Onset Of Soret-driven Convection Research Articles

Magnetic field effect on the onset of Soret-driven convection of a nanofluid confined within a Hele-Shaw cell

The effect of a magnetic field on the early stages of Soret-driven convection of a nanoparticle suspension with large negative separation ratio χ confined within a Hele-Shaw cell, heated from above, was analyzed. Taking the Lorentz force into account, new stability equations were formulated in a similar (τ, ζ)-domain as well as in a global (τ, z)-domain by introducing the Hele-Shaw Rayleigh number based on the Soret flux (RsH) and the Hele-Shaw Hartmann number (HaH). With and without the quasi-steadiness assumptions, the resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions, and also the numerical shooting method was used. The critical time of the onset of convection and the corresponding wave number were obtained as a function of RsH and HaH. It was found that the magnetic field plays a critical role in the onset of convective instability. The onset time increases with increasing HaH and decreasing RsH. The linear stability limits are independent of the solution methods, if the trial functions for the disturbance quantities are properly chosen. Based on the results of the linear stability analysis, a non-linear analysis was conducted using direct numerical simulations. The non-linear analysis revealed that the convective motion can be apparent far after the linear stability limit.

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.

CONVECTION IN COLLOIDAL SUSPENSIONS OF SOLID PARTICLES: A COMPARATIVE STUDY BETWEEN THE HOMOGENEOUS MIXTURE AND THE PARTICULATE MEDIUM MODELS

The convection process in colloidal suspensions of solid particles is usually investigated by adopting either a homogeneous binary mixture (HM) or a particulate medium (PM) model. The present study aims only at comparing the instability threshold conditions for the onset of convection in the particle-dominated regime obtained through these two models. We consider a colloidal suspension of solid particles in a Rayleigh-Bénard set up. A PM model is adopted which accounts for the effects of thermophoresis, sedimentation, and Brownian diffusion. We assume that the suspension layer is subjected to a vertical temperature gradient that is not thermally destabilizing as in the case of negligibly small coefficient of thermal expansion. Thus, we consider the idealized situation wherein the thermally induced buoyancy is absent and the focus is solely on the particle-dominated convection regime. We show that the coupled effects of thermo-migration, sedimentation, and Brownian diffusion give rise to a weak convection regime that sets in on the long particle diffusion time scale. A small wave number expansion is undertaken to determine the stability threshold conditions. When contrasted with those obtained through the HM model, the latter are found to have the same functional dependence on parameters as those describing the onset of Soret-driven convection for the case of a positive and large separation ratio. However, we show that a PM model, unlike the HM model, yields stability threshold conditions that can be mapped to corresponding experimental parameters such as the size of the particles and of the fluid cell.

Soret-driven convection and separation of binary mixtures in a porous horizontal slot submitted to a heat flux

The onset of Soret-driven convection in a shallow porous horizontal layer filled with a binary mixture and submitted to a vertical heat flux on the two horizontal walls is investigated. We study the species separation between the two vertical ends of the cell, which appears for low values of the Rayleigh number and for positive separation ratio. An analytical solution is performed and the separation is expressed in terms of thermal Rayleigh number, Lewis number, separation ratio and aspect ratio of the cell. These analytical results are corroborated by direct non-linear numerical simulations. Then, the results are compared with those obtained in a differentially heated vertical cavity.

Onset of Soret convection in a nanoparticles-suspension heated from above

The onset of Soret-driven convection in a nanoparticles suspension heated from above is analyzed theoretically based on linear theory and relative instability concept. A new set of stability equations are derived and solved by using the dominant mode method. The dimensionless critical time τ c to mark the onset of instability is presented here as a function of the Rayleigh number, the Lewis number and the separation ratio. Available experimental data indicate that for large Rayleigh number convective motion is detected starting from a certain time τ≈3 τ c . This means that the growth period of initiated instabilities is needed for convective motion to be detected experimentally. It seems evident that during τ c ≤ τ ≤ 3 τ c convective motion is relatively very weak and the primary diffusive transfer is dominant.

The onset of Soret-driven convection in a binary mixture heated from above

The onset of buoyancy-driven convection in an initially quiescent, horizontal fluid layer heated from above is analyzed theoretically. The present system of binary mixtures is a thermally stable one but the Soret diffusion can induce buoyancy-driven motion. With highly unstable density gradients the convective motion sets in during the transient diffusion stage. Here the onset time of convective motion is analyzed by employing the propagation theory. The dimensionless critical time τc and the critical wavenumber ac to mark the onset of convective motion is presented as a function of the Rayleigh number Ra, the Lewis number Le, and the separation ratio ψ. The results show that the onset time decreases with increasing buoyancy force Ra(Le∕ψ)−1 and the predicted ac-values agree well with available experimental data. For the ethanol-water system the predicted critical reduced Rayleigh number rc(=Rac∕1708)=−0.0464 agrees reasonably with existing experimental results of r=−0.1. It is found that the visible motion can be detected from a certain time τ≅43∕4τc.

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number (Ra(T)), the vibrational parameter (R), the Prandtl number (Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (alpha). For different sets of parameters, the bifurcation diagrams are plotted Ra(c) = f(S) and k(c) = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra(c)-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.

Naissance de la convection thermo-solutale en couche poreuse infinie avec effet Soret

The onset of Soret-driven convection in an infinite cell filled with a porous medium saturated by a binary fluid is studied. The impermeable horizontal walls are maintained at different and uniform temperatures. For a cell heated from below, the motionless solution loses its stability via a stationary bifurcation when the separation ratio ψ is higher than a Lewis and normalized porosity dependent value ψ 0 ; for ψ<ψ 0 , it loses its stability via a Hopf bifurcation. For a cell heated from above, the motionless solution is infinitely linearly stable if ψ>0, while a stationary bifurcation occurs if ψ<0. These results are widely corroborated by direct numerical simulations.