Experimental investigation of the stability boundary for double‐diffusive finger convection in a Hele‐Shaw cell
Clay A. Cooper, Robert J. Glass, Scott W. Tyler · Water Resources Research · 1997
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 ≥ Rs c , where Rs 1 and Rs 2 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 ≤ 4π 2 ). For cases where Rs c /| Rs 1 | ≪ 1, the above result can be simplified to − R ρ < 1/т, where R ρ 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.