Instability of a drop moving in a Brinkman porous medium

Sedimentation of a spherical drop of one fluid in the porous medium saturated by another is analyzed in the framework of the Brinkman model. The formula for the stationary velocity is obtained, which reproduces the results for the drop motion in a viscous fluid (Hadamard-Rybczynski formula) and for the Darcy model in the corresponding limiting cases. The steadily moving drop is found to be unconditionally unstable to interface perturbations. It is shown that the Brinkman model eliminates the unphysical features of the instability inherent to the Darcy model.