Effects of cake formation on flow and transport in a pleated membrane filter

Pleated membrane filters play a crucial role in various industrial applications due to their enhanced surface area to volume ratio compared to flat filters. This study presents a mathematical model for fouling mechanisms, with a particular focus on cake formation, and flow transport in pleated membrane filters. The proposed three-dimensional model considers the membrane pleated region as consisting of four distinct sub-regions: the support layer plus, the cake layer, the membrane layer, and the support layer minus. By incorporating Darcy's law, the Stokes equation and the advection-diffusion equation, we model the flow and transport within the pleated membrane regions as well as the filter cartridge. To overcome the complexity of the model and filter geometry, we employ asymptotic analysis techniques based on the small aspect ratios of the filter cartridge and pleated membrane. The results obtained from our study offer valuable insights into optimizing pleat packing density and filter performance while ensuring particle concentration remains below predefined thresholds.