Experimental investigation of the stability boundary for double-diffusive finger convection in a Hele-Shaw cell

Double-diffusive convection may be an important transport phenomenon in subsurface porous media and fractures. The classic linear stability analysis derived for a porous medium with two components stratified such that each affects the vertical density gradient in an opposing manner predicts double-diffusive finger instability to occur when Rs(1) + Rs(2) greater than or equal to Rs(c), where Rs(1) and Rs(2) are the Rayleigh numbers of the faster and slower diffusing components, respectively, and Rs, is a critical value dependent upon the boundary conditions (0 less than or equal to Rs(c) less than or equal to 4 pi(2)). For cases where Rs(c)/\Rs(1)\ much less than 1, the above result can be simplified to -R(rho) < 1/tau, where R(rho) is the buoyancy ratio of the fluid and tau is the ratio of diffusivities (0 < tau < 1). We experimentally tested the applicability of both stability criteria for situations where a narrow transition zone exists bounded above and below by constant concentrations and within a domain of uniform permeability. Experiments were conducted in a Hele-Shaw cell using a digital imaging technique which provided pixel-scale (similar to 0.2 mm) resolution of the evolving concentration field during convection. Within experimental error, our experiments support both criteria within their predicted ranges of applicability.