Buoyant-thermocapillary instabilities in medium-Prandtl-number fluid layers subject to a horizontal temperature gradient

Parmentier, Patrice; Regnier, Vincent; Lebon, Georgy

doi:10.1016/s0017-9310(05)80125-5

Cited by 77 publications

(72 citation statements)

References 8 publications

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“…Later on, Gershuni et al [8] found steady rolls in the case of conducting surfaces for Pr > 1. Parmentier et al [9] and Mercier and Normand [10] performed calculations by taking into account buoyancy e¤ects and thermal transfer properties at the interface, and confirmed theoretically the existence of oblique hydrothermal waves for intermediate Pr.…”

Section: Introductionmentioning

confidence: 85%

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: Introductionmentioning

confidence: 85%

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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“…When the free surface is thought to be deformable, the instability of surface wave was obtained. And then the theoretical analysis of the thermocapillary instabilities have been made up by Parmentier [5] for the consideration of buoyant effect, Mercier and Normand [6] for the introduction of heat exchange to the atmosphere and Kuhlmann [7] for three-dimensional flow. Experiments on thermocapillary instability have been conducted by Riley and Neitzel [8].…”

Section: Introductionmentioning

confidence: 99%

Transition to chaos in thermocapillary convection

Zhu

Kang

2013

International Journal of Heat and Mass Transfer

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a b s t r a c tWe present experiments on transition to chaos in thermocapillary convection in a rectangular pool of silicone oil. The applied temperature difference between the two sidewalls is adjusted in the range of 0-43°C to observe various dynamic states. The applied temperature gradient along the fluid-gas interface drives shear flow along the free surface from hot to cold and a back flow in the underlying layer. With the increase of the temperature gradient, the thermocapillary convection will transit from steady flow to regularly oscillatory flow, and finally to chaos. A temperature measurement system, which consists of thermocouple, voltmeter and data-acquiring computer, is used to record the temperature of the liquid dynamically. In order to identify the different dynamic regimes from steady flow to chaos, fast Fourier transform and fractal theory are used to analyze the experimental data. The critical conditions for transition have been obtained and discussed by non-dimensional analysis. The quasi-periodic route and Feigenbaum route were observed for different experimental conditions, and the relationship between oscillatory frequency and Marangoni number Ma has been discussed.

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“…The mechanisms for the hydrothermal wave instability have been described by Smith. 5 The stability of buoyant-thermocapillary instabilities has been addressed by Laure and Roux 6 for low Prandtl numbers and by Gershuni et al 7 and Parmentier et al 8 for values of the Prandtl number up to 10. The former analysis considers the case of adiabatic surfaces whereas the latter considers conducting boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient

et al. 2001

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We report experiments on buoyant-thermocapillary instabilities in differentially heated liquid layers. The results are obtained for a fluid of Prandtl number 10 in a rectangular geometry with different aspect ratios. Depending on the height of liquid and on the aspect ratios, the two-dimensional basic flow destabilizes into oblique traveling waves or longitudinal stationary rolls, respectively, for small and large fluid heights. Temperature measurements and space-time recordings reveal the waves to correspond to the hydrothermal waves predicted by the linear stability analysis of Smith and Davis ͓J. Fluid Mech. 132, 119 ͑1983͔͒. Moreover, the transition between traveling and stationary modes agrees with the work by Mercier and Normand ͓Phys. Fluids 8, 1433 ͑1996͔͒ even if the exact characteristics of longitudinal rolls differ from theoretical predictions. A discussion about the relevant nondimensional parameters is included. In the stability domain of the waves, two types of sources have been evidenced. For larger heights, the source is a line and generally evolves towards one end of the container leaving a single wave whereas for smaller heights, the source looks like a point and emits a circular wave which becomes almost planar farther from the source in both directions.

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Buoyant-thermocapillary instabilities in medium-Prandtl-number fluid layers subject to a horizontal temperature gradient

Cited by 77 publications

References 8 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

Transition to chaos in thermocapillary convection

Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient

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