If a denser solution of a solute A lies above a less dense solution of a solute B in the gravity field, the Rayleigh-Taylor (RT) instability can trigger convective motions which enhance the mixing of the two solutions. Double-Diffusion (DD) and Diffusive-Layer-Convection (DLC) regimes can also develop in the case of an initially stable stratification, provided A and B diffuse at different rates. Here, we analyze numerically for bulk flows described by the Navier-Stokes equation coupled to evolution equations for the concentration of species A and B how the buoyancy-driven mixing induced by such instabilities can be affected by differential diffusion effects. We quantify the length of the mixing zone as well as the onset time and the growth rate of the instability as a function of the two parameters of the problem, namely, the buoyancy ratio $R$ and the ratio $\delta$ of diffusion coefficients. We show that, when nonmonotonic density profiles with a dynamic density difference $\mathrm{\Delta }{\rho }_m$ are triggered by differential diffusion, convection can be more intense and appear faster than in the single-solute case. We derive the scalings of the growth rate $\alpha$ of convective plumes and of the onset time of the instability as a function of $\mathrm{\Delta }{\rho }_0$ and $\mathrm{\Delta }{\rho }_m$ both in the RT regime affected by differential diffusion effects and in the pure DD or DLC regimes. These scalings allow to control how two miscible solutions can buoyantly mix by a careful choice of the two solutes involved.

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• Doubly diffusive convection
• Flow instability
• Instability control
• Mixing enhancement
• Pattern formation
• Rayleigh-Taylor instability
• Binary fluids
• Buoyancy
• Direct numerical simulations
• Navier-Stokes equation