Transport of ions through a cylindrical membrane: Effect of radius

Abstract

The performance of a cylindrical ion‐selective membrane of arbitrary radius is investigated theoretically. In particular, the effect of the radius of the membrane on its current efficiency is examined without assuming local electroneutrality and Donnan equilibrium. Two types of fixed charge distribution are considered, namely, linear and sinusoidal. The results of numerical simulation reveal that the boundary condition at the axis of a membrane should be assumed appropriately. We show that if the inner radius of a membrane is smaller than its thickness, assuming bulk conditions at the membrane axis is inadequate. Also, the potential drop across a membrane will change its sign, which is disadvantageous to the transport of ions.