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

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. Published under an exclusive license by AIP Publishing.

Automated summary

The article investigates the stability of a two-layer miscible system to the double-diffusive instability by considering the effect of a concentration-dependent diffusion coefficient. A closed-form analytical expression for the time-dependent density profile is derived and validated by direct numerical simulation. The experiments confirm the theoretical predictions and show opposite results for different solute pairs.