The equations for a model of water and solute transport across membranes bearing surface charges are derived. Charged species can be transported actively and by a combination of passive diffusion and convection through pores. Separate pores for each ion can be incorporated. Because convection is present, no simple Goldman-like equation for the overall potential difference across the membrance is obtainable. It is shown that for the range of surface charge densities reported in the literature, the potential drop through the external double layers is a significant portion of the measured transmembrane potential difference.
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