Filters whose porosity decreases with depth are often more efficient atremoving solute from a fluid than filters with a uniform porosity. Weinvestigate this phenomenon via an extension of homogenization theory thataccounts for a macroscale variation in microstructure. In the first stage ofthe paper, we homogenize the problems of flow through a filter with anear-periodic microstructure and of solute transport due to advection,diffusion, and filter adsorption. In the second stage, we use thecomputationally efficient homogenized equations to investigate and quantify whyporosity gradients can improve filter efficiency. We find that a porositygradient has a much larger effect on the uniformity of adsorption than it doeson the total adsorption. This allows us to understand how a decreasing porositycan lead to a greater filter efficiency, by lowering the risk of localizedblocking while maintaining the rate of total contaminant removal.
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