VOLUME 72, NUMBER 2 PHYSICAL REVIEW LETTERS 10 JANUARY 1994 Onset of Traveling Waves in Isothermal Double Diffusive Convection A. A. Predtechensky, * W. D. McCormick, J. B. Swift, Z. Noszticzius, and Harry L. Swinney Center for Nonlinear Dynamics and the Department of Physics, The University of Texas, Austin, Texas 78718 (Received 6 May 1993) Experiments on double diffusive convection sustained by imposed vertical concentration gradients have been conducted in a novel thin isothermal parallelepiped cell. The measured critical Rayleigh number and the frequency of traveling waves are in reasonable accord with a stability analysis that predicts a tricritical condition cled along the instability boundary. Visualization of the pattern from the side reveals that the asymptotic state immediately above the onset of instability consists of packets of traveling finite amplitude plumes. PACS numbers: 47.20. Bp, 47.20. Ky, 92.10.Mr raveling wave patterns spontaneously form in a wide variety of systems as they are driven away from equilib- rium. Thermally driven convection in binary mixtures is an example that has been extensively studied experi- mentally [1 — 5] and theoretically [6 — 8]. However, quanti- tative comparison of the observations with the perturba- tion theory analyses (amplitude equations) for thermal convection in mixtures has not been achieved [6] because the primary bifurcation is subcritical over most of the stability boundary [7] and thre=-dimensional effects de- velop beyond onset [4]. We describe here experiments on another system that exhibits an instability to trav- eling waves: convection in an isothermal Quid driven by appropriately imposed gradients of concentration of two species with difFerent difFusion rates (a ternary mixture). We are able to examine essentially two-dimensional be- havior by using a thin (Hele-Shaw) cell that has been considered in theoretical studies but has not been used in experiments on thermal convection because of the prob- lem of heat conduction through the side walls. In our isothermal system the corresponding condition, imper- meable side walls, is perfectly satisfied. In this paper we consider mainly the primary instability of this system, and we give some examples of pattern formation beyond the onset. We find some interesting difFerences between the be- havior of the isothermal ternary mixture and that in ther- mal convection in binary mixtures. For example, theoret- ically the ternary system in a thin cell satisfies a tricritical condition all along the oscillatory instability boundary. Experimentally, the bifurcation is "vertical, " leading to finite amplitude traveling waves but with no measurable hysteresis. Another difference is that the Lewis number ~, which is the ratio of the diffusion coeFicients, is 0. 5— 0.8 for the mixtures studied here, and can be varied from 0.1 to 1 by appropriate choice of the two solutes. This makes the neighborhood of the codimension-two point, where the onset behavior changes from traveling waves to steady rolls, experimentally accessible; this is not the case in binary mixtures [5] where the Lewis number is very small (10 ~). Most experiments on convection with two diferent SALT SOLUTION GEL-F1LLED MEMBRANES (thickness -0.1 mm) -. . %RS ENE GLYCOL OLUT1ON observ dire FIG. 1. Diagram of the convection cells. Cell A: d = 3.0 mm, m=0. 762mm, L =60mm; ceQB: d=6.0mm, tu = 1.5 mm, and L = 60 mm. The long side walls are made of polished quartz and the ends are stainless steel. The up- per reservoir contains the rapidly ousia@ species, sodium choride (concentr|Ltions 0.2-6.0 g/1), and the lower reservoir contains the slowly difFusing species, propylene glycol (0.3 — 45 g/1) [18]. The cell temperature is maintained at 22.8+ 0. 1'C. types of diffusing species have concerned transient be- havior in thermohaline systems [9]: A tank of fluid with impermeable boundaries is prepared with a vertical gra- dient in salt concentration, then heated from below and observed as the salt solution becomes well mixed [10]. We have developed a technique for studying sustained double difFusive convection using an isothermal aqueous solution with two solutes of different difFusion coefficients. The convection cell is shown in Fig. 1. The innovation here is the use of thin (0.06 mm) gel-impregnated membranes for the top and bottom surfaces of the cell [11]; the gel prevents mass flow in the membrane [9]. The outer sur- face of each membrane is in contact with a continuously refreshed reservoir so that well-defined concentrations are imposed: c, of the slowly difFusing species at the lower cell boundary (where cf = 0) and cy of the fast species at the upper boundary (where c, = 0). The resultant den- sity gradient for the slow species is stabilizing, while that for the fast species is destabilizing. The imposed con- centration differences constitute two independent control parameters and can be sustained indefinitely. In nondi- mensional form these control parameters are the Rayleigh 218 0031-9007/94/72 (2)/218 (4) $06.00 1994 The American Physical Society