A Cell Model of an Ion-Exchange Membrane. Hydrodynamic Permeability
A cell model formulated in terms of the thermodynamics of nonequilibrium processes has been proposed for an ion-exchange membrane. The membrane is assumed to consist of an ordered set of porous charged spherical particles placed into spherical shells filled with a binary electrolyte solution. The problem of determining all the kinetic coefficients in the Onsager matrix has been set and the general solution of the boundary value problem has been obtained for the cell. The consideration has been realized within the framework of small deviations of system parameters from their equilibrium values upon imposition of external fields. The boundary value problem has been analytically solved for determining the hydrodynamic permeability of the membrane under the Kuwabara boundary condition imposed on the cell surface. It has been found that, when the volume charge disappears, the equation for the permeability is transformed into the equation derived previously for an uncharged membrane. It has been shown that the hydrodynamic permeability (direct kinetic coefficient) of a cation-exchange membrane grows, tending to its limiting value, with increasing electrolyte concentration and decreases with a rise in the exchange capacity of ion exchanger grains.
This work was supported by the Russian Foundation for Basic Research (project no. 17-08-01287) (theoretical part) and the Ministry of Education and Science of the Russian Federation (project no. 14.Z50.31.0035) (processing of experimental data).
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