JXB Advance Access originally published online on November 3, 2006
Journal of Experimental Botany 2006 57(15):4215-4224; doi:10.1093/jxb/erl198
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RESEARCH PAPER |
A permeation–diffusion–reaction model of gas transport in cellular tissue of plant materials
1BIOSYST-MeBioS, Faculty of Bioscience Engineering, Katholieke Universiteit Leuven, Willem de Croylaan 42, B-3001 Leuven, Belgium
2Scientific Computing Research Group, Computer Science Department, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
* To whom correspondence should be addressed. E-mail: quangtri.ho{at}biw.kuleuven.be
Received 18 May 2006; Accepted 12 September 2006
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Abstract |
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Gas transport in fruit tissue is governed by both diffusion and permeation. The latter phenomenon is caused by overall pressure gradients which may develop due to the large difference in O2 and CO2 diffusivity during controlled atmosphere storage of the fruit. A measurement set-up for tissue permeation based on unsteady-state gas exchange was developed. The gas permeability of pear tissue was determined based on an analytical gas transport model. The overall gas transport in pear tissue samples was validated using a finite element model describing simultaneous O2, CO2, and N2 gas transport, taking into account O2 consumption and CO2 production due to respiration. The results showed that the model described the experimentally determined permeability of N2 very well. The average experimentally determined values for permeation of skin, cortex samples, and the vascular bundle samples were (2.17±1.71)x10–19 m2, (2.35±1.96)x10–19 m2, and (4.51±3.12)x10–17 m2, respectively. The permeation–diffusion–reaction model can be applied to study gas transport in intact pears in relation to product quality.
Key words: Controlled atmosphere, diffusion, gas transport, measurement set-up, modelling, permeation, storage, Pyrus communis
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Introduction |
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Gas exchange plays a fundamental role in biological plant materials. Gas transport is caused by differences in gas composition between the applied external atmosphere and the internal atmosphere due to O2 consumption and CO2 production during respiration and fermentation (Kader, 1988). In fruit tissue, the gas-filled intercellular spaces are thought to be the main pathways for gas transport through plant organs needed for respiration. Several methods have been developed to measure the gas transport properties of various horticultural commodities (Cameron and Yang, 1982; Banks, 1985) for which it was assumed that the skin was the only barrier to gas diffusion and the fruit internal gas concentration was constant. This assumption does not hold for all types of commodities, especially not for fruit with a high tissue density (Banks and Kays, 1988; Lammertyn et al., 2003a). Due to barriers between the ambient atmosphere and the cells, where respiration takes place, considerable gas gradients between the external and internal atmospheres may occur (Rajapakse et al., 1990; Lammertyn et al., 2003a). Some controlled atmosphere storage disorders such as core breakdown in pear have been related to limited gas transport inside the fruit (Lammertyn et al., 2003a, b).
Gas transport in fruit and other bulky storage organs have macroscopically been described with Fick's laws of diffusion, assuming an effective diffusion process which is driven by concentration gradients (Burg and Burg, 1965; Cameron and Yang, 1982; Banks, 1985). During gas exchange, O2 in the gas phase diffuses through the skin of the fruit followed by diffusion in the intercellular system of pore spaces. Subsequently, O2 exchange between the intercellular atmosphere and the cellular solution occurs through the cell membrane. Finally, the O2 diffuses within the cytoplasm to the point of O2 consumption. Respiratory CO2 follows the reverse path. The rate of gas movement depends on the properties of the gas molecules and the physical properties of the intervening barriers (Kader, 1988; Nobel, 1991). Development of the theory that connects the microscopic to the macroscopic description of mass transport in biological materials has been subjected to several investigations (Wood and Whitaker, 1998; Wood et al., 2002; Quintard et al., 2006). In these studies, the transport on the microscale was volume-averaged to a macroscopic equation containing effective parameters for the macroscopic properties of the biological materials. Recently, a macroscopic reaction–diffusion model for the macroscopic level that incorporates both gas diffusion and respiration was found appropriate for calculating the gas transport inside the fruit (Mannapperuma et al., 1991; Lammertyn et al., 2003a, b). Effective diffusion properties of the fruit were determined by measuring the concentration of gas exchange between two chambers of a measurement set-up separated by a tissue slice (Lammertyn et al., 2001; Schotsmans et al., 200, 2004; Ho et al., 2006a). The results showed that the CO2 diffusivity of the tissue was much higher than O2 diffusivity. It was hypothesized that CO2 is not only transported in the gas phase but also in the water phase from cell to cell, due to its high solubility in the solution, while O2 is mainly transported in the gas phase of the gas-filled intercellular spaces. If the CO2 diffusivity is higher than that of O2, the produced CO2 leaves the fruit at higher rates than O2 is entering the fruit. This would lead to a pressure difference between the internal parts of the fruit and the external atmosphere. Therefore, besides gas diffusion driven by concentration gradients, gas transport in the fruit occurs by permeation due to total pressure gradients in the fruit tissues.
