Simulation of the internal diffusion process for the ternary exchange of equally charged counterions

The kinetic model previously developed for binary exchange was extended to ternary selective systems. The ternary exchange processes of equally charge d counterions of type (B + E)HA ("sorption") and of type A/(HB + HE) ("rege neration") were considered. The basic assumption of the model was that, dur ing the exchange process within the grains of a selective ion exchanger; co unterions i, are immobile in the bound state (Hi), and diffuse in the free state. The model involves mass balance equations for all ions, including th e colon (Y); the ionic fluxes are expressed by Nernst-Planck relations. The influence of the association constants K-RA. K-RB, and K-RE On concentrati on waves of the diffusing components B, E, A, and Y and on the rate of the internal diffusion selective kinetic process in the grains at identical val ues of the diffusion coefficient for the three counterions (D-A = D-B = D-E ) was considered on the basis of a theoretical analysis of computer simulat ion results. The effects of the main factors on the characteristics of conc entration waves in the-kinetic process were represented in the concentratio n-radius-time pseudo-three-dimensional space. A maximum in the sorption-int ermittent desorption kinetic curve was found. This unusual effect was obser ved only for the exchange (sorption) branch of the curve only for one of th e two entering counterions (B and E), namely,for the counterion with lower selectivity. In this case, early in the process, the concentration front of the least selective entering counterion was displaced toward the grain cen ter by the wave of the more selective counterion.