A model of electrodiffusion and osmotic water flow and its energetic structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies is dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.

► We propose a PDE model for electrodiffusion and osmosis appropriate for cell physiological systems. ► The model consists of PDEs for ionic concentrations and fluid flow, with interface conditions at deforming membranes. ► The model has a free energy functional that is decreasing when active currents are not present. ► Non-dimensionalization is performed to derive reduced models. ► A simple application to cell volume control is presented.