Hydrodynamic permeability of fluctuating porous membranes

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.