Asymptotic behaviour in the pressure-driven separations of ions of different mobilities in charged porous membranes

Abstract

The pressure-driven transport of electrolyte mixtures with common coion through charged porous membranes has been studied theoretically. The mode of exponential increase of rejection of more mobile counterions with increasing transmembrane volume flow previously predicted in the approximation of one dominant salt has been found to occur at quite noticeable feed mole fractions of more mobile counterions, too. That is caused by their dynamic exclusion from the membrane phase by the electric field of filtration potential. The rejection of less mobile counterions may become strongly negative at larger transmembrane volume flows. The exponential increase in the rejection of more mobile counterions accompanied by negative rejections of less mobile ones corresponds to their strong separation. Concentrational polarisation has been accounted for within the scope of model of unstirred Nernst layer. Moderate concentrational polarisation does not suppress the exponential mode, and the separation remains quite strong whereas a stronger concentrational polarisation suppresses it completely. Criteria of acceptable concentrational polarisation have been formulated. Some of predicted qualitative features of rejection of counterions of different mobilities by charged porous membranes have been confirmed by experimental data found in the literature.