EQUIVALENCE BETWEEN NERNST-PLANCK AND CORRECTED FICKS LAW IN MODELINGFIXED-BED ION-EXCHANGE PROCESSES

An equivalence between the Nernst-Planck approach, which takes into ac count the diffusive and electrical contributions for intraparticle mas s transfer, and Fick's law, which considers only the diffusive contrib ution, is developed in this paper. This equivalence leads to the deter mination of a ''corrected'' diffusivity that enables the simulation of ion-exchange processes with the Fick approach. The development is bas ed on the comparison of the behavior of the processes in an infinite b ath, measured by the filling times for the particles; the ''corrected' ' Fick diffusivity obtained is tested against the solution with the Ne rnst-Planck model for column ion-exchange processes. It is able to sim ulate the processes in all but the cases when favorable equilibrium an d kinetics coexist. To cope with this situation, another equivalence i s developed based on the variance of the derivative of the breakthroug h curves. The same test shows that this last approach is able to simul ate all the situations.