Abstract
A theoretical model of crossflow microfiltration which includes the time-dependent decline of permeate flux due to particle layer buildup is presented. The model is based on the shear-induced hydrodynamic diffusion mechanism of particle motion within a concentrated flowing layer near to the membrane surface, balancing the convectively-driven flux of particles toward the membrane surface. The complete convective-diffusion equation is satisfied when integrated across the concentrated particle layer. This model is an extension of an earlier model which describes the steady-state behavior of crossflow microfilters and it includes the possibility of a stagnant particle layer forming between the membrane surface and the concentrated flowing layer. The method of characteristics is used to solve the partial differential equation governing the variation of the permeate flux and of the particle layer thickness and structure, with both time and axial position. The effects of suspension concentration, particle size, shear rate and other parameters are discussed.
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