Instability of thermocapillary–buoyancy convection in shallow
 layers. 
Part 1. Characterization of steady and oscillatory instabilities

Riley, R. J.; Neitzel, G. Paul

doi:10.1017/s0022112097008343

Cited by 209 publications

(176 citation statements)

References 25 publications

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“…These observations were completed by Muckolobwiez et al [16] in an annular geometry. 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: 87%

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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: Introductionmentioning

confidence: 87%

“…(17) are equivalent to a cusp (pinching) point. We use this property to determine the absolute instability threshold.…”

Section: Convective/absolute Instabilitymentioning

confidence: 99%

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 flow field is also rendered more complex due to the strong gravitational effects. Vigorous circulation would enhance heat transfer but could also prove detrimental by causing instabilities leading to dryouts and ruptures observed in falling films, 10 liquid layers, 53 and liquid bridges. 11 Thus, thermocapillary convection becomes much more critical in twophase systems.…”

Section: B Scaling Analysismentioning

confidence: 99%

Experimental investigation of steady buoyant-thermocapillary convection near an evaporating meniscus

et al. 2007

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Micro-particle image velocimetry measurements of the three-dimensional ͑3D͒ convection patterns generated near an evaporating meniscus in horizontally oriented capillary tubes are presented. Analysis of the vapor diffusion away from the meniscus reveals a zone of intense heat flux near the solid-liquid-vapor junction that creates a temperature gradient along the meniscus. This results in a surface tension gradient which, coupled with buoyancy effects, causes buoyant-thermocapillary convection in the liquid film. The relative influence of buoyancy and thermocapillarity on the flow was investigated for tube diameters ranging from 75 to 1575 m. A transition from a pure two-dimensional thermocapillary flow to a 3D buoyant-thermocapillary flow is observed with an increase in tube diameter. For the 75 m tube, a symmetrical toroidal vortex is observed near the meniscus. For larger tubes, buoyancy effects become apparent as they dominate the flow field. The high mass fluxes in smaller-diameter tubes drive stronger vortices. Particle streaks and micro-particle image velocimetry images obtained in multiple horizontal and vertical planes provide an understanding of this three-dimensional flow behavior. A scaling analysis shows the importance of thermocapillary convection in evaporating menisci.

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“…The exact characteristics of the waves depend strongly on these parameters and on the aspect ratios of the containers [18,24,42]. For the hydrothermal waves instability considered here, only Ma and Bo are relevant.…”

Section: Hydrothermal Wavesmentioning

confidence: 99%

“…They correspond to the first instability of a thin liquid layer with a free surface subjected to a horizontal temperature gradient [23]. Different experimental configurations have been used to study those traveling waves: rectangular cells with different aspect ratios [13,24,25,18,15], annular cells [26,14], cylindrical cells [27,17] and linear hot wire under the surface of a liquid [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

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We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatiotemporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper [1] extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

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Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities

Cited by 209 publications

References 25 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

Experimental investigation of steady buoyant-thermocapillary convection near an evaporating meniscus

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

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