Modeling of concentration polarization layer evolution and breakthrough concentrations in dead-end hyperfiltration

An explicit determination of concentration correlations and auxiliary parameters for solutions may be paramount in assessing the geometry of concentration polarization layer (CPL) during dead-end hyperfiltration and transport of ions through low permeability clays. Different models have been proposed for hindered transient transport of water and ions. Most of these models depend on solute permeability, solute diffusivity, and reflection coefficient of the membrane. Some models can predict various parameters for simple ionic molecules well but few of these can be immediately extended to organo macromolecules without special modifications. A model that estimates effluent concentrations for simple molecules and macromolecules like ionic azo dyes prior to the gelation period on homoionic membranes is proposed. The proposed model depends on evolution of the CPL of whose evolution can also be estimated from Karman–Pohlhausen and film model methods. Sensitivity analyses indicated relative dependence of this model on the diffusion coefficient.