Modeling of fouling in cross‐flow microfiltration of suspensions

Cross‐flow filtration of fine suspensions through microsieves occurs in microprocessing. The interaction of particles with surfaces in microenvironments has been extensively studied, but predominantly in monolayers and not with an eye to microfiltration. Here, we introduce a microfiltration model that pertains to particles that might be seen as fine in a macroscopic environment, but are large enough to intrude significantly into the shear layer of a microchannel. Thus, particle accumulation upon the sieve couples the steady‐state filtrate flux and the suspension flow through the microchannel that feeds the sieve. We envision and create a stable, stationary multilayer of particles whose thickness is shear‐limited and we identify and verify the structure and parameters that limit steady filtration in this environment. At first, a packed bed of particles forms, growing into and regulated by the micro channel's shear flow. A critical shear stress is shown to determine the thickness of the bed, seen as a stationary and stable multilayer of particles through which filtration may occur. As the bed thickens, at the expense of channel area for suspension flow, surface shear stress increases until no further particle adherence is possible. We built a simple example using hard noninteracting polymer microspheres and conducted cross‐flow filtration experiments over Aquamarijn™ microsieves (uniform pore size of 0.8 μm). We observed a steady cake‐layer thickness and because of the simple geometry afforded by uniform spheres, we could approximate the force balance, cake resistance, and filtration rate from first principles. The good fit of our data to the proposed mechanism lays a firm basis for the semiquantitative analysis of the behavior of more complex suspensions. © 2018 American Institute of Chemical Engineers AIChE J, 65: 207–213, 2019