DIMENSIONAL ANALYSIS OF STEADY-STATE FLUX FOR MICROFILTRATION AND ULTRAFILTRATION MEMBRANES

Dimensional analysis of the mass, length and time shows that the stead y state flux observed for microfiltration or ultrafiltration through i norganic composite membrane can be expressed using two dimensionless n umbers. The shear stress number N-s compares the shear stress against the membrane wall to the driving pressure, while the resistance number N-f compares the convective cross-flow transport to the drived transp ort through a layer, whose resistance is the sum of all the resistance s induced by the different processes which limit the mass transport. E xperimental data obtained in ultrafiltration of hydrocarbon emulsions and microfiltration of methanogenic bacteria suspensions and secondary treated wastewater were recalculated in terms of these dimensionless groups. Straight lines were plotted whose slope depends solely on the suspension and the membrane and not on the solute concentration. A neg ative slope and a positive intersection with the Na axis means that a cake layer or a polarization layer can be completely eliminated at a c ritical cross-flow velocity; this was the case for an inorganic partic les suspension and for the methanogenic suspension. A straight line of negative slope followed by a plateau means that an irreversible fouli ng is superimposed to the reversible phenomenon; this was observed for a secondary treated wastewater. A positive slope means that fouling p redominates; this was observed with hydrocarbon emulsions. (C) 1998 El sevier Science B.V.