How cake formation alters flow and transport in pleated membrane filters

Pleated membrane filters play a crucial role in various filtration applications, offering a greater surface area-to-volume ratio compared to flat filters. This research presents a mathematical model to explore fouling mechanisms, with an emphasis on cake formation and feed flow dynamics in pleated filters. Our model is three-dimensional and divides the pleated filter into six sub-regions: the empty region, support layer plus, cake layer, membrane, support layer minus, and hollow region. We utilize Darcy's law and the Stokes equations to describe the feed flow, while the advection-diffusion equation is employed to simulate particle transport within these regions. To manage the model's complexity, we apply asymptotic analysis, leveraging the small aspect ratios of the filter cartridge and pleated membrane. The insights gained from our study are pivotal for improving filter efficiency. We focus on maximizing the filtrate volume while maintaining particle concentrations within acceptable limits and investigate the impact of cartridge geometry on filtration performance. Furthermore, we analyze the influence of particle characteristics on the filtration process, providing a deeper understanding of how to optimize filter design and operation.