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A pleated membrane filter consists of a porous membrane layer, which is surrounded by two supporting layers, and the whole structure is pleated and placed into a cylindrical cartridge. 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. In this work, we introduce a novel three-dimensional model of a pleated membrane filter that consists of an empty region, 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 Stokes equation is used for the flow in the empty region and the hollow region. We further use the key assumptions of our model based on small aspect ratios of the filter cartridge and the pleated membrane to simplify the governing equations, which can be easily solved by 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. 

Pleated membrane filters are widely used to remove undesired impurities from a fluid in many applications. A filter membrane is sandwiched between porous support layers and then pleated and packed into an annular cylindrical cartridge with a central hollow duct for outflow. Although this arrangement offers a high surface filtration area to volume ratio, the filter performance is not as efficient as those of equivalent flat filters. In this paper, we use asymptotic methods to simplify the flow throughout the cartridge to systematically investigate how the number of pleats or pleat packing density affects the performance of the pleated membrane filters. The model is used to determine an optimal number of pleats in order to achieve a particular optimum filtration performance. Our findings show that only the “just right”—neither too few nor too many—number of pleats gives optimum performance in a pleated filter cartridge.