Gas permeation can be defined as the transport process in a porous medium in which the gas flow is described by Darcy's law (Geankoplis, 1993; Bird et al., 2002). In fruit tissue, the intercellular space existing within a highly complicated network of gaseous channels can be considered as such a porous medium. Several authors have studied the gas diffusion properties of fruit tissue; however, gas permeation in fruit has only received attention in early work of the 1960s (Marcellin, 1974) A further complication caused by small pressure gradients is the flow of N2 which may contribute on the alleviation of this gradient. Pressure changes inside packages filled with horticultural produce, due to O2, CO2, and N2 transport in relation to package shrinkage, were described by Talasila and Cameron (1997). However, with the exception of the model of Schotsmans et al. (2003) for gas transport, no models reported in the literature include transport of N2 in fruit tissue.
The objectives of this paper are (i) to determine gas permeation properties of pear tissue, (ii) to determine N2 diffusivity in pear tissue, and (iii) to expand existing diffusion models for O2 and CO2 transport in fruit with N2 and permeation transport.
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Materials
Pears (Pyrus communis L. cv. ‘Conference’) were harvested on 8 September 2004 at the preclimacteric stage at the Fruitteeltcentrum (Rillaar, Belgium), cooled, and stored according to commercial protocols for a period of 21 d at –0.5 °C preceding CA storage (2.5 kPa O2, 0.7 kPa CO2 at –0.5 °C) until they were used for the experiments.
Pear flesh samples were first cut with a professional slice cutter (EH 158-L, Graef, Germany), subsequently small cylinders with a diameter of 24 mm were cut with a cork borer. The thickness of the sample was measured with a digital caliper (Mitutoyo Ltd., UK, accuracy ±0.01 mm) and ranged from 1–2 mm. For the skin samples, a razor blade was used to remove the flesh until a thickness of less than 1 mm was obtained. Cortex tissue samples were taken in the radial direction at the equatorial region of the pear and in the vertical axis, containing vascular bundles. Because a pear has an asymmetric shape, large gradients in gas concentration were not expected in the two tangential directions perpendicular to the radial direction inside the fruit. It is, therefore, not important to know the gas transport properties in these directions accurately. A schematic view of the sampling protocol is given in Fig. 1.
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Model of gas transport in pear tissue
Flux of gas transport:
A mass flux of a gas component j (mol m–2 s–1) describing the diffusion and permeation processes through the pear tissue samples is given by
 | (1) |
Permeation through the tissue by a pressure gradient can be described by Darcy's law for laminar flow in porous media (Bird et al., 2002).
 | (2) |
the gradient operator. For laminar flow in porous media such as tissue, permeation coefficients can be determined empirically and are usually considered to be independent of the gas passing the tissue.
The gas diffusion through the tissue can be approximated by Fick's first law of diffusion (Bird et al., 2002), which states that the flux of a gas diffusing through a barrier of tissue jd is proportional to the concentration gradient over this barrier, 
with the effective diffusion coefficient D (m2 s–1) acting as a proportionality coefficient
 | (3) |
Representative elemental volume:
The tissue structure of the fruit is a combination of cells, cell walls, and intercellular spaces. A representative elemental volume (REV) of the tissue is considered to contain two phases, namely the intracellular liquid phase of the cells and cell walls and the air-filled intercellular space (Fig. 2). The volume fraction of the intercellular space is assigned a value 
, the porosity of the tissue. Assuming local equilibrium at a certain concentration of the gas component i in the gas phase Ci,g (mol m–3), the concentration of the compound in the liquid phase of fruit tissue normally follows Henry's law. If the tissue has a porosity , the volume-averaged concentration Ci,tissue (mol m–3) of species i is then defined as:
 | (4) |
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From this definition, the following property of the tissue is derived
 | (5) |
i is called the gas capacity of the component i in the tissue.
