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Effect of buoyancy ratio on the development of double‐diffusive finger convection in a Hele‐Shaw Cell
Author(s) -
Cooper Clay A.,
Glass Robert J.,
Tyler Scott W.
Publication year - 2001
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2001wr000343
Subject(s) - buoyancy , double diffusive convection , convection , instability , diffusion , mechanics , layering , hele shaw flow , thermodynamics , chemistry , physics , natural convection , reynolds number , rayleigh number , biology , botany , turbulence
We consider the evolution of double‐diffusive finger convection for a two‐ solute (salt‐sucrose) system in a Hele‐Shaw cell. A high‐resolution, full‐field, light transmission technique was used to study the development of the instability that resulted from layering a lighter sucrose solution over a denser salt solution. The buoyancy ratio ( R ρ ), which is a ratio of fluid density contributions by the two solutes and defines the degree of system disequilibrium, was varied systematically from conditions that were nearly stable ( R ρ = 2.8) to those that were moderately unstable ( R ρ = 1.4). In all experiments, fingers are found to form continuously throughout time from a finger “generation” zone that straddles the location of the initial interface between solutions. At low R ρ , fingers develop rapidly, merge with adjacent fingers, and grow far beyond the finger generation zone through a series of finger “conduits.” In the higher R ρ experiments, fingers are slower to evolve, do not interact as dynamically, and do not grow far beyond the generation zone. Solute mass fluxes at low R ρ quickly reach a constant many times greater than that of a purely diffusive system; at high R ρ , mass fluxes decay as t −½ and behave diffusively but with effective diffusion coefficients much greater than those for molecular diffusion.