Double-Diffusive Fingering in Porous Media

Laboratory experiments were conducted on a double-diffusive fluid with components of dissolved salt and sucrose contained within a porous medium of nearly spherical glass beads. The fluid is stabilized by the faster diffuser (Sa) and destabilized by the slower diffuser (Su) arranged in such a way so that the system is finger-favorable. The experiments were conducted in a tank of depth 30 cm, with initial vertical opposing linear profiles of Sa and Su between two reservoirs, the top containing a Su solution and the bottom a Sa solution of known values. Measurements show that the Rayleigh-Darcy number experimental range is up to |Rsa|~10^5 and density ratio ranges from Rrho= 1.1 to 1.4 with spherical bead range of d = 0.01 to 0.80 cm. The finger flux for salt was Fsa~CRsa^a with a = 0.17 to 0.25 and was Fsu~CRsu^b with b = 0.12 to 0.14 for sugar. The spacing of the fingers was measured and non-dimensionalized using the height of the test reservoir. The non-dimensional spacing lambda was found to be related to the salt Rayleigh-Darcy number lambda~Rsa^m with m = -0.31 for glass bead size d = 0.05 cm and m = -0.55 for d = 0.10 cm and related to the sucrose Rayleigh-Darcy number lambda~Rsu^n with n = -0.41 for d = 0.05 cm and n = -0.69 for d = 0.10 cm, compared to the prediction of lambda~Rsa^0.5 from linear theory.