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.

We report on the behavior of small particles of dilute concentration in time-dependent ͑oscillatory͒ thermocapillary flow in cylindrical liquid bridges. The particles accumulate in a dynamic string for certain aspect ratios of the liquid bridge and at, typically, two times the critical Marangoni number for the onset of time dependence. This was observed for particles with a density larger and smaller than that of the fluid and for the isodense case. If looked at in a snapshot, this string would be wound m times around the thermocapillary vortex as a deformed spiral. If one looked at the full dynamics, it would be seen that the spiral string is rotating around its ring-shaped axis. The phenomenon is called a dynamical particle accumulation structure ͑dynamical PAS͒. The mode m is the mode number of the oscillatory flow field with m wavetrains of the hydrothermal wave ͑HTW͒ traveling in the azimuthal direction. We visualize and describe the different modes m in detail. We give direct experimental evidence for the gathering of liquid with particles during the cold phases of the HTW and the injection of liquid with particles into the return flow in azimuthally traveling "cold spots." We varied the particle diameter at constant density and the ratio of the particle density to fluid density at constant particle diameter to measure the time of the formation of PAS and discuss and explain the experimental results in comparison with possible mechanisms underlying the formation process. We describe the results of an experiment under microgravity to exclude gravity as a PAS-forming mechanism. We conclude by describing a possible mechanism that could account for the observed particle accumulation in certain regions of the flow. This mechanism involves the observed gathering and injection of liquid during the cold phases of the HTW and the particle enrichment of the injected fluid due to particle migration in sheared flow. PAS occurs at a resonance between the azimuthally traveling wave and the "turnover time" of the PAS-string in the thermocapillary vortex.

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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Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side-wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time-dependent flow states (t) was observed. Two different t-flow states have been identified by thermocouple measurements and by visualization of the dynamic-free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short-wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long-wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.

Thermocapillary convection is induced in a liquid bridge by a nonuniform surface tension distribution caused by an axial temperature difference. A toroidal vortex is formed by the thermocapillary force over the free surface. The induced flow is visualized by using fine particles as tracers. At a sufficiently high Marangoni number, three-dimensional standing and traveling oscillatory flows appear, and under certain flow conditions, the tracer particles form particle accumulation structures ͑PAS͒. In the present study, the conditions for the occurrence of PAS have been carefully investigated with focus on the spiral loop PAS ͑SL-PAS͒ that appears when the flow exhibits a traveling mode. The particles gather along a closed spiral loop that winds itself around the toroidal vortex. Observed from above, the spiral loop looks as if it is rotating azimuthally. The number of spirals corresponds with the azimuthal wave number of the traveling wave and each spiral consists of either single or double turns. The azimuthal traveling direction of the particles trapped on the SL-PAS is opposite to that of the SL-PAS pattern and of the hydrothermal wave under the presently focused conditions. By varying particle diameter and density within a certain range, it was revealed that the SL-PAS appears almost independently of the particle properties. The path line of each particle trapped in the SL-PAS is different from the shape of the SL-PAS itself. The Stokes number of a particle is examined and found to be much smaller than unity. Furthermore, a structure similar to the SL-PAS was also visualized by injecting colored dye. Thus, the shape of the SL-PAS is primarily determined not by the particle-particle interaction but by the flow field itself.

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