Convective Instability in a Fluid Mixture Heated from Above

Abstract

Convection patterns in ethanol-water mixtures with negative c are studied when the fluid is heated from above. Although the linear analysis predicts that the instability occurs at zero wave number, a large wave number pattern is observed. The onset is supercritical with a threshold that is experimentally indistinguishable from zero. The convection amplitude exhibits damped oscillations for sudden change in the forcing parameter. At the constant Rayleigh number the patterns first coarsen, then exhibit growth of narrow plumes. The instability appears to be related to salt fingering. [S0031-9007(98)05952-3] PACS numbers: 47.20.Bp, 47.20.Ky, 47.54. + r When a fluid mixture is driven far from equilibrium by the flow of heat or material into one or more surfaces of the fluid volume, the system may become unstable to a convective flow which enhances the material and heat transport. There are many important examples of this type of flow in nature and technology. For instance, thermohaline convection in the oceans can be driven by temperature gradients or by salinity gradients [1], and double diffusive convection can be important in crystal growth. Finally, convection in fluid mixtures continues to be an important model system for the study of pattern formation in systems driven far from equilibrium [2].In this Letter, we describe experiments on convection in a fluid mixture with negative separation ratio in which the fluid is heated from above, a regime of parameters which has not been studied extensively. We find that a short wavelength convection pattern appears, despite the fact that the linear instability occurs at zero wave number. The onset of the pattern appears to be supercritical bifurcation to a steady flow, although damped oscillations in the pattern amplitude are observed when the forcing parameter is changed rapidly. The patterns continue to undergo stochastic motion even after they have reached a statistically stationary state.The experiments were performed in the RayleighBénard configuration, in which a thin layer of fluid mixture is confined between horizontal plates which are held at a fixed temperature difference. The thermal driving of the system is characterized by the Rayleigh number,where n is the viscosity, k is the thermal diffusivity, g is the acceleration of gravity, a is the thermal expansion coefficient, and h is the cell height. (Below, we will use the reduced Rayleigh number, r ϵ Ra͞1708, which is normalized to the onset of convection in a pure fluid.) In principle, it would be simplest to impose similar boundary conditions on temperature and concentration by fixing the concentration difference between the top and bottom plates. In laboratory experiments, however, the system boundaries are typically impermeable to both components of the fluid mixture, so that only the average concentration of solute in the fluid is directly controllable. The Soret effect introduces a coupling between concentration transport and the local temperature gradient in the mixture, and this causes a concentration...

Surface tension-driven convection patterns in two liquid layers

“…17. This pattern is very similar to that observed by La Porta and Surko [31] of thermo-solutal convection for T < 0. The pattern was transient and lasted for a period of several hours depending on the strength of the applied temperature difference and on the amount of Galden condensed on the sapphire window.…”

Linear and Nonlinear Double-Diffusive Convection in a Fluid-Saturated Porous Layer with Cross-Diffusion Effects

“…They used the linear stability analysis to find the criteria for the onset of oscillatory convection. A study of convective instability in a fluid mixture heated from above with negative separation ratio (Soret coefficient) was performed experimentally by La Porta and Surko (1998). Straughan and Hutter (1999) have investigated the double-diffusive convection with Soret effect in a porous layer using Darcy-Brinkman model.…”

Inclined layer convection in a colloidal suspension with negative Soret coefficient at large solutal Rayleigh numbers

“…The relevant parameter in this case is the solutal Rayleigh number Ra s = gΔρ c h 3 /(ηD) = RaΨ/Le. Studies on simple fluids [17][18][19] and binary mixtures and colloidal suspensions [20][21][22][23][24][25] performed at large (solutal) Rayleigh numbers of the order of 10 5 < Ra s < 10 9 have shown that the planform of the instability is a spoke pattern made by two staggered networks ( fig. 1) with loops that are on average quadrilateral [25].…”