  Ionic electrodiffusion and osmotic water flow are central processes in many
physiological systems. We formulate a system of partial differential equations
that governs ion movement and water flow in biological tissue. A salient
feature of this model is that it satisfies a free energy identity, ensuring the
thermodynamic consistency of the model. A numerical scheme is developed for the
model in one spatial dimension and is applied to a model of cortical spreading
depression, a propagating breakdown of ionic and cell volume homeostasis in the
brain.
