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