Expression for the transport of ions through a spherical ion-exchange membrane

The current efficiency of a spherical ion-selective membrane is examined theoretically. A perturbation method is adopted to solve the Nernst-Planck equation governing the spatial variation of the concentration of ions in the membrane phase for the case where the distribution of fixed charge is a linear function of radial position. The result of numerical simulation reveals that the qualitative behavior of spherical membranes is similar to that of cylindrical membranes. For example, if the fixed charge is uniformly distributed, the current efficiency is independent of both the inner radius (or curvature) of a membrane and the applied current density, and the current efficiency of a membrane can be raised by choosing its parameters appropriately. A general expression for planar, cylindrical, and spherical membranes is also discussed. (C) 1999 Elsevier Science B.V. All rights reserved.