Gas transport equation in tissue:
On the microscale, gas transport by diffusion and permeation in the intercellular spaces and diffusion and respiration in the cellular liquid phase were considered. Transport of gas i in those two phases is governed by the following equations
 | (6) |
 | (7) |
Since gas transfer in the intercellular spaces was considered to be in equilibrium with the liquid phase of the cells, the mass transport of component i in the liquid phase in equation (7) could be rewritten as
 | (8) |
Adding equations (6) and (8) yields a single volume-averaged transport equation over the REV:
 | (9) |
Using the effective diffusivity Di (m2 s–1), the effective permeation velocity vector u (m s–1) and the effective respiration term Ri (mol m–3 s–1) of the tissue, respectively, defined by
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 | (11) |
 | (12) |
 | (13) |
 | (14) |
(mol m–3) are the concentration of gas i at the boundary surface of tissue and the external condition, respectively.
Permeation was described using Darcy's law (equation 2). The relation between the concentration C and pressure P can be expressed by using the ideal gas law P=CRT. Therefore, equation (2) can be rewritten as follows
 | (15) |
The estimation of permeation coefficient K and the effective diffusivity will be discussed in the next section. The respiration of tissue was described by Ho et al. (2006a).
Measurement of gas transport parameters
Measurement set-up:
The system used to measure gas transport properties of fruit tissue consisted of two chambers (measurement chamber and flushing chamber) separated by a disc-shaped tissue sample (Fig. 3; Ho et al., 2006a). The chambers were metal cylinders screwed together, holding a PVC ring containing a tissue sample glued on it with cyano-acrylate glue. A rubber O ring was used to seal the PVC ring between the two chambers and to ensure that all gas transport between the two chambers took place through the tissue sample. Two inlet and outlet gas channels were used to flush the gases in the measurement chamber and flushing chamber. Pressure sensors (PMP 4070, GE Druck, Germany, accuracy ±0.04%) monitored the pressure changes in each chamber during the measurements. The temperature of the system was kept constant at 20.0±0.5 °C by submerging the set-up in a temperature-controlled water bath (F10-HC, Julabo Labor Technik GmbH, Seelbach, Germany, accuracy ±0.5 °C). The preparation of the samples was described by Ho et al. (2006a). The sealing of chambers was checked and validated before the experiments by rapidly changing the temperature of the water bath. When the pressure inside the measurement chamber increased correspondingly this indicated proper sealing.
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Diffusion coefficients of O2, CO2, and N2:
Data of diffusion coefficients of respiratory gasses (O2 and CO2) were reported by Ho et al. (2006b), the diffusivity of N2 was measured with the same set-up described by Ho et al. (2006a, b). Once the sample was attached to the diffusion cell, the measurement and the flushing chambers were flushed with, respectively, 70 kPa N2, 30 kPa O2, 95 kPa N2, and 5 kPa O2, at 10 l h–1, humidified, and passed through a heat exchanger to prevent the sample from drying and cooling down while flushing the two chambers. After 30 min, the in- and outlet valves of the measurement chamber were closed, and the decrease in O2 partial pressure and total pressure of the measurement chamber was monitored for 6 h. The O2 concentration was measured in the measurement chamber with fluorescent optical probes (Foxy-Resp, Ocean Optics, Duiven, The Netherlands). The difference in total pressure between the two chambers was logged and was kept smaller than 1.5 kPa to minimize permeation. The (second) permeation term was correspondingly omitted in equation (13); the CO2 production was negligible for this case. The N2 concentration was determined indirectly from the total pressure and the O2 concentration.
and 
were estimated by fitting the solution of the transport equation (13) for O2 and N2 to the measured concentration profiles in the measurement chamber. Equation (13) was solved numerically according to the procedure described in Ho et al. (2006a). The CO2 diffusivity was available from previous experiments (Ho et al., 2006b). 
was set to –2.47x10–4 mol m–3 s–1 (Ho et al., 2006a).
Permeation coefficient:
In the permeation experiment, the measurement and the flushing chambers were flushed with nitrogen at 10 l h–1, humidified, and passed through a heat exchanger to prevent the sample from drying and cooling down while flushing the two chambers. Nitrogen gas was used in the experiment as it has no physiological activity so that the source term 
vanishes from equation (13). The pressure in the measurement set-up was adjusted to get a 6 kPa pressure difference between the measurement and flushing chambers. The total pressure difference between the two chambers was not higher than 7 kPa, to prevent mechanical deformation and even damage of the tissue which would falsify the results. Finally, the in- and outlet valves of the measurement chamber were closed, and the decrease in pressure of the measurement chamber was monitored for at least 4 h.
