A mathematical model of steady-state cross-flow microfiltration in a woven hose support

Prediction of particle deposition and layer growth in the preparation of a dynamic membrane with cross-flow microfiltration

“…29 It was known that particle quantity transported from bulk uid to the dynamic layer surface would equal the quantity from the surface back to bulk uid when the steady permeate ux was achieved. [22][23][24] In an addition to the lateral migration, the shearinduced and Brownian diffusions were the two major mechanisms to govern this back transport, which were all in the opposite depositional direction. [29][30][31] Brownian diffusion favored the transport of smaller particles while the shear-induced diffusion increased as particle sizes increased.…”

“…Schulz and Ripperger, Hunt et al and Perkins et al developed their own similar models. [22][23][24] Before the permeate ux had been stabilized, the particle concentration, uid velocity and pressure varied along the radial direction; when the ux was stabilized, the particle quantity transported from the bulk stream to the membrane surface was equal to the quantity from the membrane surface back to the bulk stream. Based on classical mechanics, Blake et al proposed a force balance model by analyzing the forces exerting on a single particle deposited on the dynamic layer.…”