Influence of the convective term in the Nernst-Planck equation on properties of ion transport through a layer of solution or membrane

The one-dimensional boundary-value problem of steady-state ion transport, which takes into account the convective component, is formulated and solved in terms of the Nernst-Planck model. This problem is investigated in connection with the diffusion layer, which is understood in a broad sense. This can be the diffusion layer as it is usually understood, i.e., located adjacent to a hydraulically permeable membrane. In another context it can be regarded as a capillary connecting two reservoirs filled with solutions of different concentration or as an uncharged macropore permeating the membrane and separating two solutions. Finally, the solution to the problem is applied to the membrane itself, which is represented as a quasi-homogeneous gel. In the latter case, a virtual electroneutral solution in local equilibrium with a small volume of membrane is considered. The problem is investigated in dimensionless form as a function of the Peclet number. It is shown that the Peclet number is numerically equal to the absolute value of the dimensionless convection velocity. The limiting current, concentration profiles, distributions of the field strength and potential, and effective transport numbers are analyzed as functions of the convective component.