig. 4. Constants K 1 and K 2 in Eq. (11) were obtained from experimental data through the curve fittings. Results of fitting for K 1 and K 2 were mg kg 1 h 1 and mol O 2 mol total 1, respectively. The predictions of the respiration rate model [Eq. (11) with fitted constants] are shown in Fig. 4 together with experimental RR (mg O 2 kg -1 h -1 ) y = x R ² = O 2 mole fraction (yo 2 ), % Figure 4. Respiration rate of tomato as a function of O 2 mole fraction at 10 C.

12 S1434 P. KANDASAMY Table 2. Different parameters for predicting the model for diffusion channel length. Treatments A c M s D O2 N2 a 1 a 2 y O2 ωo2 y O2air y O2chamber T T T T T T T T T T T T T T T T results. The linear tendency shown by the model in this range of O 2 concentrations is in accordance with the predictions of enzymatic reaction theory. The diffusion coefficient of O 2 (D O2 N 2 ) through the diffusion channel was determined through Eq. (14) by fitting the experimental data, and the results obtained are presented in Table 2. The diffusion coefficient of O 2 depends on length and cross-sectional area of the diffusion channel, mass flow rate of O 2 through diffusion channels, and difference in gas concentration between inlet and outlet end of the diffusion channel. [22] It is clearly noticed from Table 2 that the decreasing trend in diffusion coefficient of O 2 was observed when increasing the channel length and diameter. The constants a 1 and a 2 were obtained through Eqs. (15) and (16), respectively, by fitting the experimental data such as diffusion coefficient of O 2 through the channel (Table 2), constants (K 1 and K 2 ), and total gas molar concentration, that is, mol cm 3. Results of fitting for a 1 and a 2 are presented in Table 2. The constant a 1 was found to be varied because the diffusion coefficient of O 2 varied depending on the channel length and cross-sectional area. O 2 molecular weight ( ωo2 ), O 2 mole fraction in sealed chamber (y O2 ), and O 2 mole fraction in air (y O2air ) were 32 kg mol 1, 0.025, and 0.189, respectively. Moreover, O 2 mole fraction in storage chambers equipped with diffusion channel (y O2chamber ) was determined using experimental data and the results obtained are presented in Table 2. The diffusion channel length model (Eq. 17) was fitted to the experimental data (Table 2) and the results obtained were found negative. Since the length cannot be negative, the model (Eq. 17) was rewritten as follows: L ¼ A C a 1 a 2 þ y O2 ω O2 ln 1 y ð O 2chamber Þ (20) M S y O2 ð1 y O2air Þ Then the corrected model (Eq. 20) was fitted to the experimental data, and channel lengths were obtained. Predicted length of diffusion channel for maintaining the steady-state O 2 concentration is presented in Fig. 5. The channel lengths, respectively, were predicted in the range of mm, mm, mm, and mm for maintaining the O 2 concentration of 4%, 8%, 12%, and 16% irrespective of the channel diameter (3, 6, 9, and 12 mm). It is clearly noticed that the longer diffusion channel maintained lower range of O 2 steady-state concentration, whereas shorter diffusion channel maintained higher range of O 2 steady-state concentration irrespective of the channel diameter. These results were confirmed with the results reported by Ratti et al. [14] for cauliflower, Chimphango [16] for spinach, and Karthiayani et al. [18] for banana. The model (Eq. 20) developed for predicting the length of diffusion channel fits the experimental data well when individual channel

13 S1435 Diffusion channel length, mm mm dia 6 mm dia 9 mm dia 12 mm dia Steady-state O 2 concentration, % Figure 5. Predicted length of diffusion channel for maintaining the steady-state O 2 concentration at 10 C (error with 5% value). diameters were considered, and is more appropriate for establishing the controlled atmosphere condition for storage of tomato. The model suggests that the desired O 2 level in the storage chambers for any length can be precisely obtained if the diameter of the channel is known. To get same O 2 level as in a chamber installed with a shorter diffusion channel length of a small diameter, one can use a longer diffusion channel of a larger diameter. A parallel trend was observed when these results (predicted) were compared with the experimental results. The steady-state O 2 concentration in experimental storage chambers equipped with diffusion channel at 10 C is presented in Fig. 6. From the figure, it is noticed that the longer diffusion channel (240 mm) maintained lower O 2 concentration (7 9%), whereas shorter diffusion channel (60 mm) maintained higher O 2 concentration (11 15%) depending on the channel diameter. On the other hand, higher channel diameter (12 mm) maintained higher O 2 concentration (9 15%), whereas lower channel diameter (3 mm) maintained lower O 2 concentration (7 12%) depending on the channel length. It is evident from the results that the steady-state O 2 concentration was inversely proportional to the length of channel and directly proportional to the channel diameter. The statistical analysis showed that the effect of different length and diameter of the diffusion channel on concentration of O 2 was found to be significant at 5% level. Similar trends in the steady-state O 2 concentration under diffusion channel system were observed by Chimphango [16] and Karthiayani et al. [18] for modified atmosphere packaging of spinach and banana, respectively. Moreover, the tomatoes were stored up to 40 days at 10 C under diffusion channel length of 180 mm and diameter Steady-state O 2 conc., % mm dia 6 mm dia 9 mm dia 12 mm dia Diffusion channel length, mm Figure 6. Steady-state O 2 concentration in experimental storage chambers with diffusion channel at 10 C (error with 5% value).