Because of the absence of O2, there was no transport of this gas in the experiment. Similarly, based on some preliminary simulations it was found that the CO2 production through fermentation was also negligible, so that transport of CO2 could be omitted as well. For this particular measurement set-up, a lumped mass balance of a one component gas (N2) in the measurement chamber could be used in one-dimensional form as follows:
 | (16) |
 | (17) |
The relation between the concentration C and pressure P can be found from the ideal gas law. Equation (3) can then be rewritten in one dimension as follows
 | (18) |
Permeation through the tissue by a pressure gradient can be deduced for one-dimensional laminar flow in porous media as follows
 | (19) |
The gradient of total pressure can be approximated as the difference in total pressure between two chambers over a barrier which is the sample with a thickness L (m).
 | (20) |
Substitution of equation (20) into equations (18) and (19), respectively, and substituting the results into equation (17) yields
 | (21) |
The analytical solution of equation (21) describing the pressure change in the measurement chamber P(t) (kPa) with the time t (s) then is
 | (22) |
The permeation K of the tissue was determined by fitting the experimental data to equation (22) by using an iterative least squares estimation procedure written in MATLAB (The Mathworks, Inc., Natick, USA).
Validation experiments
The aforementioned experiments were used to determine permeation properties of the pear tissue by using only N2. However, air is a mixture of three main components: O2, CO2, and N2 and the gas transport in the tissue is a combination of diffusion and permeation processes. Validation experiments were performed to verify whether the measured permeation properties could also be applied to O2 and CO2. In addition, a gas transport model was used to predict the effect of permeation on the estimation of diffusion coefficient.
For model validation purposes, an experiment was performed with gradients applied such that transport of O2 and CO2 took place in the opposite direction. This experimental validation was done based on the diffusion experiment described by Ho et al. (2006a). In validation experiment 1 (measurement chamber 30 kPa O2, 0 kPa CO2, and 70 kPa N2; flushing chamber 5 kPa O2, 30 kPa CO2, and 65 kPa N2) and 2 (measurement chamber 20 kPa O2, 5 kPa CO2, and 75 kPa N2; flushing chamber 10 kPa O2, 20 kPa CO2, and 70 kPa N2), the initial gas conditions were chosen such that there was pressure built-up in the measurement chamber. In validation experiment 3, gas conditions were such that the difference in total pressure between the two chambers remained smaller than 1.5 kPa and permeation was negligible (measurement chamber 30 kPa O2, 3 kPa CO2, and 67 kPa N2; flushing chamber 5 kPa O2, 8 kPa CO2, and 87 kPa N2).
Transport of O2, CO2, and N2 was described by means of the convection diffusion model (equations 13 and 14) in which permeation through the barrier of tissue by the pressure gradient is described by Darcy's law (equation 15). The parameters of O2 and CO2 diffusion and respiration were described by Ho et al. (2006a). The porosity of the pear tissue was taken equal to 0.07 (Schotsmans et al., 2004). was set to –2.47x10–4 mol m–3 s–1 and 
was set equal to 
(Ho et al., 2006a). The system (13) to (15) of transport equations was solved by means of the finite element method. The measurement chamber and the sample tissue were considered as two materials consisting of 20 1D linear elements each resulting in 41 nodes in total. The diffusion coefficient of the gas molecules in air at 20 °C was set equal to 6x10–5 m2 s–1 (Lide, 1999). The discretization was carried out in the Femlab 3.1 package (Comsol AB, Stockholm, Sweden). More details can be found in Ho et al. (2006a).
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Results |
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O2 and N2 diffusivities
In Fig. 4, the O2 and total pressure profiles in the measurement chamber are shown as a function of time. The O2 partial pressure decreased while the total pressure profiles were almost constant during the measurement. As there was no pressure built-up in the measurement chamber, permeation was negligible in this case; the permeation term in the left-hand side of equation (13) was therefore omitted. At the beginning of the experiment, a step decrease of the total pressure in the measurement chamber in Fig. 4 indicated that the in- and outlet valves of the measurement chamber were closed to stop flushing. In the measurement chamber the high O2 partial pressure caused O2 transport from the measurement to the flushing chamber while N2 diffused in the opposite direction from the flushing chamber to the measurement chamber, which was at a lower N2 partial pressure. The diffusivity of N2 was estimated based on the total pressure profile and the O2 partial pressure profile in the measurement chamber. In addition, the diffusivity of O2 was also estimated and compared with N2 diffusivity. The results are given in Table 1. The diffusivity of N2 was more or less equal to the diffusivity of O2 in the cortex tissue. A paired t test showed that there was no significant difference between the O2 and N2 diffusivity. Furthermore, a t test between groups of samples showed that the diffusivity of the skin was the smallest, and the diffusivity in the vertical axis was higher than the diffusivity along the radial direction.
