Analytical solution of the Poisson–Nernst–Planck–Stokes equations in a cylindrical channel

Abstract

We present a complete analytical solution for electro-kinetic flow of an acidic solution in an infinite, circular, cylindrical channel. The flow of protons and water is described by Poisson–Nernst–Planck equations, coupled to Stokes flow, while negative charges, situated along the walls, maintain electro-neutrality. Several system characteristics are computed in closed form such as the velocity profile, mass flux, current and water drag. The two latter quantities allow for a comparison of analytical results with experimental data of systems such as polymer electrolyte membranes.