14 S1436 P. KANDASAMY of 9 mm (Treatment 11) with harvest-fresh appearance, better texture, good colour, retained nutritional values, and good marketability conditions. Conclusion The experimental results showed that the diffusion channel system can well maintain the O 2 concentration in the storage chamber. The model for predicting length of diffusion channel fits the experimental data well when individual channel diameters were considered and was more appropriate for establishing the controlled atmosphere condition for storage of tomato. The fitted model closely represented the experimental results and can be used to predict the length of diffusion channel for the same commodity. The model suggests that the desired O 2 level in the storage chambers for any length can be precisely obtained if the diameter of the channel is known. The model was very useful for predicting the diffusion channel length and more appropriate for establishing the controlled atmosphere condition for storage of tomato. References 1. Pila, N.; Gol, N.B.; Ramanarao, T.V. Effect of Postharvest Treatments on Physico-chemical Characteristics and Shelf Life of Tomato (Lycopersicon esculentum Mill.) Fruits during Storage. American-Eurasian Journal of Agriculture and Environmental Sciences 2010, 9(5), Arah, I.K.; Ahorbo, G.K.; Anku, E.K.; Kumah, E.K.; Amaglo, H. Postharvest Handling Practices and Treatment Methods for Tomato Handlers in Developing Countries: A Mini Review. Advances in Agriculture 2016, Doi: /2016/ , Wills, R.B.H.; McGlasson, W.B.; Graham, D.; Lee, T.H.; Hall, E.G. Post Harvest. An Introduction to the Physiology and Handling of Fruits and Vegetables. 3rd ed.; AVI: New York, Kader, A.A.; Zagory, D.; Kerbel, E.L. Modified Atmosphere Packaging of Fruits and Vegetables. Critical Review in Food Science and Nutrition 1989, 28, Fonseca, S.C.; Oliveira, F.A.R.; Brecht, J.K. Modelling Respiration Rate of Fresh Fruits and Vegetables for Modified Atmosphere Packages: A Review. Journal of Food Engineering 2002, 52, Raghavan, G.S.V.; Gariepy, Y. Structure and Instrumentation Aspects of Storage Systems. Acta Horticulture 1985, 157, Kader, A.A. Prevention of Ripening in Fruits by Use Controlled Atmospheres. Food Technology 1980, 34(3), Tasdelen, O.; Bayindirli, L. Controlled Atmosphere Storage and Edible Coating Effects on Storage Life and Quality of Tomatoes. Journal of Food Processing and Preservation 1998, 22, Yang, C.C.; Chinnan, M.S. Modeling the Effect of O 2 and CO 2 on Respiration and Quality of Stored Tomatoes. Transactions of the American Society of Agricultural Engineers 1988, 31, Kandasamy, P.; Moitra, R.; Shanmugapriya, C. Preservation of Fruits and Vegetables under Various Techniques of Controlled Atmosphere Storage. Indian Food Industry Journal 2011, 30(4), Emond, J.P.; Castaigne, F.; Toupin, C.J.; Desilets, D. Mathematical Modeling of Gas Exchange in Modified Atmosphere Packaging. Transactions of the American Society of Agricultural Engineers 1991, 34, Baugerod, H. Atmosphere Control in Controlled Atmosphere Storage Rooms by means of Controlled Diffusion Through Air-filled