  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.
