Effect of buoyancy ratio on the development of double-diffusive finger convection in a Hele-Shaw cell

Abstract

We consider the evolution of double-diffusive finger convection for a two-solute (salt-sucrose) system in a Hele-Shaw cell. A high-resolution, full-field, light transmission technique was used to study the development of the instability that resulted from layering a lighter sucrose solution over a denser salt solution. The buoyancy ratio (Rρ), which is a ratio of fluid density contributions by the two solutes and defines the degree of system disequilibrium, was varied systematically from conditions that were nearly stable (Rρ = 2.8) to those that were moderately unstable (Rρ = 1.4). In all experiments, fingers are found to form continuously throughout time from a finger "generation" zone that straddles the location of the initial interface between solutions. At low Rρ, fingers develop rapidly, merge with adjacent fingers, and grow far beyond the finger generation zone through a series of finger "conduits". In the higher Rρ experiments, fingers are slower to evolve, do not interact as dynamically, and do not grow far beyond the generation zone. Solute mass fluxes at low Rρ quickly reach a constant many times greater than that of a purely diffusive system; at high Rρ, mass fluxes decay as t-1/2 and behave diffusively but with effective diffusion coefficients much greater than those for molecular diffusion.