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

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 ≤ Rs(c), where Rs1 and Rs2 are the Rayleigh numbers of the faster and slower diffusing components, respectively, and Rs(c) is a critical value dependent upon the boundary conditions (0 ≤ Rs(c) ≤ 4π2). For cases where Rs(c)/|Rs1| << 1, the above result can be simplified to -R(ρ) < 1/τ, where R(ρ) is the buoyancy ratio of the fluid and τ is the ratio of diffusivities (0 < τ < 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.