Étude de la thermogravitation dans une couche fluide horizontale

Abstract

_____________________________________________________________________________________ RésuméNous présentons une étude analytique et numérique de l'action conjuguée de la thermodiffusion et de la convection, dite diffusion thermogravitationnelle, dans les mélanges binaires. Il s'agit de quantifier l'importance de la séparation dans le cas d'une cavité parallélépipédique horizontale remplie d'un mélange binaire et soumise à des gradients horizontaux de température constants sur les deux parois horizontales, les autres parois sont imperméables à la matière et thermiquement isolées. Cette nouvelle procédure diffère de celle habituellement utilisée et qui consiste à obtenir la séparation thermogravitationnelle dans une cellule verticale dont deux parois verticales sont maintenues à des températures constantes et différentes. AbstractStudy of the thermogravitation in a horizontal fluid layer. We propose an analytical and numerical study of the combined action of the thermodiffusion and the convection in a binary mixture. The combination of these two phenomena is called the thermogravitational diffusion. We are interested in quantifying the separation in a horizontal parallelepipedic cavity filled with a binary mixture and subjected to a constant horizontal temperature gradient on the two horizontal walls, the other walls being thermally insulated and impermeable. This new procedure is different from the classical one where the cavity is vertical and differentially heated on the two vertical walls.Mots-clés : Convection; Thermodiffusion; Thermogravitation; Effet Soret; Mélanges binaires ; Séparation Keywords : Convection; Thermodiffusion; Thermogravitation; Soret effect; Binary mixtures; Separation 2 Abridged English versionThermodiffusion is a physical process occurring when a thermal gradient is applied to a fluid mixture. The concentration gradient is created by the temperature field; the mass flux is given by [1]:Where D is the coefficient of mass diffusion, D T the coefficient of thermodiffusion, ρ the density, and C the mass fraction of the denser component.The thermogravitational diffusion is the combination of two phenomena: the convection and the thermal diffusion. The coupling of these two phenomena leads to species separation.Thermogravitational technique consists usually in vertical [2] or tilted cavity [6] bounded by two rigid differentially heated vertical walls and adiabatic horizontal walls, and filled by a binary fluid or by a homogeneous isotropic porous medium saturated by a two-component fluid [3].In the present work, we propose a new procedure coupling the convection and the thermodiffusion, to obtain a greater separation compared to the procedures already used. This approach permits us to obtain thermogravitational diffusion in a horizontal box heated from above. On the other hand we impose a constant temperature gradient, according to the horizontal axis x on each of the two horizontal walls of the box, which generates an unicellular convective flow similar to that produced in the vertical cell d...

Species separation of a binary mixture in the presence of mixed convection

“…In order to increase the separation, Platten et al [7] used an inclined cavity, heated from the top. Elhajjar et al [8] suggested a new method to obtain species separation in a binary fluid mixture. They used a horizontal cavity heated from above and subjected to a constant horizontal temperature gradient on the two horizontal walls to improve the separation process depending on two control parameters.…”

Separation in an inclined porous thermogravitational cell

“…Once the velocity field has been obtained, we determine the function g(x) using the first equation of system (6). In order to find the constants of integration, we use the equation of conservation of the mass of the denser species:…”

“…Platten et al [5] used an inclined cavity, heated from the top, to increase separation. Elhajjar et al [6] used a horizontal cavity heated from above with temperature gradients imposed on the horizontal walls to improve the separation process with the use of two control parameters. Bennacer et al [7] suggested splitting the column into three sub-domains in order to increase the separation.…”

Disturbance of Thermodynamic Equilibrium of the Quartz-Water System and Silica Separation from the Liquid Phase at a Small Temperature Gradient

“…One way to increase separation is to slow down the convection by inclination of the column [7]. The separation can be increased also in thermal diffusion cell by its inclination or creation of horizontal TG [8]. In our lower autoclaves, ampoules were inclined and probably they were under the conditions of not only vertical but also horizontal TG.…”