The Nernst-Planck flux equations and Poisson's equation are used to describe the transport of ions across a membrane carrying a fixed charge. The resulting problem is studied using a perturbation theory in order to derive the so-called “electroneutrality” condition as a certain limiting case. It is found that the electroneutrality condition is a consequence of Poisson's equation when a certain dimensionless parameter is small. It is also shown that a Donnan equilibrium at the membrane boundaries is a consequence of the Nernst-Planck equations when this dimensionless parameter is small, and a separate assumption of such an equilibrium is redundant. The small parameter can be interpreted as the ratio of a Debye length and the membrane thickness.

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ABSTRACT. The boundary-value problem e/G") = [/ /'" -/' /"], /(0) = /"(0) = /'(I) = 0, /(I) = 1, is a version of Berman's problem and its solutions describe a laminar flow in a channel with porous walls. When 0 < e

The equation considered isIt is shown that for all R there is at least one solution, and for sufficiently large R there are at least three solutions. The asymptotic behavior as R -m is also studied. This equation arises in studying laminar flow in a porous channel.

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