Thermocapillary flows in liquid bridges of molten tin with small aspect ratios

Abstract

a b s t r a c tNumerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8 and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (nonoscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed.

Marangoni flow in floating half zone of molten tin

“…It should be noted that the free surface flow does not follow the Marangoni effect, i.e., velocity vectors near the surface indicate that surface moves from cold spots to hot spots against the Marangoni effect. This kind of transition between 3D non-oscillatory flows was also found in short FHZ (As = 0.8) of molten tin under lG [27].…”

Stability of thermocapillary flow in liquid bridges fully coupled to the gas phase

“…The second critical Reynolds number was further investigated by Motegi et al (2017a) using a numerical Floquet stability analysis. Further investigation of the low-Prandtl-number instabilities are due to Takagi et al (2001), Imaishi et al (2001), Li et al (2007Li et al ( , 2008 and Fujimura (2013).…”

The Role of Marangoni Convection in Crystal Growth

“…Here, numerals beside keys in the figure represent the modes, the azimuthal wave number, and the tempo-spatial oscillation behaviors. The numerical simulations for much realistic bridge geometry by Li et al [72], in which a half-zone liquid bridge of molten tin was held between two supporting rods of smaller thermal conductivity than the liquid bridge and under ramped temperature difference, revealed that Ma LB c1 and Ma LB c2 fall close to, but slightly larger than, those in Figure 22.23. Also, (m þ 1) near the Re LB gc2 key represents an oscillation mode that is characterized by a superposition of m ¼ 1 type oscillating three-dimensional disturbance over a steady three-dimensional flow pattern of m (in case of Figure 22.24(a), m ¼ 2).…”