Abstract
During dead-end filtration, spatial non-uniformities in the velocity profile upstream of the membrane (for example, Poiseuille flow) can potentially lead to non-uniform retentate accumulation on the rejecting membrane. To investigate this effect, we model the filter plus accumulated retentate as a thin porous layer with spatially variable Darcian permeability. By replacing the thin porous layer with an appropriate distribution of stokeslets, expressions for the transmembrane velocity profile for a variety of retentate accumulation profiles and permeabilities are obtained. The time evolution of the retentate accumulation is then considered. Our results indicate that for physically realistic parameter values the retentate will almost always accumulate uniformly on the rejecting membrane. Thus spatial non-uniformities in the upstream velocity can be ignored in the analysis of dead-end ultrafiltration.
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