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

Abstract

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.

Gravitational convection of magnetic colloid in a horizontal layer

“…As it was shown in [19], for particles in the nanosize range in the case of a negligibly small thermal expansion coefficient, when the thermally induced buoyancy was absent, threshold conditions for instability derived through the particulate medium model were consistent with ones obtained through the binary mixture model for Soret-driven convection with a large and positive separation ratio. Works [20,21] extended the study of Hadji [19] by considering the effect of thermal field and the dependence of viscosity and diffusion coefficient on concentration. The authors revealed that an increase in the fluid viscosity and decrease in the diffusion coefficient due to the presence of particles had an overall destabilizing effect on the onset of convection.…”

“…The first concerns the Soret-driven convection of a suspension with particles in the nanosize range (binary mixture model) [15][16][17]. The second one involves both the particle size and particle volume fraction and deals with the sedimentation and thermo-migration of particles under an imposed temperature gradient in the gravity field (particulate medium model) [18][19][20][21]. A long wave-length asymptotic analysis was conducted to obtain a stability boundary for a mass-dominated regime of convection in a dilute suspension [19][20][21].…”

“…There are a number of studies on the impact of particles sedimentation in the gravity field on the excitation of Soret-driven convection in a horizontal layer of a colloidal suspension [14][15][16][17][18][19][20][21]. Experiment on natural convection with aluminum oxide microparticle aqueous suspensions was carried out by Chang et al [14].…”

“…The second one involves both the particle size and particle volume fraction and deals with the sedimentation and thermo-migration of particles under an imposed temperature gradient in the gravity field (particulate medium model) [18][19][20][21]. A long wave-length asymptotic analysis was conducted to obtain a stability boundary for a mass-dominated regime of convection in a dilute suspension [19][20][21]. Relations for critical parameters included experimental coefficient b proposed by Chang et al [14] and accounting for the balance between thermophoretic and sedimentation velocities of particles.…”

“…The theoretical investigation of sedimentation effect on convective instabilities in colloidal suspensions for a Rayleigh-Benard geometry setup presented in works [15][16][17][18][19][20][21]. There are two theoretical models used to describe the convection.…”