Nernsthyphen;Planck Equations and the Electroneutrality and Donnan Equilibrium Assumptions

摘要

The Nernsthyphen;Planck flux equations and Poisson's equation are used to describe the transport of ions across a membrane carrying a fixed charge. The resulting problem is studied using a perturbation theory in order to derive the sohyphen;called ldquo;electroneutralityrdquo; condition as a certain limiting case. It is found that the electroneutrality condition is a consequence of Poisson's equation when a certain dimensionless parameter is small. It is also shown that a Donnan equilibrium at the membrane boundaries is a consequence of the Nernsthyphen;Planck equations when this dimensionless parameter is small, and a separate assumption of such an equilibrium is redundant. The small parameter can be interpreted as the ratio of a Debye length and the membrane thickness.