Convective Instability of Magnetized Ferrofluids: Influence of Magnetophoresis and Soret Effect

Abstract

Convective instability in a ferrofluid layer heated from below or from above in the presence of a uniform vertical magnetic field is investigated theoretically. Convection is caused by a magnetic mechanism based on the temperature and concentration dependence of magnetization. An imposed temperature gradient establishes (by the Soret effect) a concentration gradient of magnetic particles of which the ferrofluid is composed. Both these gradients cause a spatial variation in magnetization, which induces a gradient of magnetic field intensity within the fluid layer. The field gradient induces in its turn an additional redistribution of magnetic grains due to magnetophoresis. Resulting self-consistent magnetic force tries to mix the fluid. A linear stability analysis predicts oscillatory instability in a certain region of the magnetic field strength and the fluid parameters. The instability owes magneto- and thermophoresis its origin: were the particle diffusion not operative, then only stationary instability would occur. A discovery of predicted convective oscillations is expected in ferrofluid layers about 1 mm thick, where the buoyancy mechanism is negligible and the characteristic diffusion time is not too long.