The effect of concentration-dependent diffusion on double-diffusive instability

Abstract

The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.