In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.
Thermocapillary convection (TC) in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49 is investigated experimentally. The zones have been heated from above or from below to study the influence of buoyant forces. Fourier analyses of temperature signals from zones covering systematically wide ranges of aspect ratios A and Marangoni numbers Ma have shown the existence of various forms of periodic and nonperiodic TC. This paper reports on periodic TC existing under certain conditions between the onset of time-dependent TC at the critical Marangoni number Mac and 7×Mac. From the measurements of the onset of periodic TC the dependence is reported for the threshold Mac and the period near the threshold τc on the aspect ratio. The development of periodic TC when further increasing Ma is shown by typical examples from measurements of the frequency and the amplitude of the oscillations. By correlation analyses from three temperature signals, different structures of periodic TC in the investigated A–Ma–Pr range were identified. Both the running waves with an azimuthal component (m≥1) and the axially running waves (m=0) were found and the findings of these and various other spatiotemporal structures of periodic TC were displayed in A–Ma/Mac state maps. These maps indicate as well the influence of the Prandtl number and of the buoyant forces on the preferred spatial structure of periodic TC, as discussed in the light of an already existing theory.
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