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Short-term microfiltration (MF) fouling is commonly abated by periodically reversing the flow to remove foulants that weakly adhered to the membrane. Strong oxidants (i.e., chlorine) can be added to hydraulic backwash water to augment its efficacy—a process called chemically enhanced backwashing (CEB). Herein, we report a rigorous mathematical model for constant flux MF incorporating hydraulic backwashing and CEB, and validate it with laboratory data obtained using untreated and alum-coagulated water from the Foss Reservoir in Oklahoma, USA. We implemented an optimal control procedure and used it to predict MF behavior long past experimental timescales. We identified a frequency threshold beyond which the necessary transmembrane pressure (TMP) reached an asymptotic value, indicating a pseudo steady-state, periodic solution to the model when coupling hydraulic backwashing with CEB. We report differences in TMP saturation values and timescales by simulating transient MF of untreated and pretreated water. Numerical simulations revealed that the operating flux could be increased 10-fold after pretreatment (compared with raw water) before reaching the maximum manufacturer-recommended pressure for the hollow-fibers. The predicted higher flux and extended duration between cleaning-in-place demonstrated advantages of coagulation pretreatment under hydraulic backwashing and CEB. Model observations could guide decision making for CEB timing and frequency. 

Liquid lithography represents a robust technique for fabricating three-dimensional (3D) microstructures on a two-dimensional template. Silanization of a surface is often a key step in the liquid lithography process and is used to alter the surface energy of the substrate and, consequently, the shape of the 3D microfeatures produced. In this work, we present a passive technique that allows for the generation of silane gradients along the length of a substrate. The technique relies on a secondary diffusion chamber with a single opening, leading to a directional introduction of silane to the substrate via passive diffusion. The secondary chamber geometry influences the deposited gradient, which is shown to be well captured by Monte Carlo simulations that incorporate the passive diffusion and grafting processes. The technique ultimately allows the user to generate a range of substrate wettabilities on a single chip, enhancing throughput for organ-on-a-chip applications by mimicking the spatial variability of tissue topographies present in vivo. 

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.