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

Pleated membrane filters are essential in various filtration applications due to their greater surface area-to-volume ratio compared to flat filters. This research introduces a mathematical model to understand several fouling mechanisms, especially focusing on cake formation as well as the feed flow dynamics in pleated filters. Our three-dimensional model assumes the pleated filter consisting of six distinct sub-regions: the empty, support layer plus, cake layer, membrane, support layer minus, and hollow regions. We use Darcy's law and the Stokes equations to model the feed flow, and the advection-diffusion-reaction equation to simulate the particle transport within the corresponding aforementioned regions. To reduce the complexity of the model, we apply asymptotic analysis, based on the small aspect ratios of the filter and pleated membrane. The implications of our findings provide critical insights to improve the filter efficiency in terms of maximizing the filtrate fluid while keeping the particle concentration within designated limits and discovering the effects of the filter geometry. We find that the total accumulated particle concentration steadily decreases as the number of pleats increases, while an optimal pleat packing density maximizes the total throughput. Additionally, the presence of a cake layer enhances the total throughput of the filter, albeit at the cost of a slower filtration process.