Simulation of internal diffusion for a selective ternary exchange of equally charged counterions

Variants of the exchange of three equally charged counterions [(B + E)/RA ( sorption)] at different values of the diffusion coefficients and selectivit y of the counterions were considered in terms of a model previously develop ed by the authors for the kinetic process in a selective ternary system. Th e basic assumption of the model is that, during the exchange process in gra ins of a selective ionite [accompanied by chemical reactions of B, E, and A counterions with fixed groups R: RA + (B + E) reversible arrow (RB + RE) A], these counterions can exist in fixed and free states. Counterions i ar e immobile in the bound state (Ri) and diffuse in the free state. The model involves mass balance equations for all ions, including the coion Y; the i onic fluxes involved in the equations are presented by the Nernst-Planck re lations. The influence of the association constants (K-RA, K-RB, and K-RE) and the diffusion coefficients (D-A, D-B, and D-E) of the counterions on th e character of the concentration waves of the diffusing components B, E, A, and Y and on the rate of the internal diffusion selective kinetic process in grains was considered on the basis of a theoretical analysis of computer simulation results. The effects of the main factors on the concentration w aves in the kinetic process were represented in the concentration-radius-ti me pseudo-three-dimensional space. It was found that the distinctions obser ved in the profiles of the concentration waves of the counterions and the d ifferences in the rates of the kinetic processes are due to different combi nations of the diffusion coefficients and selectivity, constants. It was sh own that these factors have an influence on the height of the maximum in th e sorption-intermittent desorption kinetic curve, an anomalous effect that is occurred only in the exchange-sorption regime and for only one of the tw o entering counterions (B or E). In this case, early in the process, the di splaced counterion diffuses counter to the concentration gradient of the mo re mobile selectively entering counterion (the concentration front is displ aced toward the grain center). This effect is due to the action of the elec tric field arising during the process.