Hydrodynamic forces on steady and oscillating porous particles

TL;DR

This paper presents new analytical formulas for the hydrodynamic forces on oscillating porous particles, validated by simulations, advancing understanding of fluid-structure interactions in porous media.

Contribution

It introduces novel analytical solutions for oscillating porous particles using the DBB model, validated against detailed Navier-Stokes simulations.

Findings

Analytical results agree with simulations across various porosities.

The formulas accurately predict forces in the Stokes limit.

The study extends dynamic theories for porous particle hydrodynamics.

Abstract

We derive new analytical results for the hydrodynamic force exerted on a sinusoidally oscillating porous shell and a sphere of uniform density in the Stokes limit. The coupling between the spherical particle and the solvent is done using the Debye-Bueche-Brinkman (DBB) model, i.e. by a frictional force proportional to the local velocity difference between the permeable particle and the solvent. We compare our analytical results and existing dynamic theories to Lattice-Boltzmann simulations of full Navier-Stokes equations for the oscillating porous particle. We find our analytical results to agree with simulations over a broad range of porosities and frequencies.