Abstract

We discuss the transport properties of an ion-exchange membrane which separates two 1-1 type electrolyte solutions of different concentration. With the help of the Boltzmann independent scattering assumption, we construct two different models of diffusion of ion pairs through the membrane under the concentration gradient (biased diffusion). The first model is the phenomenological one-step Markov process, where in the mean-field type approximation we obtain the exact formulae for the total probability flux of the ion pairs through the membrane and their profile density. The second model is constructured in a similar way, but it includes the exact two-dimensional geometry of the percolating network. We compare these two models near the percolation threshold and find that they have similar behavior for small values of the bias field.

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