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.

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

“…This instability has been the subject of numerous studies as it impacts several climatic, environmental, and industrial applications. The double-diffusive (DD) instability is another buoyancy-driven instability, 4,5 which arises when two different contributions to the density profile are opposing (classically heat and mass, but it can also be that of two different solutes 2,6,7 ). DD occurs when the total density profile is stable (i.e., density increases downwards along the gravitational field) but the destabilizing component (heat, for instance) diffuses faster than the stabilizing one (mass).…”

Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells

“…The literature on the salt fingering instability is vast and so the reader is referred to recent reviews for more details (Kunze 2003;Schmitt 2003). DD instabilities occur not only in mass/heat problems but also whenever two different solutes are present (Turner 1979;Cooper, Glass & Tyler 1997;Pringle & Glass 2002;D'Hernoncourt, Zebib & De Wit 2006;D'Hernoncourt, De Wit & Zebib 2007;Pritchard 2009). Hence, the term 'double diffusive instability' is often used in a general sense to refer to hydrodynamic instability scenarios implying simultaneous transfer of heat and mass or more generally of two scalar quantities diffusing at different rates.…”

Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes

“…1(b) and 1(c) participate in density gradients starting from an initially stable density stratification. [13][14][15][16][17] Because of the large range of spatial scales involved in applications of RT and double diffusive instabilities, theoretical modeling backed up by laboratory-scale experiments have been developed to analyze their dynamics. Up to now, these classical buoyancy-driven instabilities have been characterized individually, but the dynamics resulting from the interaction between them has not yet been considered, in contrast to numerous other pattern-forming systems.…”