The constant field approximation: Numerical evaluation for monovalent ions Migrating across a homogeneous membrane

Abstract

This paper has numerically evaluated the “error” incurred by assuming constant electric field for electro-diffusion processes across homogeneous membranes. For the constant field assumption to be exact, the net electric charge density in the membrane must be zero. However, the assumption of constant field, ΔV/δ and the consequent integration of the Nernst-Planck flux equation leads to ion concentration profiles which give a non-zero charge density which we call the “error charge density”, ϱ e( x). ϱ e( x) was integrated via the Poisson equation to determine an “error electric field”, E e( x). The constant field assumption, the Nernst-Planck flux equations and the Poisson equation are all mutually compatible within the error specified by ∥ E e ( x)∥[ ΔV/ δS] −1..