A new process for species separation in a binary mixture using mixed convection

Abstract

In this paper, a numerical and analytical analysis is performed in order to improve the species separation process in a binary fluid mixture by decoupling the thermal gradient from the convective velocity. The configuration considered is a horizontal rectangular cavity, of large aspect ratio, filled with a binary fluid. A constant tangential velocity is applied to the upper horizontal wall. The two horizontal impermeable walls are maintained at different and uniform temperatures T1 and T2 with ΔT = T1 − T2 Species separation is governed by two control parameters, the temperature difference ΔT and the velocity of the upper plate Uex. The intensity of the thermodiffusion is controlled by the temperature, while the velocity Uex controls the convective flow. This problem depends on six dimensionless parameters, namely, the separation ratio, ψ, the Lewis number, Le, the Prandtl number Pr, the aspect ratio of the cell, A and two control parameters: the thermal Rayleigh number, Ra and the Péclet number Pe. In this study, the formulation of the separation (mass fraction difference between the two ends of the cell) as a function of the Péclet number and the Rayleigh number is obtained analytically. For a cell heated from below, the optimal separation m = √42/15 is obtained for Pe = √42/Le and Ra = 540/(Leψ). 2D numerical results, obtained by solving the full governing equations, are in good agreement with the analytical results based on a parallel flow approach.