Dynamic crossflow ultrafiltration of colloids: a deposition probability cake filtration approach

Abstract A description of the dynamic, time-dependent ultrafiltration of charged colloids has been developed by combining an adhesion model for crossflow filtration of non-interacting particles with a Wigner–Seitz cell model for frontal filtration of charged colloidal dispersions. The adhesion model helps provide a criterion for the deposition of particles in a filter cake on the membrane surface. The Wigner Seitz cell model provides a quantitative description of the hydraulic resistance of the resulting filter cake. Two means of evaluating the deposition probability of charged colloidal particles have been considered — a cell based approach and an adjustable parameter approach, which was subsequently combined with multiple linear regression. The latter combined approach gave excellent agreement with experimental filtration flux–time data for silica colloids as a function of applied pressure, particle concentration, ionic strength and pH. Overall, this is a relatively simple yet useful means of correlating the time-dependent performance of such a membrane process over a wide range of operating conditions.