LAW OF SUBSTANCE SEPARATION ON CROSS-FLOW FILTRATION IN TURBULENT-FLOW

Cross-flow filtration is a filtration process for separation of a disp erse phase from liquids. Suspension flows tangentially to a membrane a nd the filtrate is drawn off perpendicular to the direction of flow. F ormation of a filter cake on the membrane is thus prevented, reduced, or its composition modified. The principle of the separation is based on two opposing effects: on the one hand, the particles are transporte d by the filtration flux to the membrane where they cause an increase in concentration; on the other hand, concentration differences are aga in reduced by the turbulence of the cross-flow and by Brownian motion of the particles. The two mechanisms compete with each other and depen d upon particle size in different ways. An energetic comparison of the two effects yields the separation law of cross-flow filtration asa st eady state solution of the Fokker-Planck equation. The separation law has an exponential form and assigns each particle size a separation pr obability with which it reaches the membrane. Once on the membrane the particles may form a filter cake, flow through the pores or return to the bulk flow. If the particles remain on the membrane the ranges of layer-free and cake-forming filtration can be calculated from the hydr odynamic and geometric conditions of the cross-flow filter. Convention al cake filtration is regarded as limiting case. In continuous cross-f low filtration processes a low separation probability through the filt ration pressure on selection of the filter medium resistance.