Stability of diffusion fronts of magnetic particles in porous media (Hele-Shaw cell) under the action of an external magnetic field

On the basis of the Darcy equation with account for ponderomotive magnetic forces the fingering instability of the magnetic particle diffusion front is considered. It is shown that there exists a threshold value of the magnetic field strength depending on the diffusion coefficient of the magnetic particles above which vortex-like fluid motion at the diffusion front arises. In the limit of the steplike magnetic particle concentration distribution the critical value of the magnetic field strength is calculated exactly. Smearing of the magnetic particle concentration distribution due to the thermal diffusion leads to the increase of the critical magnetic field strength and shift of the fastest growing mode to the larger wavelengths. Existing ex-perimental results relevant to the approach considered in the present paper are pointed out.