Thermal Diffusion and Convective Stability. II. An Analysis of the Convected Fluxes

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Abstract
The stability of a horizontal, two-component fluid layer subjected to a positive vertical temperature gradient (heating from above) is investigated taking advantage of the fact that the time scales for thermal relaxation and concentration relaxation are widely separated. Based on this hypothesis a buoyancy driven instability owing to the separation by thermal diffusion is found even when the density gradient favors stability. This is in agreement with the previous findings of Schechter, Prigogine, and Hamm thus verifying that the difference in time scales is the essential feature giving rise to this unexpected instability. A convective state in which rolls are assumed to be stable is then studied by solving the nonlinear problem. The analysis shows that the contribution of the convective heat flux to the total heat flux vanishes to the approximation studied here, but that the convective mass flux is an important part of the total. Thus, the separation by thermal diffusion tends to be destroyed by the instability.