The influence of particle diffusion on the onset of thermoconvective instability in magnetized ferrofluids

Finlayson's linear theory of Rayleigh-Bénard convection in magnetized ferrofluids is extended to allow for Soret diffusion and magnetodiffusion of the colloidal particles over long time spans. An analysis of the long-time behavior of the governing equations is performed for a fixed magnetic strength. It suggests that when the thermal diffusion ratio (proportional to the Soret coefficient) exceeds a specified value, the critical Rayleigh number for the onset of stationary convection is normally either large and negative or exceedingly small and positive. When the thermal diffusion ratio is less than this specified value, oscillatory convection sets in for large positive Rayleigh numbers, but stationary convection is preserved when the Rayleigh number is very small and negative. This behavior differs both qualitatively and quantitatively from the short-time-scale instabilities investigated by Finlayson.