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Gas permeation properties
In Fig. 5, the pressure profile in the measurement chamber as a function of time is shown for a typical permeation experiment with pure N2. The gas transport from the measurement chamber to the flushing chamber by permeation caused a pressure decrease during time. Figure 5 shows that the decrease of pressure for tissue samples along the vertical axis of the pear was faster compared with tissue samples along the radial direction. The model described the experimentally determined values very well. The resulting estimated permeation coefficients are shown in Table 1. The average values for the permeation coefficients of the skin, cortex tissue along the radial direction and vertical axis were (2.17±1.71)x10–19 m2, (2.35±1.96)x10–19 m2, and (4.51±3.12)x10–17 m2, respectively (Table 1). A high variation was found for the estimated values. From a statistical analysis, the estimated permeation values of the skin and cortex tissue along the radial direction were not significantly different, while the permeation coefficient of tissue along the vertical axis was much higher compared with the permeation coefficient of cortex tissue along the radial direction. The temperature of the set-up was also important since the total pressure in the measurement chamber changed with temperature according to the ideal gas law. Small fluctuations of the experimental values are due the fluctuation of the temperature during the measurement. A change of 0.5 °C in temperature gave an effect of about 0.17 kPa on the total pressure in the measurement chamber.
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Validation
In validation experiments 1 and 2, the initial gas conditions in the measurement chamber were chosen in such a way that large CO2 concentration between the two chambers was created. Due to the larger diffusivity of CO2 in cortex tissue compared with those of O2 and N2, a pressure rise was noticed during the measurement. Plots of the measurement data, the simulation of gas transport with permeation and without permeation are shown in Fig. 6. At the beginning of the experiment, a step decrease of the total pressure in the measurement chamber in Fig. 6 indicated that the in- and outlet valves of the measurement chamber were closed off from flushing. Validation showed that the model with permeation was more in agreement with the experiment compared with the diffusion only.
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In validation experiment 3, the difference in total pressure between the two chambers was smaller than 1.5 kPa. A good agreement was found for both simulations between measurements and model predictions (Fig. 6). The effect of the permeation term in the equation on the gas transport was small in this experiment. The simulated profile of the O2 partial pressure in the measurement chamber as a function of time in the diffusion model coincided with the diffusion model incorporating permeation. The permeation term in the left-hand side of the equation (13) is not important in this case and gas permeation can be considered negligible for estimating diffusion parameters.
The total pressure in the measurement chamber for the three validation experiments is shown in Fig. 7. Variability between replicate measurements due to biological variability is clearly visible. A good agreement was found between the models and experiments with different initial gas conditions.
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Discussion |
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O2 and N2 diffusivity
The results show that there was no significant difference between O2 and N2 diffusivity. During the whole experiment the total pressure drop over the sample was constant and very small to non-existent (<0.5 kPa). Because the experiment was done for binary gas mixtures, the constant pressure in the measurement chamber implied that N2 molecules diffuse at the same rate in the opposite direction to the O2 molecular diffusion. Further, O2 and N2 have a comparable and low solubility in water. Therefore, gas exchange through the tissue for O2 and N2 probably happens through gas-filled intercellular space, where diffusion is the main mechanism.
The results obtained in this research for the diffusivity of O2 of the skin, cortex tissue along the radial direction, and cortex tissue along the vertical direction were (0.1±0.034) x10–9 m2 s–1, (0.28±0.15)x10–9 m2 s–1, and (1.11±0.71)x10–9 m2 s–1 while the diffusivity of N2 of the skin, cortex tissue along the radial direction, and cortex tissue along the vertical direction were (0.106±0.032)x10–9 m2 s–1, (0.267±0.17)x10–9 m2 s–1, and (1.08±0.71)x10–9 m2 s–1. Measurement of the O2 and CO2 diffusivity by Ho et al. (2006b) showed that O2 diffusivities in the skin, cortex tissue along the radial direction, and cortex tissue along the vertical direction was (0.186±0.078)x10–9 m2 s–1, (0.222±0.037)x10–9 m2 s–1, and (1.11±0.72)x10–9 m2 s–1 while the CO2 diffusivity in the skin, cortex tissue along the radial direction, and cortex tissue along the vertical direction was (0.506±0.315)x10–9 m2 s–1, (2.32±0.21)x10–9 m2 s–1, and (6.97±3.79)x10–9 m2 s–1. A good agreement was found between the O2 diffusivity in the present experiment compared to the values reported by Ho et al. (2006b).
