Capillary Model of a Charged Membrane With Variable Hydrophilicity and Hydrophobicity

The paper proposes a capillary model of a charged membrane consisting of a set of separated by impenetrable material plane-parallel slit hydrophilic pores, on the surface of which a zeta potential can be set, or a fixed charge density and a liquid adhesion condition, and hydrophobic pores that differ from hydrophilic ones in size, zeta potential (fixed charge density), and Navier slip condition. The hydrodynamic and electroosmotic permeability of the membrane and its electrical conductivity are derived as functions of relative hydrophilic and hydrophobic porosity, electrolyte concentration, surface charges or potentials, dielectric properties of the solution, ion diffusion coefficients and their charge numbers, and the sizes of both types of pores. In all cases, compliance with the Onsager reciprocity principle for cross coefficients L and L, responsible for the electroosmosis and the streaming current is shown. All boundary value problems for the four types of pores are solved analytically in the Debye-Hückel approximation. It has been established that, under the action of external pressure and electric potential gradients, in the case of aqueous organic mixtures against the background of a weak electrolyte solution, a multidirectional flow of components through the hydrophilic and hydrophobic pores of the membrane is possible. The results obtained make it possible to predict the transport properties of a charged membrane depending on the ratio between the fractions of hydrophilic and hydrophobic pores.