Numerical modelling of nonequilibrium electrokinetic phenomena in porous media containing ion-permselective spatial domains

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This work is concerned with a three-dimensional, high-resolution numerical simulation of electrokinetic transport through porous media containing discrete ion-permselective, i.e., charge-selective spatial domains, covering coupled mass and charge transport through nanopores in ion-exchange membranes (flat interface) and porous particles in fixed beds (curved interfaces). By implementing novel, advanced numerical schemes (lattice-Boltzmann method and lattice-based algorithms) for a solution of the coupled Poisson-Nernst-Planck and electrohydrodynamic problems in three-dimensional porous media, it is possible to correlate microscopic details of a solid-liquid interface (surface charge density; local pH and ionic strength; surface geometry) and actual pore space morphology (pore shape, interconnectivity, and size distribution; average porosity) with the electrokinetics and hydrodynamics evolving on mesoscopic length scales, as well as with the macrotransport theory. Particular attention will be devoted to the spatio-temporal dynamics of concentration polarisation and extended, electrical field-induced space charge regions which may develop due to coupled mass and charge transport normal to a charge-selective interface under the influence of externally applied electrical fields. The induced-charge electroosmosis (part of a yet hardly discovered class of nonlinear electrokinetic phenomena) can explain the occurence of overlimiting conductance in electrodialysis, or electrokinetic instability in sphere packings. These phenomena are analysed and tailored for reducing limitations to coupled mass and charge transport in porous media arising from concentration polarisation.