  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 are 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.
