Influence of sedimentation on the threshold for Soret-driven convection in colloidal suspensions

The onset of Soret-driven convection in a horizontal layer of a colloidal suspension is investigated by considering a particulate medium model. We consider a dilute suspension of spherical solid particles being subjected to convection in a Rayleigh-Bénard geometry setup. The mathematical model takes into account the effects of thermophoresis, particle sedimentation, and Brownian diffusion. The equations governing the convective motion consist of the momentum equation which includes an extra body force term to account for the thermophoretic force effect, the conservation of particles equation whose mass-flux term couples the Soret and particle diffusion effects and whose advective term includes the sedimentation force, and the heat and mass balance equations. The horizontal boundaries are assumed rigid, perfectly thermally conducting, and impervious to mass flow. Furthermore, the model makes use of the effective viscosity of the suspension whose dependence on the particle concentration is through Einstein's formula. Moreover, we take into account the decrease of both the coefficient of Brownian diffusion and the mixture thermal diffusion with particle concentration due to the particles hindrance effect. The nondimensionalization leads to the emergence of an experimental parameter, β, which depicts the competition between the effects of thermophoresis, sedimentation, and particle diffusion. The parameter β is a function of the particles radius, the shape of which is an inverted parabola having two zeros. A combination of asymptotic and numerical computations is used to determine the threshold for the onset of the mass dominated convection, which corresponds to 0<β≪1. Our findings shed light on the role of particle sedimentation and particle size, as well as the influence of other processing variables on the fluid instability.