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

Abstract

Abstract 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 (P1/2) 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.