Marangoni flow in half-zone liquid bridge of molten tin under ramped temperature difference

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

“…The free surface temperature generates oscillations at Ma = 74.47 (normalized distance from the second bifurcation: e 2 = (Ma À Ma c2 )/Ma c2 = 0.035). A similar phenomenon was observed in the case of As = 1.22 (Li et al, 2005). During the process of development of the oscillatory flow, different wave numbers and oscillation modes were observed as shown in Fig.…”

“…Such a two-step bifurcation of the non-oscillating thermocapillary flow (see Fig. 6) has never been observed in our numerical simulations with ramped temperature difference (Yasuhiro et al, 2004;Li et al, 2005). Oscillations in the flow field starts at t = 1640.1 s, DT e = 5.16 K and Ma c2 = 70.84 at the critical frequency of 0.067 Hz.…”

“…2b). The ramping rate of the temperature difference, d(T H À T C )/dt = 1.93 K/min, was calculated based on the experimental value measured by thermocouples located at 0.5 mm apart from the melt/rod interfaces by means of a steady conduction model (Yasuhiro et al, 2004;Li et al, 2005). The Pr and Marangoni numbers in this study are defined as Pr = m/a and Ma ¼ À ar T DTe qma , respectively, where DT e acting on the melt/solid interfaces is expressed as follows:…”

“…0,z = 0. 5L)j max was chosen due to its sensitivity to the incipience of oscillatory flow (Li et al, 2005). Fig.…”

“…In these experimental studies, the free surface temperature oscillations were successfully observed by using radiation thermometers, however, the oscillations possess greater amplitudes and lower frequencies than those predicted by the numerical studies. For investigating the causes of these discrepancies, long-run numerical simulations were conducted based on realistic liquid bridge models of molten tin with As = 1.22 and 2.0 (Yasuhiro et al, 2004;Li et al, 2005) in which the heat transfer in the supporting iron rods was taken into account, further, in these simulations a ramped temperature difference was imposed to mimic the experimental condition. The numerical studies revealed that velocity oscillations with small amplitudes and high frequencies occur in the interior regions of the melt zone at the second bifurcation.…”