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Phenomenological Relations for Water Diffusion Across Ion-Exchange Membranes
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Measurements have been made of water diffusion across ion-exchange membranes induced by chemical and electrical potential differences. The experimental results have been interpreted in terms of linear phenomenological equations. These relationships have been used to estimate the magnitudes of the phenomenological coefficients for water transfer across ion-exchange membranes. The validity of the linear phenomenological equation for water transfer under combined chemical and electrical potential differences has been tested by direct measurements. The dependence of the phenomenological coefficients on membrane properties and the ion species has been determined.

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Measurements of electromotive force and transport numbers across ion-exchange membranes
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Direct measurements of electromotive force and transport numbers for sodium ion and water have been made across polystyrene-sulfonic acid ion-exchange membranes separating different solutions of sodium chloride over a wide range of external solution concentration. The results indicate that the electrochemical potentials corresponding to the reversible transport of sodium chloride and water may be measured with a reasonably high degree of precision using polystyrene-sulfonic acid ion-exchange membranes even in highly concentrated solutions. The measured electrical transference numbers for sodium ion verify the estimates of transference numbers which have been made from ion-interchange fluxes obtained in counter-diffusion experiments across the same …

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Solvent Mass Transfer across Ion-Exchange Membranes
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A study of water diffusion across polystyrenesulfonic acid ion-exchange membranes, induced by osmotic pressure and cation diffusion potentials, has been made. The experimental results have been interpreted in terms of viscous interactions within the membrane during the transport process, between the ion and water, and between the water and membrane pore wall. Equations have been derived which relate solvent and ion transport rates with the viscous interactions within the membrane. These relationships were used to estimate friction coefficients for the interchange processes. The dependence of the ion-water interaction coefficient on inorganic and organic counterion diameter was determined.

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