Note on the validity of constant field assumption in relation to the exact solution of Nernst-Planck equations

Abstract

By means of the exact solution of the Nernst-Planck equations, it can be demonstrated that the constant electric field assumption is incompatible with the stationary flows of ions in the homogeneously charged membrane. The exact solution of the Nernst-Planck equation system is readily given by the power series expansion method. The constant field assumption is valid for membrane in which the fixed charge can move freely and neutralize the charge of permeating ions. The parabolical electric potential is shown to be incompatible with the homogeneously charged membranes including the neutral membranes.