Hydrodynamic forces on steady and oscillating porous particles

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 the 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.