Reversal permanent charge and concentrations in ionic flows via Poisson-Nernst-Planck models

Mofidi, Hamid

doi:10.1090/qam/1593

Author: Hamid Mofidi
Journal: Quart. Appl. Math. 79 (2021), 581-600
MSC (2020): Primary 34B15, 92B05; Secondary 34A26, 34E15
DOI: https://doi.org/10.1090/qam/1593
Published electronically: May 6, 2021
MathSciNet review: 4328139
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Abstract: This work examines the behavior of geometric mean of concentrations in various conditions when there is no electric current and studies the reversal permanent charge problem, the charge sharing seen in x-ray diffraction. The geometric mean of concentrations is an average of concentrations, which indicates the central tendency of concentrations by using the product of their values. Observations are acquired from analytical results established using geometric singular perturbation analysis of classical Poisson-Nernst-Planck models. For ionic mixtures of multiple ion species, Mofidi and Liu [SIAM J. Appl. Math. 80 (2020), 1908–1935] centered two ion species with unequal diffusion constants to acquire a system for determining the reversal potential and reversal permanent charge. They studied the reversal potential problem and its dependence on diffusion coefficients, membrane potential, boundary concentrations, etc. Here, we look at the dual problem of reversal permanent charge, its uniqueness, and its dependence on other conditions with the same approach. We consider two ion species with positive and negative charges, say Ca$^+$ and Cl$^-$, to determine the specific requirements under which the permanent charge is unique. Furthermore, we investigate the geometric mean of concentrations for various membrane potential and permanent charges values.

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