Solutal natural convection flows in ternary mixtures

Identifier:  PC:3143

Handle: https://hdl.handle.net/20.500.11797/PC3143

Authors:  Jordi Pallarés; Jna. Gavaldà; X. Ruiz

Abstract:
It is known that the cross diffusion terms generate four different types of solutions to the 11 one-dimensional unsteady diffusion equations for ternary mixtures. The stability of the 12 fluid column corresponding to these solutions can be classified depending on the sign of 13 the first derivative of density with respect to the direction of the gravity vector (i.e. 14 ⁄) and the sign of (22⁄)/, where =0 is located at the center of the 15 diffusion layer. The type of solution depends on the initial conditions and on the set of 16 diffusion coefficients considered. One type of solution corresponds to a stable fluid 17 column with (⁄<0) and (22⁄)/>0 . Two types of solutions generate fluid 18 layers with unstable density stratification (⁄>0) and the fourth type shows a fluid 19 layer with (22⁄)/<0 . We analyzed the unsteady diffusion processes in a ternary 20 mixture under the conditions of experiments carried out to determine the four diffusion 21 coefficients of the the ternary system 1,2,3,4-tetrahydronaphthaline-isobutylbenzene-22 dodecane (THN-IBB-nC12). These measurements; performed in diffusion cells with an 23 initially stable stratification within the cell, with the denser mixture at the bottom and the 24 lighter at the top; are usually based on the validity of the one-dimensional unsteady 25 diffusion mass transfer equations. The linear stability analysis for the onset of convection 26 in the unstable layers with unstable density stratification (⁄>0) indicates that the 27 critical thickness of these layers depends on the Rayleigh numbers, on the diffusion 28 2 coefficients and on the initial conditions. To illustrate the flow structures that can be 1 generated in these unstable conditions, we performed numerical simulations for selected 2 sets of diffusion coefficients at different Rayleigh numbers. The results of these 3 simulations are in general agreement with the predictions of the linear stability analysis 4 and indicate that, under specific conditions, the convective motions developed in the cell 5 produce significant departures of the concentration distributions from the pure diffusion 6 situation. 7 8