Flow structure and dynamic particle accumulation in thermocapillary convection in a liquid bridge

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 (PAS). In the present study, the conditions for the occurrence of PAS have been carefully investigated with focus on the spiral loop PAS (SL-PAS) 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.