Magnetic field driven micro-convection in the Hele-Shaw cell

Micro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering are determined by particle image velocimetry measurements and qualitatively correspond well to the results of numerical simulations of the micro-convection in the Hele-Shaw cell carried out in the Darcy approximation, which account for ponderomotive forces of the self-magnetic field of the magnetic fluid. Gravity plays an important role at the initial stage of the fingering observed in the experiments.