Schotsmans et al. (2003) found that the O2 diffusivity of cortex and skin after 3 months of storage were (0.33±0.24)x10–9 m2 s–1 and (0.43±0.17)x10–9 m2 s–1, respectively. In a more recent publication, the same authors (Schotsmans et al., 2004) found that O2 diffusivity in the flesh of ‘Jonica’ (52.8x10–9 m2 s–1) and ‘Braeburn’ (16.2x10–9 m2 s–1) apples was much higher than that of pear flesh tissue. Zhang and Bunn (2000) also found similar O2 diffusivity values (18.1–19.0x10–9 m2 s–1) for different apple cultivars. We believe that the differences in diffusivity in fruit cultivars can be attributed to differences in intercellular space volume. In this context, Schotsmans et al. (2004) showed that the intercellular space volume of cortex tissue of ‘Jonica’ and ‘Braeburn’ apples was 16% and 10% while it was only 5–7% for ‘Conference’ pear. Ongoing research concentrates on multiscale models to provide further evidence for this hypothesis.
A higher diffusivity in the vertical axis compared with the diffusivity along the radial direction was observed. While vascular bundles are filled with sap in intact plants, they may be not fully filled with sap during storage of the fruit as it typically loses water. It is, therefore, well possible that the vascular bundles along the axis of the pear indeed facilitate gas transport. Moreover, the orientation of the cells along the vertical axis could be different from that of cells in the radial direction, and further difference in gas transport properties may be due to enhanced interconnectivity of the gas intercellular space along the vertical axis compared with the radial direction. Sorz and Hietz (2006) also found that O2 diffusion in wood in axial direction was one to two orders of magnitude faster than in the radial direction.
Effect of gas permeation
The results indicate that estimated permeation values of the skin and cortex tissue in the radial direction were not significantly different while the permeation of tissue along the vertical axis was much higher compared with the permeation in the cortex tissue in the radial direction. The permeation coefficient for the gas along the vertical axis was high compared to the radial direction (Table 1). The bulk gas transport along the vertical axis is probably facilitated by means of better continuity of the gas filled spaces.
The permeation coefficient of the tissue may contribute to gas transport besides diffusion; the CO2 diffusivity of the tissue was higher than the O2 diffusivity (Marcellin, 1974; Lammertyn et al., 2001; Schotsmans et al., 2003, 2004; Ho et al., 2006a). The produced CO2, therefore, leaves the fruit at higher rates than O2 is entering the fruit. This may lead to a pressure difference between the inside of the fruit and the external atmosphere. A pressure rise was found in the measurement chamber in diffusion measurement for specific initial gas conditions (Ho et al., 2006a). In gas transport experiments with a mixture of gases, for example gas diffusion in fruit, the total pressure changes should be considered carefully, and if significant, permeation should be included. Because the O2 consumption rate and CO2 production rate were not the same in pear, permeation plays an important role in balancing the total pressure inside the fruit to the external environment.
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Conclusion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionConclusionReferences |
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A measurement set-up for gas permeation in fruit tissue based on unsteady-state gas exchange was developed. An analytical model described the experimental estimated permeation well. Permeation coefficients of the skin and tissue along the radial direction were more or less equal while permeability in the vertical axis was higher than along the radial direction. The permeation–diffusion–reaction model can be applied to study the gas transport in whole intact fruit.
While the model validation results were reasonably well correlated, a discrepancy between measured gas concentrations and model predictions remains. We believe that this is mainly due to the fact that, contrary to typical engineering materials such as steel or brick, biological tissue cannot be considered as a continuum material because of its cellular nature. A continuum model such as the one proposed in this article should, therefore, be considered as phenomenological and the transport properties as apparent properties. Multiscale transport models are currently being developed by the authors to quantify the cellular and intercellular pathways for gas transport and to improve agreement further between measured and predicted gas concentrations at the expense of much more computer resources.
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Acknowledgements |
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The authors wish to thank the research council of the KU Leuven (project IDO/00/008, OT 04/31) for financial support. Acknowledgement is extended to the International Relations Office of the KU Leuven (IRO Scholarship). Pieter Verboven is postdoctoral researcher of the Flemish fund for Scientific Research (FWO-Vlaanderen).
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References |
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