Permeate flux inflection due to concentration polarization in crossflow membrane filtration: A novel analytic approach.

A convection-diffusion equation for membrane filtration is analytically solved assuming fast crossflow velocity of a simple shear flow tangential to the membrane surface. In the direction normal to the membrane surface, solute concentration varies in a partially exponential and partially power-wise manner. The permeate flux in an asymptotic limit is proportional to the inverse square root of the distance from the inlet of the membrane channel. Osmotic pressure due to retained solutes on the membrane surface controls the profile of the permeate flux, which undergoes an inflection along the tangential direction if applied pressure is more than four times the feed osmotic pressure.