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.