Quantifying the maximum efficiency of diffusiophoresis-driven filtration

Diffusiophoresis —the migration of particles in a fluid induced by a chemical gradient— has attracted increasing attention in recent years, with studies showing its relevance in processes ranging from fabric cleaning to particle delivery in porous materials. One of its particularly promising applications is water remediation, demonstrated using a CO2 gradient perpendicular to a flow of water contaminated with solid micro-beads [Shin et al., Nat. Commun. (2017)]. The resulting phoretic motion concentrates the solids on the channel sides and, after the particle-rich stream is diverted, results in membraneless water cleaning with an efficiency comparable to microfiltration. Here, we present a model of this effect for fully-developed species and particle concentrations, when the separation of solids is highest after the particle-free exclusion zone has reached its maximum thickness. The asymptotic theory produces quantitative predictions for the filtration efficiency as a function of three parameters that depend on the chemistry and particle properties. These results are then discussed and compared to measurements performed in microfluidic channels.