Homogenization theory captures macroscopic flow discontinuities across Janus membranes

Author:

Zampogna Giuseppe A.ORCID,Ledda P.G.ORCID,Wittkowski K.ORCID,Gallaire F.ORCID

Abstract

Janus membranes, thin permeable structures with chemical and geometrical asymmetric properties, show great potential in industrial separation processes. Yet the link between the micro- and macro-scale behaviours of these membranes needs to be established rigorously. Here, we develop interface conditions to describe the solvent–solute flow across Janus membranes within a homogenization-based framework. Upstream and downstream spatial averages are introduced to account for discontinuities induced by the microstructure. The homogenized model quantifies the macroscopic jump, across the membrane, in the solvent velocity and stresses, and in the solute concentration and fluxes through coefficients obtained via closure problems at the micro-scale. The model paves the way towards a better understanding of fundamental interface phenomena such as osmosis and phoresis via homogenization.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics

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