Interaction of Ionic Solution with Permeable Membranes: A Variational Approach (Journal of Mathematical Study, 2024)
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 isall about the movement of ionic solutions, on various scales. Many cells, tissues, andorgans of animals and plants depend on osmosis, as the movement of fluids is calledin biology. Indeed, the movement of fluids through channel proteins (that have a holedown their middle) is fluidics on an atomic scale. Ionic fluids are complex fluids, withenergy 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 ofsharp interface models are derived for ionic solution with permeable membranes. Byusing the energy variation method, the unknown flux and interface conditions are derived consistently. We start from the derivation the generic model for the general casethat the density of solution varies with ionic solvent concentrations and membrane isdeformable. Then the constant density and fix membrane cases are derived as specialcases of the generic model.
Keywords: Permeable membrane; ionic solution; osmotic pressure; transmembrane flux.