Influence of viscosity variation on salt-finger instability in a fluid layer, a porous layer, and their superposition

Abstract

We consider the effect of temperature-dependent viscosity on the onset of buoyancy-driven salt-finger convection (stratifications of salt and temperature being destabilizing and stabilizing, respectively) in a horizontal fluid layer, a horizontal layer of a stratified porous medium, and in a horizontal fluid layer overlying a saturated porous medium. It is found that the viscosity variation affects the stability characteristics through two mechanisms. One is the formation of a relatively viscous sublayer which leads to multicellular convection and stabilizing; the other is the decrease of viscosity which favors the onset of convection. In a horizontal porous layer, the destabilizing mechanism prevails so that the motionless state becomes less stable as γ=ln(νmax/νmin), where ν is kinematic viscosity of the fluid, increases, and a general relation between critical solute (Rcsm) and thermal (Rm) Rayleigh numbers is found as Rcsm = Rm + 4π2H(γ), where H(γ) is determined by curve fitting on the basis of calculated results. In a horizontal fluid layer, the first mechanism predominates the convection when γ<6.86 and the second mechanism prevails when γ≳6.86; the motionless state is most stable at approximately γ=6.86. Another general relation between critical solute (Rcs) and thermal (R) Rayleigh numbers is also determined based on the calculated results as Rcs = R + 1070.76 G(γ). For superposed fluid and porous configuration, the stability characteristics become more complex and depend on the variations of γ,ζ (ratio of fluid layer depth to porous layer depth), and Rm, and so on. In general, the unicellular convection occurs for ζ=0.1 and the multicellular convection is observed for ζ≥ (R18)0.2; for Rm = 1, the stabilizing mechanism and destabilizing mechanism compete with each other; for Rm = 50, nevertheless, the stabilizing mechanism prevails so that increasing γ leads to stabilization; the fluid layer dominates the superposed system by convection at large γ for all ζ considered. The current results would provide valuable information for understanding the double-diffusive convection during the directional solidification of binary alloys.