The Stability of a Thermocapillary-Buoyant Flow in a Liquid Bridge with Heat Transfer Through the Interface

Abstract

a b s t r a c tThe hydrodynamic stability of a thermocapillary flow in a finite-size liquid bridge, with a non-deformable interface, heated from above and surrounded by a passive gas is examined by means of three-dimensional direct numerical simulations. Convective flow in 1 cSt silicone oil with Pr ¼ 18 is driven by combined effects of buoyancy and thermocapillary forces. Effects of the interfacial heat exchange on hydrothermal stability of the bulk flow are evaluated for various external thermal conditions in the gas phase. Cooling the interface can significantly shift the bifurcation point where the thermocapillary flow becomes oscillatory. If the Biot number Bi, which is a measure of the rate of the heat exchange, is not large, the effect of the interfacial heat flux can be either stabilizing or destabilizing, depending on both the temperature profile in the gas and the height of the liquid bridge. For a high value of heat loss rate, stabilization occurs regardless of the temperature distribution in the ambient gas. Various flow regimes are identified, and detailed stability maps are made for the flow under the considered ambient thermal conditions. It was found that the critical azimuthal mode of the flow changes according to the surrounding conditions in the gas phase. Observations have revealed three distinct azimuthal modes: m ¼ 0 (critical for a long liquid bridge at small Biot numbers), m ¼ 1 and m ¼ 2. Any mode change of the flow is accompanied by an abrupt change of the frequency of temperature oscillations.

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

“…2014; Watanabe et al. 2014). Also, the possibility of imposing an external gas flow shows promise for a control of the onset of hydrothermal waves.…”

“…A recent study by Romanò & Kuhlmann (2019) has shown, however, that modelling the heat transfer across the interface by Newton's law tends to underestimate the thermocapillary driving, except very close to the cold rod. Motivated by the experimental evidence of the strong impact of the heat transfer across the interface (Kamotani et al 2003;Yano et al 2017), and with improved computing capabilities, more recent numerical approaches take into account the flow and heat transport in the surrounding gas phase (Shevtsova et al 2014;Watanabe et al 2014). Also, the possibility of imposing an external gas flow shows promise for a control of the onset of hydrothermal waves.…”

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

“…The first experiments controlling ambient conditions around a LB (Kamotani et al 2003;Mialdun & Shevtsova 2006;Irikura et al 2007;Watanabe et al 2014) indicated that heat exchange between the liquid and the ambient gas is an important factor that influences the instability mechanisms. However, in numerical studies, in order to optimize the computing time the problem is typically modelled as a single-phase liquid flow when the gas phase next to the LB is ignored, assuming that the viscosity and thermal conductivity of the gas are negligible.…”

Experimental Study on Formation of Particle Accumulation Structures by a Thermocapillary Flow in a Deformable Liquid Column

“…We will not supply further details on the experimental setup and procedure. The related information could be found in, e.g., Melnikov et al (2013a) and Watanabe et al (2014). Results of the data processing are shown in Section "Chaos Analysis of Experimental Data".…”