Photon Correlation and Scattering Conference

A shadowgraph optical setup is used to study the time evolution of Soret induced convection in a colloidal suspension. We obtain a scale invariant behavior for the solutal Nusselt number as a function of the Rayleigh number. In a typical Rayleigh-Bénard experiment a horizontal slab of a fluid is contained between a top and bottom plates maintained at two different temperatures (higher temperature at the bottom plate). The order parameter of the system is the Rayleigh number Ra and when Ra exceeds 1708 the configuration becomes gravitationally unstable and a macroscopic convective flow takes place inside the enclosure: the warm fluid near the bottom plate rises toward the top plate, where eventually cools and begins to sink back to the warm bottom plate. When the temperature difference between the plates becomes large, the process becomes boundary layer dominated. As soon as the temperature difference is applied two thin conductive boundary layers grow near the isothermal plates until they are eventually destabilized by ascending and descending thermal plumes. For low values of the Prandtl number Pr = ν/κ (the ratio of the momentum diffusivity over the temperature one) the transition to turbulence takes place for Rayleigh numbers of the order of 10. This is due to the relatively high value of the thermal diffusivity κ that favors a chaotic diffusive mixing of plumes. On the contrary, for high values of Pr, a plume can cross the entire layer height without being distorted in shape by heat diffusion and the transition to turbulence takes place at much higher Rayleigh numbers. One of the most interesting information in convecting systems is given by the Nusselt number Nu: the enhancement of the heat flux beyond the conductive value due to convection across the layer. For high Rayleigh numbers (Ra > 10) [1] it is expected a scaling law in the form: ∝ p Nu Ra the numerical value for the exponent p depending on Pr. Boundary layer convection takes also place in binary mixtures at large Rayleigh numbers, where the concentration differences induced by the Soret effect play the same role of temperature ones. The sudden imposition of a temperature gradient between the plates induces a steady mass flow by means of the Soret effect. Near one impermeable plate mass starts gathering (and getting depleted near the opposite one) and two thin concentration boundary layers are instantaneously formed. Again the boundary layers are rapidly destabilized by concentration plumes. A formal analogy between thermal and solutal convection has been proved [2] providing the mapping of the relevant parameters into equivalent ones with concentration playing the role of temperature: the usual (thermal) Rayleigh number and Prandtl numbers are mirrored by the solutal Rayleigh number Ras and the Schmidt number Sc = ν/D (the ratio of the momentum diffusivity over the concentration one). In this work we present experimental results on the transient regime of a Soret driven boundary layer convective instability at high solutal Rayleigh numbers. The sample is a diluted aqueous colloidal suspension of silica spheres with an unusually large negative Soret coefficient ST. The mass diffusion coefficient D is so low is so low that the mixture has a virtually infinite Schmidt number. The experiment is conducted by heating from above so to be sure that the traditional Rayleigh-Bénard instability is not possible, and very high solutal Rayleigh numbers can be easily reached. The study is conducted by using a quantitative Shadowgraph technique to visualize directly the pattern of solutal refractive index modulations in the cell without renouncing to characterize the convective flow within the cell. The root mean square of the shadowgraph intensity signal gives an information equivalent to the turbidity of usual light scattering experiments. In such a way it is possible to estimate the amplitude of the convective flow as a function of time. As is evident in Fig. 1, this latter exhibits a fast onset followed by a set of damped oscillations that lead to a steady state value. NASA/CP—2004-213207 9 Figure 1: Root mean square of the shadowgraph signal as a function of time for different values of the solutal Rayleigh number. The curves taken at higher Rayleigh numbers are characterized by smaller latency times and larger steady state values. The characteristic onset time τp and oscillation period τosc show power law behavior