A number of CFD studies have demonstrated that there is a considerable inhomogeneity of extent of Concentration Polarization (CP) over the membrane surface especially in spacer-filled feed channels. However, the consequences of this inhomogeneity for the interpretation of measurements of solute rejection in pressure-driven membrane processes have received little attention. This study uses a simple model of locally-1D CP combined with a postulated probability distribution of unstirred-layer thickness over the membrane thickness. In this way, we obtain transparent analytical results and can consider qualitative consequences of inhomogeneous distribution of CP over membrane surface. Our analysis shows that disregarding the CP distribution under-estimates the CP of strongly positively-rejected solutes and over-estimates the CP for the negatively-rejected ones. This observation is especially important for the interpretation of ion rejection from multi-ion solutions in nanofiltration where strong positive and pronounced negative rejections can occur simultaneously for solutes of different charges. We conclude that for reliable interpretation of pressure-driven membrane measurements it is desirable to reduce the inhomogeneity of CP distribution to a minimum in membrane-testing devices

Peer Reviewed