The three-dimensional stationary instability in dynamic thermocapillary shallow cavities

In various configurations with thermal convection, three-dimensional stationary patterns occur that consist of pairs of counter-rotating longitudinal rolls. These rolls are investigated in this paper under a variety of experimental conditions. The liquids used are ethanol and the silicone oil hexamethyldisiloxane. The upper surface of the liquid volume is free and very flat because measures against menisci at the side and end walls have been taken. The temperature gradient is applied horizontally via thermally conducting but transparent sapphire end walls, leading to thermocapillary forces at the free surface in addition to the buoyant forces at normal earth's gravity. The geometry of the liquid volume is either rectangular or axisymmetrical (annular). The rectangular setup is transparent and especially suited for optical observations of tracers in the bulk of the liquid. The annular setup has the advantages of a large azimuthal (transversal) extent and the absence of side walls. In it a wavelength of lambda approximate to 1.3d was observed (where d is the depth of the liquid volume). Temperatures and velocities are measured and used to characterize the instability. Also the region of existence of the instability is studied in layers shallower than in earlier experiments in order to give a larger ratio between thermocapillary and buoyant forces. To find the onset of the instability when increasing the temperature gradient, the amplitude of the instability was derived from measurements and extrapolated. This yields a significantly lower threshold (Ma(c) = 2300 +/- 1000 for d = 5 mm) than previous experimental studies. One implementation of the annular gap experiment was performed under microgravity (experiment MAGIA), the other experiments under normal gravity. The results of the experiment under microgravity indicate the absence of the three-dimensional stationary pattern under the absence of gravity.