Double-diffusive finger convection: influence of concentration at fixed buoyancy ratio

Abstract

Double-diffusive finger convection is studied experimentally in a transparent Hele-Shaw cell for a two-solute system. A less dense sucrose solution is layered on top of a more dense salt solution using a laminar flow technique, and convective motion is followed photographically from the static state. We systematically increase solute concentrations from dilute to the solubility limit of the salt solution while maintaining a fixed buoyancy ratio of approximately 1.08. Across the 14 experiments conducted, the convective motion shows considerable variation in both structure and time scale. We find that new finger pairs form continuously within a finger generation zone where complexity increases with Rayleigh number, reaches a peak, and then decreases for highly concentrated solutions. The vertical fnger length scale grows linearly in time across the full concentration range. The vertical finger velocity also increases linearly with Rayleigh number, but as the concentrations increase, deviation from linearity and asymmetrical convection occur. The horizontal length scale grows as a power law in time with the exponent constant over most of the range; again, deviations are observed for highly concentrated solutions. The observed deviations at high concentrations are attributed to the increasing nonlinearity in the governing equations as the solutions approach their solubility limits. There, the fluid properties become functions of solute concentration and vary significantly within the experimental fields suppressing structural complexity, imparting asymmetry to the convective motion, and influencing emergent vertical and horizontal length scales and their growth.