Kinetics of multicomponent ion-exchange mass transfer in ion exchangers with nonmonotonic behavior of kinetic curves: the displacement effect for diffusion concentration waves of ionic components

Abstract

A theoretical approach to simulation of the multicomponent mass transfer of ionic components in ion exchangers is reported. A computer model is proposed for use in contemporary theoretical studies of the kinetics of the nonlinear multicomponent mass transfer of ions in the matrix of ion exchangers. Propagating diffusion concentration waves in multicomponent ion-exchange systems for the mass transfer of ions in the ion-exchange matrices of arbitrary forms—namely, planar L membrane, r grain, and ro fiber—are calculated. All the results are presented within the framework of the notion of propagating diffusion concentration waves of ionic components in the matrices of ion exchangers. The idea that is used of concentration waves for the description of the multicomponent kinetics of the diffusion mass transfer yields a clear interpretation of the computer simulation results. The kinetics of the process of the multicomponent mass transfer of components is described theoretically on the basis of computer simulation by solving the set of differential equations in partial derivatives for the mass balance of components. The propagation of concentration waves is illustrated by my simulation graphs and animations showing visually the propagation and interaction-interference of multicomponent concentration waves in the matrices of the various above-mentioned forms. Different ion-exchange systems with simulation of the anomalous behavior of the Fi(T) kinetic curves (non-monotonic and with the presence of the maximum, Fmax) for one of the B+ + C+ ions entering into the R− matrix in the case of the R−A+/(B+ + C+) exchange version, with simultaneous computer simulation of the diffusion propagation of the multicomponent Xi concentration waves within the nonlinear mass transfer kinetics, are examined.