On the performance of multilayered membrane filters

Multilayered membrane filters, which consist of a stack of thin porous membranes with different properties (such as pore size and void fraction), are widely used in industrial applications to remove contaminants and undesired impurities (particles) from a solvent. It has been experimentally observed that the performance of well-designed multilayer structured membranes is markedly better than that of equivalent homogeneous membranes. Mathematical characterization and modeling of multilayered membranes can help our understanding of how the properties of each layer affect the performance of the overall membrane stack. In this paper, we present a simplified mathematical model to describe how the pore-scale properties of a multilayered membrane affect the overall filter performance. Our results show that, for membrane stacks where the initial layer porosity decreases with depth, larger (negative) porosity gradients within a filter membrane are favorable for increasing throughput and filter lifetime, but at the expense of moderately poorer initial particle retention. We also found that the optimal layer thickness distribution that maximizes total throughput corresponds to a membrane stack with larger (negative) porosity gradients in which layer thickness increases slightly between successive layers in the depth of the membrane.