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Computational Modeling of Membrane Blockage via Precipitation: A 2D Extended Poisson-Nernst-Planck Model

In: Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

Author

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  • H. Lefraich

    (Faculty of Sciences and Technology, Department of Mathematics and Computer Science, University Hassan First, Laboratory (MISI))

Abstract

The mathematical modeling and simulation of ion transport through biological membranes are a challenging problem with direct applications in biology and biophysics. The most important aim of this research is to develop a generalized mathematical model for a diffusion-migration-reaction system, which incorporates a pore blockage effect caused by the generation of insoluble precipitates in a porous membrane. While creating such model, both the electrostatic interactions of ions and the effects due to the buildup of solid reaction products in the membrane have to be taken into account. Consequently, the system behavior is investigated via the numerical simulation of an extended, highly nonlinear equation set based on the classical Poisson-Nernst-Planck equations for ion transport. This formulation incorporates both a reaction term and a space-and time-dependent diffusivity which often seem to be ignored and are not computed in currently used models. The need of incorporating nonlinear mobilities is demonstrated in an investigation of the time-dependent concentration profiles for all ions in the membrane and also the effects of precipitate buildup in the pore space.

Suggested Citation

  • H. Lefraich, 2023. "Computational Modeling of Membrane Blockage via Precipitation: A 2D Extended Poisson-Nernst-Planck Model," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, pages 375-388, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33050-6_21
    DOI: 10.1007/978-3-031-33050-6_21
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