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

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Abstract
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 Rs1 + Rs2 ≥ Rsc, where Rs1 and Rs2 are the Rayleigh numbers of the faster and slower diffusing components, respectively, and Rsc is a critical value dependent upon the boundary conditions (0 ≤ Rsc ≤ 4π2). For cases where Rsc/|Rs1| ≪ 1, the above result can be simplified to −Rρ < 1/т, where Rρ is the buoyancy ratio of the fluid and т is the ratio of diffusivities (0 < т < 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 (∼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.