Hydrodynamic permeability of fluctuating porous membranes

TL;DR

This study investigates how porosity fluctuations in membranes influence their hydrodynamic permeability, introducing a fluctuating Darcy model that reveals significant effects of matrix fluctuations on fluid transport.

Contribution

The paper introduces a fluctuating Darcy model coupling Navier-Stokes equations with porosity fluctuations, providing a new theoretical framework for understanding permeability in dynamic porous matrices.

Findings

Porosity fluctuations significantly alter membrane permeability.

The Dyson equation relates permeability to fluctuation spectra.

Matrix excitations like breathing and phonons impact fluid transport.

Abstract

In this paper we examine how porosity fluctuations affect the hydrodynamic permeability of a porous matrix or membrane. We introduce a fluctuating Darcy model, which couples the Navier-Stokes equation to the space- and time-dependent porosity fluctuations via a Darcy friction term. Using a perturbative approach, a Dyson equation for hydrodynamic fluctuations is derived and solved to express the permeability in terms of the matrix fluctuation spectrum. Surprisingly, the model reveals strong modifications of the fluid permeability in fluctuating matrices compared to static ones. Applications to various matrix excitation models - breathing matrix, phonons, active forcing - highlight the significant influence of matrix fluctuations on fluid transport, offering insights for optimizing membrane design for separation applications.