Convective, absolute, and global instabilities of thermocapillary-buoyancy convection in extended layers

Priede, Jānis; Gerbeth, Günter

doi:10.1103/physreve.56.4187

Cited by 54 publications

(45 citation statements)

References 17 publications

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“…Thresholds for the absolute, convective and stationary instability are given by the solid thick, dashed-dotted and dotted lines, respectively. The curves for the convective and stationary instabilities are similar to those reported by Priede and Gerbeth [18] for Pr ¼ 13:9. The curve for the absolute instability presents two branches that could be related with the two wave regimes reported by Burguete et al [20] in narrow rectangular enclosures, and by Garnier and Chi¤audel [22] in annular containers.…”

Section: Results and Comparison With Experimentssupporting

confidence: 76%

“…This direction may be correctly determined by the sign of the real part of the group velocity [18]. Consequently, the wavenumber k 0 corresponding to a vanishing group velocity…”

Section: Convective/absolute Instabilitymentioning

confidence: 99%

“…Moreover, Riley and Neitzel [17] confirmed regimes of hydrothermal waves, steady multicellular flow, and oscillatory multicellular flows in silicone oil of 1 cSt ðPr ¼ 13:9Þ in a wide rectangular container. These results were interpreted some years later by Priede and Gerbeth [18] in terms of absolute and convective instability.…”

Section: Introductionmentioning

confidence: 99%

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Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Pérez–García

Madruga

Echebarria

et al. 2004

Journal of Non-Equilibrium Thermodynamics

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The stability of a liquid layer with an undeformable interface open to the atmosphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature difference applied on the system. Depending on the liquid depth, this basic flow is destabilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturbations are driven by the basic flow and therefore one must distinguish between convective and absolute thresholds. The instability mechanisms as well as the di¤erent regimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr ¼ 10Þ. In particular, it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally.

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Section: Results and Comparison With Experimentssupporting

confidence: 76%

“…This direction may be correctly determined by the sign of the real part of the group velocity [18]. Consequently, the wavenumber k 0 corresponding to a vanishing group velocity…”

Section: Convective/absolute Instabilitymentioning

confidence: 99%

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Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Pérez–García

Madruga

Echebarria

et al. 2004

Journal of Non-Equilibrium Thermodynamics

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“…Daviaud and Vince [3] reported the first observation of hydrothermal waves in a shallow layer of 0.65 cSt silicon oil. These observations were complemented by other authors considering different liquids and geometries (Mukolobwiez et al [7], Riley and Neitzel [12], Priede and Gerbeth [11], Pelacho et al [9], Burguete et al [1]). …”

Section: Introductionmentioning

confidence: 85%

Instabilities in two-liquid layers subject to a horizontal temperature gradient

Madruga

Pérez–García

Lebon

2004

Theor. Comput. Fluid Dyn.

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Abstract. We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B 2 O 3 , a configuration of considerable technological importance. Four different flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscillatory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques.

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“…In the presence of lateral walls the linear theory based on the calculation of the convective instability threshold may not be valid, as shown by Priede and Gerbeth [41]. They reported that in the presence of buoyancy and lateral walls (though in extended systems) the direction of the propagation of the unstable mode is defined by the sign of the real part of group velocity.…”

Section: Two-dimensional Oscillatory Instability Of the Flowmentioning

confidence: 93%

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

Watanabe

Melnikov

Matsugase

et al. 2014

Microgravity Sci. Technol.

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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.

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Convective, absolute, and global instabilities of thermocapillary-buoyancy convection in extended layers

Cited by 54 publications

References 17 publications

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids

Instabilities in two-liquid layers subject to a horizontal temperature gradient

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

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