Interaction of Ionic Solution with Permeable Membranes: A Variational Approach

Interaction of Ionic Solution with Permeable Membranes: A Variational Approach

Year:    2024

Author:    Shixin Xu, Zilong Song, Robert Eisenberg, Huaxiong Huang

Journal of Mathematical Study, Vol. 57 (2024), Iss. 1 : pp. 24–52

Abstract

The movement of ionic solutions is an essential part of biology and technology. Fluidics, from nano-to microfluidics, is a burgeoning area of technology which is all about the movement of ionic solutions, on various scales. Many cells, tissues, and organs of animals and plants depend on osmosis, as the movement of fluids is called in biology. Indeed, the movement of fluids through channel proteins (that have a hole down their middle) is fluidics on an atomic scale. Ionic fluids are complex fluids, with energy stored in many ways. Ionic fluid flow is driven by gradients of concentration, chemical and electrical potential, and hydrostatic pressure. In this paper, a series of sharp interface models are derived for ionic solution with permeable membranes. By using the energy variation method, the unknown flux and interface conditions are derived consistently. We start from the derivation the generic model for the general case that the density of solution varies with ionic solvent concentrations and membrane is deformable. Then the constant density and fix membrane cases are derived as special cases of the generic model.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v57n1.24.02

Journal of Mathematical Study, Vol. 57 (2024), Iss. 1 : pp. 24–52

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Permeable membrane ionic solution osmotic pressure transmembrane flux.

Author Details

Shixin Xu

Zilong Song

Robert Eisenberg

Huaxiong Huang