Understanding how porosity gradients can make a better filter using homogenization theory

TL;DR

This paper uses homogenization theory to analyze how porosity gradients in filters enhance efficiency by improving adsorption uniformity and reducing clogging risk, providing a theoretical foundation for better filter design.

Contribution

It extends homogenization theory to account for macroscale porosity variations and explains how porosity gradients improve filter performance.

Findings

Porosity gradients significantly improve adsorption uniformity.

Decreasing porosity reduces localized blocking risk.

Homogenized equations efficiently predict filter behavior.

Abstract

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.