Modeling convection onset in colloidal suspensions of particles

Abstract

A particulate medium model is used to investigate the onset of Rayleigh–Bénard convection in a colloidal suspension of inert solid particles. The model accounts for the effects of thermophoresis, sedimentation and Brownian diffusion. Depending on the size of the particles, the problem has up to four time scales. These are due to thermal diffusion, particle diffusion, particle migration due to thermophoresis and particle sedimentation. The ratios of these time scales lead to the emergence of three parameters, one of which is the Lewis number τ. The smallness of the latter makes the differential eigenvalue system governing convection onset singular. The other two are the density number Γ and the dimensionless migration velocity β. For a given experimental set-up, β has a quadratic functional dependence on the particles radius. A combination of asymptotics and numerical computation is used to capture the effect of the resulting thin particle concentration boundary layers on the leading order instability thresholds. Results, which are depicted as function of Γ and β, reveal a non-monotonic dependence of the critical Rayleigh number ℛ_c on β. The curve ℛ_c(β) is bimodal and it exhibits a maximum , the value of which increases very sharply with |Γ| while the critical wavelength decreases. Experimental conditions can be fixed so that occurs at β values that correspond to nanoparticles. Therefore, experimental parameters can be controlled so that the mixing of a small amount of nano-size particles has a substantial stabilizing effect. An investigation of the flow patterns in the range of parameters associated with this sharp increase in ℛ_c reveals a decrease in the effective thickness of the stratified layer.