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One tool in efforts to tackle the ever growing problem of water scarcity is municipal wastewater reclamation to produce drinking water. Microfiltration (MF) is a central technology for potable reuse because it is highly effective in removing pathogenic protozoa, bacteria, and other colloids and for reverse osmosis pretreatment. However, as microfiltered materials accumulate at the membrane surface, its productivity is reduced requiring periodic removal of foulants. A mathematical model of MF is described in the context of hollow fiber filtration that focused on optimizing constant flux operation with backwashing. Design curves were also proposed for determining backwash timing. The model analysis is evaluated against real-world MF fouling for membranes that range in age from a few weeks to three years, observed at the world’s largest water reuse facility operated by the Orange County Water District. The presented model compares well with the full-scale operational data, and model parameters accurately capture variations in fouling kinetics with membrane age, providing clues to changes in optimal regeneration timing and frequency as membrane performance declines over long time scales. 

Abstract We derive a class of exact solutions for Stokes flow in infinite and semi‐infinite channel geometries with permeable walls. These simple, explicit, series expressions for both pressure and Stokes flow are valid for all permeability values. At the channel walls, we impose a no‐slip condition for the tangential fluid velocity and a condition based on Darcy's law for the normal fluid velocity. Fluid flow across the channel boundaries is driven by the pressure drop between the channel interior and exterior; we assume the exterior pressure to be constant. We show how the ground state is an exact solution in the infinite channel case. For the semi‐infinite channel domain, the ground‐state solutions approximate well the full exact solution in the bulk and we derive a method to improve their accuracy at the transverse wall. This study is motivated by the need to quantitatively understand the detailed fluid dynamics applicable in a variety of engineering applications including membrane‐based water purification, heat and mass transfer, and fuel cells.