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

Abstract

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.

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

“…In such a context, it is convenient to introduce a "spatial way" of thinking, by which the supercritical rotating state of Marangoni flow can be imagined [5][6][7][8][9][10][11][12][13] as the superposition of an axisymmetric toroidal vortex roll (like that existing prior to the onset of 3D flow) and a wave traveling in the azimuthal direction. The two components of vorticity V     in the azimuthal, and axial directions can be written, respectively, as:…”

“…the rotating mode (or traveling wave). The apparently solid filaments, formed by the spontaneous selfassembly of tracer particles, emerge only if the Marangoni number is in a proper range and some specific conditions are satisfied [5][6][7][8][9][10][11] . In particular, Schwabe and coworkers provided some evidence 12,13 supporting the idea that PAS may occur as a resonance between the azimuthally traveling wave and the "turnover time" of the PAS-string in the thermocapillary vortex.…”

On the variety of particle accumulation structures under the effect of g-jitters

“…Since most of existing studies have considered PAS structures in liquid bridges (with the supercritical Marangoni flow in the so-called rotating regime, see (Schwabe et al, , 2007Tanaka et al, 2006;Ueno et al, 2008), the starting point of our analysis is represented by such a geometry (Figure 1). …”

Accumulation of particles in time-dependent thermocapillary flow in a liquid bridge. Modeling of experiments

“…Several research groups from Japan have experimentally studied this phenomenon in silicone oils of 2 cSt and 5 cSt, see [7], [8], [9]. Despite the extensive experimental studies a comprehensive theoretical explanation is stull lacking.…”