Channels. Acta Horticulturae 1980, 116, Ratti, C.; Raghavan, G.S.V.; Gariepy, Y. Respiration Rate Model and Modified Atmosphere Packaging of Fresh Cauliflowers. Journal of Food Engineering 1996, 28, Ratti, C.; Rabies, H.R.; Raghavan, G.S.V. Modelling Modified Atmosphere Storage of Fresh Cauliflower using Diffusion Channels. Journal of Agricultural Engineering Research 1998, 69, for_controlled_atmosphere_storage_of_spinach/links/0fcfd c pdf 17. Stewart, O.J.; Raghavan, G.S.V.; Goldena, K.D.; Gariepy, Y. MA Storage of Cavendish Bananas using Silicone Membrane and Diffusion Channel Systems. Postharvest Biology and Technology 2005, 35, Karthiayani, A.; Varadharaju, N.; Siddharth, M. Modified Atmosphere Storage of Banana (Musa acuminata) using Diffusion Channel and Mathematical Modelling of Steady-state Oxygen Concentration within the Package. Journal of Food, Agriculture & Environment 2014, 12 (3&4), Brogioli, D.; Vailati, A. Diffusive Mass Transfer by Non-equilibrium Fluctuations: Fick s Law Revisited. Physics Review 2001, 63, :1 4.

15 S Gebhart, B. Heat Conduction and Mass Diffusion; New York: McGraw Hill Inc., Kandasamy, P.; Moitra, R.; Mukherjee, S. Measurement and Modelling of Respiration Rate of Tomato (Cultivar Roma) for Modified Atmosphere Storage. Recent Patents on Food, Nutrition & Agriculture 2015, 7, Singh, D.; Muir, W.E.; Sinha, R.N. Apparent Coefficient of Diffusion of Carbon Dioxide through Samples of Cereals and Rapeseed. Journal of Stored Products Research 1984, 20, Gautier, H.; Verdin, V.D.; Benard, C.; Reich, M.; Buret, M.; Bourgaud, F.; Poessel, J.; Veyrat, C.C.; Genard, M. How Does Tomato Quality (Sugar, Acid and Nutritional Quality) Vary with Ripening Stage, Temperature and Irradiance? Journal of Agriculture and Food Chemistry 2008, 56, Zhuang, R.Y.; Beuchat, L.R.; Angulo, F.J. Fate of Salmonella Montevideo on and in Raw Tomatoes as Affected by Temperature and Treatment with Chlorine. Applied and Environmental Microbiology 1995, 61(6), Maul, F.; Sargent, S.A.; Sims, C.A.; Baldwin, E.A.; Balaban, M.O.; Huber, D.J. Tomato Flavor and Aroma Quality as Affected by Storage Temperature. Journal of Food Science 2000, 65(7), Roberts, P.K.; Sargent, S.A.; Fox, A.J. Effect of Storage Temperature on Ripening and Postharvest Quality of Grape and Mini-pear Tomatoes. Proceedings of the Florida State Horticultural Society 2002, 115, Lee, D.S.; Haggar, P.E.; Lee, J.; Yam, K.L. Model for Fresh Produce Respiration in Modified Atmosphere based on Principles of Enzyme Kinetics. Journal of Food Science 1991, 56(6), Hagger, P.E.; Lee, D.S.; Yam, K.L. Application of an Enzyme Kinetic based Respiration Model to Closed System Experiments for Fresh Produce. Journal of Food Process Engineering 1992, 15, Gong, S.; Corey, K. Predicting Steady-state Oxygen Concentrations in Modified Atmosphere Packages of Tomatoes. Journal of the American Society of Horticultural Science 1994, 119(3), Song, Y.; Kim, H.K.; Yam, K.L. Respiration Rate of Blueberry in Modified Atmosphere at Various Temperatures. Journal of the American Society of Horticultural Science 1992, 117(6),