A theoretical model of dead-end microfiltration (MF) of dilute suspensions is proposed. The model is based on a sieve mechanism of MF and takes into account the probability of membrane pore blocking during MF of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and the particle size distributions is deduced. According to the suggested model a similarity property is applicable, which allows one to predict the flux through the membrane as a function of time for any pressure, and dilute concentration, based on one experiment at a single pressure and concentration. The suggested model includes only one fitting parameter, beta > 1, which takes into account the range of the hydrodynamic influence of a single pore. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in good agreement with the measurements on different track-etched membranes. A simple approximate solution of the IDE is derived and that approximate solution, as well as the similarity principal of MF processes, is in Lood agreement with measurements using a commercial Teflon microfiltration membrane. The theory was further developed to take into account the presence of multiple pores (double, triple and so on pores) on a track-etched membrane surface. A series of new dead-end filtration experiments are compared with the proposed initial and modified pore blocking models. The challenge suspension used was nearly monodispersed suspension of latex particles of similar to0.45 mum filtered on a track-etched membrane with similar sized pores similar to0.4 mum. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the cross-membrane pressures varied from 1000 to 20,000 Pa. Three stages of microfiltration have been observed. The initial stage is well described by the proposed pore blocking model. The model required only a single parameter that was found to fit all the data under different experimental operational conditions. The second stage corresponds to the transition from the blocking mechanism to the third stage, which is cake filtration. The latter stage occurred after approximately 10-12 particle layers were deposited (mass = 0.006 g) on the surface of the microfiltration membrane. (C) 2003 Elsevier B.V. All rights reserved.
