Flow and transport in a pleated filter

Pleated membrane filters are used in a variety of industrial applications, since they offer more surface area to volume ratio that is not found in equivalent flat filters. A pleated membrane filter consists of a porous membrane layer which is surrounded by two supporting layers. The whole structure is pleated and placed into a cylindrical cartridge. In this work, we introduce a novel 3D model of a pleated membrane filter that consists of an empty area, a pleated region and a hollow region. The advection diffusion equation is used to model contaminant concentration in the membrane pores along with Darcy's law to model the flow within the membrane and support layers, while the Stoke's equation is used for the flow in the empty area and the hollow region. We further use the key assumptions of our model based on small aspect ratios of the filter cartridge, the support layers to simplify the governing equations such that the resulting reduced model can be solved with numerical methods. By performing these steps, we seek to discover an optimal pleat packing density to find the optimum filter performance, while not exceeding a threshold for the particle concentration at the filter outlet.