A COMPARATIVE THEORETICAL STUDY OF POTENTIAL DISTRIBUTION AND CONDUCTIVITY IN CATION- AND ANION-EXCHANGE NANOPOROUS MEMBRANES FILLED WITH TERNARY ELECTROLYTES

Abstract This work aims to investigate the characteristics of the radial electric potential distribution and the conductivity inside a cylindrical nanopore filled with a ternary electrolyte solution as a function of the sign of the fixed charge on the pore wall. We consider the mixture of a 1:1 symmetric electrolyte and a 2:1 asymmetric electrolyte, such as NaCl and MgCl 2 , so the solution presents two counter-ions in a cation-exchange membrane and two co-ions in an anion-exchange one. The Poisson–Boltzmann equation in cylindrical coordinates is solved by using the network simulation method. The velocity of the solution and the conductivity are obtained from the distribution of electric potential by using the modified Navier–Stokes equation and the Nernst–Planck flux equations. First, the radial electric potential distribution inside a nanopore is obtained for different values of the surface charge density on the pore wall. Second, the evolution with the fixed charge density of the average electric potential, the potential at the pore centre, the velocity or the electrophoretic mobility of the solution and the conductivity, including the convective and effective conductivities, is analysed for different values of the concentration of the divalent cation. The behaviour of all the above variables is justified by using simple analytical expressions derived from the total co-ion exclusion approximation in the limit of very high absolute values for the surface charge density on the pore wall.