Transition to chaotic thermocapillary convection in a half zone liquid bridge

Hydrothermal waves in a liquid bridge subjected to a gas stream along the interface

“…In the considered case of n-decane the static Bond number is relatively small, Bo st = ρgd 2 /σ = 2.7, and the effect of static deformation will not be considered. As concerns dynamic deformation, the recent experimental studies by Matsunaga et al (2012) showed that in the geometry of interest in the isothermal case the interface deformation by a gas stream (Re g 550) is about a few microns. In the non-isothermal case experimental (Ferrera et al 2008;) and numerical (Shevtsova et al 2008) studies reported that the interface deformation caused by a thermocapillary steady flow is proportional to the capillary number which is defined as…”

“…When ΔT = T hot − T cold exceeds a critical value ΔT cr , instability sets in as the result of Hopf bifurcation and gives rise to a number of time-dependent three-dimensional flow regimes (Kuhlmann 1999;Lappa 2010). In particular, instability may generate standing or travelling HTWs or lead to temporally chaotic dynamics (Ueno, Tanaka & Kawamura 2003;Melnikov, Shevtsova & Legros 2004;Matsugase et al 2015). A travelling wave (TW) can propagate in the azimuthal (Wanschura et al 1995;Leypoldt, Kuhlmann & Rath 2000;Lappa, Savino & Monti 2001) or axial direction and be characterized by a single integer azimuthal wavenumber m or a combination thereof (Shevtsova, Melnikov & Legros 2003;Shevtsova, Melnikov & Nepomnyashchy 2009).…”

“…The impact of a gas flow on the stability of statically deformed LBs was experimentally examined by Yano et al (2016) for Pr = 28, 67 when Re gas < 50, and it showed that the gas moving upward (downward) shifts the vertex position to the side of the smaller (larger) volume ratio. As for the dynamic interface deformation, it was obtained in several numerical (Herrada et al 2011) and experimental (Matsunaga et al 2012;Yang et al 2018) studies that the interface deformation does not exceed 10 μm in a millimetric LB when the velocity of gas is as large as 2 m s −1 . Recent results of linear stability analysis of a LB with high Prandtl number, Pr = 68, presented by Carrión, Herrada & Montanero (2020) showed that dynamic free surface deformation has very little effect on the stability of the flow.…”

“…In particular, instability may generate standing or travelling HTWs or lead to temporally chaotic dynamics (Ueno, Tanaka & Kawamura 2003; Melnikov, Shevtsova & Legros 2004; Matsugase et al. 2015). A travelling wave (TW) can propagate in the azimuthal (Wanschura et al.…”

Secondary instability induced by thermocapillary effect in half-zone liquid bridge of high Prandtl number fluid

“…While the onset conditions and the mechanism of the secondary instability have not been indicated for the high-Pr liquid bridge except an investigation (Motegi et al, 2017b) to the best of the authors' knowledge, previous researchers had indicated transition scenarios toward the chaotic/turbulent flows far beyond the threshold of the primary instability in terms of ∆T * . Quasi-periodic, period-doubling, and chaotic flows had been realized by ground- (Velten et al, 1991;Frank and Schwabe, 1997;Ueno et al, 2003) and microgravity-experiments (Matsugase et al, 2015) with several kinds of liquids of Pr ≥ 7. A series of numerical simulations was conducted with the HZ liquid bridge of Pr = 4 by focusing on the flow states beyond the threshold for the primary instability up to chaotic flow state (Shevtsova et al, 2003).…”