Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface

Abstract

Fouling mitigation using chaotic advection caused by herringbone-shaped grooves in a flat membrane module is numerically investigated. The feed flow is laminar with the Reynolds number ($\mathrm{Re}$) ranging from 50 to 500. In addition, we assume a constant permeate flux on the membrane surface. Typical flow characteristics include two counter-rotating flows and downwelling flows, which are highly influenced by the groove depth at each $\mathrm{Re}$. Poincaré sections are plotted to represent the dynamical systems of the flows and to analyze mixing. The flow systems become globally chaotic as the groove depth increases above a threshold value. Fouling mitigation via chaotic advection is demonstrated using the dimensionless average concentration (${\overline{c}}_w^{*}$) on the membrane and its growth rate. When the flow system is chaotic, the growth rate of ${\overline{c}}_w^{*}$ drops significantly compared to that predicted from the film theory, demonstrating that chaotic advection is an attractive hydrodynamic technique that mitigates membrane fouling. At each Re, there exists an optimal groove depth minimizing ${\overline{c}}_w^{*}$ and the growth rate of ${\overline{c}}_w^{*}$. Under the optimum groove geometry, foulants near the membrane are transported back to the bulk flow via the downwelling flows, distributed uniformly in the entire channel via chaotic advection.