Solutal natural convection flows in ternary mixtures

Abstract

It is known that the cross diffusion terms generate four different types of solutions to the one-dimensional unsteady diffusion equations for ternary mixtures. The stability of the fluid column corresponding to these solutions can be classified depending on the sign of the first derivative of density with respect to the direction of the gravity vector (i.e. ∂ρ/∂y) and the sign of (∂2ρ/∂y2)/y, where y=0 is located at the center of the diffusion layer. The type of solution depends on the initial conditions and on the set of diffusion coefficients considered. One type of solution corresponds to a stable fluid column with (∂ρ/∂y<0) and (∂2ρ/∂y2)/y>0. Two types of solutions generate fluid layers with unstable density stratification (∂ρ/∂y>0) and the fourth type shows a fluid layer with (∂2ρ/∂y2)/y<0. We analyzed the unsteady diffusion processes in a ternary mixture under the conditions of experiments carried out to determine the four diffusion coefficients of the ternary system 1,2,3,4-tetrahydronaphthaline-isobutylbenzene-dodecane (THN-IBB-nC12). These measurements; performed in diffusion cells with an initially stable stratification within the cell, with the denser mixture at the bottom and the lighter at the top; are usually based on the validity of the one-dimensional unsteady diffusion mass transfer equations. The linear stability analysis for the onset of convection in the unstable layers with unstable density stratification (∂ρ/∂y>0) indicates that the critical thickness of these layers depends on the Rayleigh numbers, on the diffusion coefficients and on the initial conditions. To illustrate the flow structures that can be generated in these unstable conditions, we performed numerical simulations for selected sets of diffusion coefficients at different Rayleigh numbers. The results of these simulations are in general agreement with the predictions of the linear stability analysis and indicate that, under specific conditions, the convective motions developed in the cell produce significant departures of the concentration distributions from the pure diffusion situation.