Mathematical Modeling of the Selective Transport of Singly Charged Ions Through Multilayer Composite Ion-Exchange Membrane during Electrodialysis

The deposition of several alternating anion- and cation-exchange surface layers (layer-by-layer method) is a promising technique for the modification of ion-exchange membranes, which makes it possible to essentially increase their selectivity to singly charged ions. This paper presents a one-dimensional model, which is based on the Nernst–Planck–Poisson equations and describes the competitive transfer of singly and doubly charged ions through a multilayer composite ion-exchange membrane. It has been revealed for the first time that, as in the earlier studied case of a bilayer membrane, the dependence of the specific permselectivity coefficient (P_1/2) of a multilayer membrane on the electrical current density passes through a maximum \(\left( {P_{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}^{{\max }}} \right).\) It has been shown that an increase in the number of nanosized modification bilayers n leads to the growth of \(P_{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}^{{\max }},\) but the flux of a preferably transferred ion decreases in this case. It has been established that \(P_{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}^{{\max }}\) is attained at underlimiting current densities and relatively low potential drop. The simulated dependences \(P_{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}^{{\max }}\)(n) qualitatively agree with the known literature experimental and theoretical results.