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.
