Effect of Convective Boundary Layer on the Current Efficiency of a Membrane Bearing Nonuniformly Distributed Fixed Charges

Abstract

The current efficiency η of a planar membrane bearing nonuniformly distributed fixed charges is analyzed theoretically. In particular, the effect of the convective boundary layer near the outer boundary of the membrane is discussed. Two types of fixed charge distribution are considered: a class of linear distribution and a class of exponential distribution. We show that, if the flow velocity in the membrane phase is small, increasing the inhomogeneity of fixed charge distribution is capable of raising η. However, if it is appreciable, the reverse is true. If a boundary is present, η decreases with the increase in current density; the reverse is true if it is absent. The former is due to the fact that the degree of concentration polarization in the boundary layer increases with current density. Although the existence of a boundary layer has the effect of reducing η, the convective flow of fluid perpendicular to membrane has a positive effect on η. If a boundary layer is absent and the fixed charges are di...