14-17 May 2018
New Orleans
US/Central timezone

A multiscale two-equation reaction-diffusion porous media model of gas exchange in apple fruit

17 May 2018, 09:44
New Orleans

New Orleans

Oral 20 Minutes GS 4: Porous media applications (renamed) Parallel 9-E


Dr Pieter Verboven (KU Leuven - University of Leuven, Division BIOSYST-MeBioS)


Pome fruit such as apple are harvested mature but unripe, stored at low temperature (typically -1.0 to 3°C) in combination with a reduced O2 and increased CO2 partial pressure in so-called controlled Atmosphere (CA) storage. This is done to delay climacteric ripening, and, hence, extend their storage life. The optimal storage gas composition is critical, as too low O2 levels in combination with too high CO2 levels may induce fermentation in the fruit. This causes off-flavours (e.g., ethanol) and storage disorders (e.g., flesh browning). Using a materials engineering approach fruit tissue is considered a microporous structure consisting of parenchyma cells with air spaces in between. Based on in silico experiments we have shown that large concentration gradients and anoxic zones may indeed occur in pome fruit. Porosity and connectivity of the intercellular spaces have been shown to affect O2 and CO2 transport to a large extent. We previously developed a homogenized reaction-diffusion model to study gas exchange of intact fruit at the macroscale level, which was based on the assumption of gas-liquid equilibrium in the cellular material, of which the material properties were determined from microscale simulations in a multiscale approach. Here we explore if the equilibrium assumption holds by developing and solving a two-equation model at the macroscale, which distinguishes transport in gas and liquid phase separately with mass transfer between the phases.
To identify the model parameters of the macroscale two-equation model, a microscale model was developed. To this end, the 3-D tissue geometry of apple (cv. Jonagold) tissue obtained from X-ray microtomography was processed to calculate geometrical parameters (porosity and specific surface of the interface). The microstructure was also input for an adapted voxel based finite volume code that calculated effective gas transport properties of the two phases of the apple tissue separately. The two-equation model was then solved using finite elements on the reconstructed geometry of apple fruit and the resulting internal gas profiles were compared to those obtained from the one-equation equilibrium model. Under the same conditions and values of interphase permeability and respiration rates previously used in our analyses, the two-equation model did not have significant differences with the one-equation model, which is more than 5 times faster to solve. We also explored if realistic value ranges of permeability and reaction rates exist for which the one-equation would not be valid and the two-equation solution would be required.


Ho Q., Rogge S., Verboven P., Verlinden B., Nicolai B. (2016). Stochastic modelling for virtual engineering of controlled atmosphere storage of fruit. Journal of Food Engineering, 176, 77-87.

Herremans E., Verboven P., Hertog M., Cantre D., van Dael M., De Schryver T., Van Hoorebeke L., Nicolai B. (2015). Spatial development of transport structures in apple (Malus × domestica Borkh.) fruit. Frontiers in Plant Science, 6, art.nr. 679, 679.

Herremans E., Verboven P., Verlinden B., Cantre D., Abera M., Wevers M., Nicolai B. (2015). Automatic analysis of the 3-D microstructure of fruit parenchyma tissue using X-ray micro-CT explains differences in aeration. BMC Plant Biology, 15 (264), art.nr. 10.1186/s12870-015-0650-y, 1-14.

Rogge S., Defraeye T., Herremans E., Verboven P., Nicolai B. (2015). A 3D contour based geometrical model generator for complex-shaped horticultural products. Journal of Food Engineering, 157, 24-32.

Ho Q., Verboven P., Fanta S., Abera M., Retta M., Herremans E., Defraeye T., Nicolai B. (2014). A multiphase pore scale network model of gas exchange in apple fruit. Food and Bioprocess Technology, 7 (2), 482-495.

Ho Q., Carmeliet J., Datta A., Defraeye T., Delele M., Herremans E., Opara L., Ramon H., Tijskens E., van der Sman R., Van Liedekerke P., Verboven P., Nicolai B. (2013). Multiscale modeling in food engineering. Journal of Food Engineering, 114 (3), 279-291.

Ho Q., Verboven P., Verlinden B., Herremans E., Wevers M., Carmeliet J., Nicolai B. (2011). A 3-D multiscale model for gas exchange in fruit. Plant Physiology, 155 (3), 1158-1168.

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Primary authors

Mr Siem Janssen (KU Leuven - University of Leuven, division BIOSYST-MeBioS) Dr Susana Zorrilla (INTEC (CONICET - Universidad Nacional del Litoral)) Prof. Bart Nicolai (KU Leuven - University of Leuven, Division BIOSYST-MeBioS; VCBT – Flanders Centre of Postharvest Technology) Dr Pieter Verboven (KU Leuven - University of Leuven, Division BIOSYST-MeBioS)

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