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Applied Mechanics Reviews | Volume 61 | Issue 1 | Review Article
Review Articles

Thermocapillary Convection in Floating Zones

[+] Author and Article Information
W. R. Hu

 Institute of Mechanics, Chinese Academy of Sciences, 15 4th Round Road North West, Beijing 100080, P.R.C.

Z. M. Tang

 Institute of Mechanics, Chinese Academy of Sciences, 15 4th Round Road North West, Beijing 100080, P.R.C.wrhu@imech.ac.cn

K. Li

 Institute of Mechanics, Chinese Academy of Sciences, 15 4th Round Road North West, Beijing 100080, P.R.C.

Appl. Mech. Rev 61(1), 010803 (Mar 05, 2008) (15 pages) doi:10.1115/1.2820798 History: Published March 05, 2008
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This paper provides an overview of ongoing studies in the area of thermocapillary convection driven by a surface tension gradient parallel to the free surface in a floating zone. Here, research interests are focused around the onset of oscillatory thermocapillary convection, also known as the transition from quasisteady convection to oscillatory convection. The onset of oscillation depends on a set of critical parameters, and the margin relationship can be represented by a complex function of the critical parameters. The experimental results indicate that the velocity deviation of an oscillatory flow has the same order of magnitude as that of an average flow, and the deviations of other quantities, such as temperature and free surface radii fluctuations, are much smaller when compared with their normal counterparts. Therefore, the onset of oscillation should be a result of the dynamic process in a fluid, and the problem is a strongly nonlinear one. In the past few decades, several theoretical models have been introduced to tackle the problem using analytical methods, linear instability analysis methods, energy instability methods, and unsteady 3D numerical methods. The last of the above mentioned methods is known to be the most suitable for a thorough analysis of strong nonlinear processes, which generally leads to a better comparison with the experimental results. The transition from oscillatory thermocapillary convection to turbulence falls under the studies of chaotic behavior in a new system, which opens a fascinating new frontier in nonlinear science, a hot research area drawing many recent works. This paper reviews theoretical models and analysis, and also experimental research, on thermocapillary connection in floating zones. It cites 93 references.
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Figures

Grahic Jump Location
+Typical floating zone models. (a) Floating full zone on the ground. (b) Floating half zone heated from bottom on the ground. (c) Floating half zone heated from upper on the ground. (d) Floating full zone in the microgravity environment. (e) Floating half zone in the microgravity environment.
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Typical floating zone models. (a) Floating full zone on the ground. (b) Floating half zone heated from bottom on the ground. (c) Floating half zone heated from upper on the ground. (d) Floating full zone in the microgravity environment. (e) Floating half zone in the microgravity environment.
Figure 1

Typical floating zone models. (a) Floating full zone on the ground. (b) Floating half zone heated from bottom on the ground. (c) Floating half zone heated from upper on the ground. (d) Floating full zone in the microgravity environment. (e) Floating half zone in the microgravity environment.

Grahic Jump Location
+The schematic diagram of the floating half zone convection
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The schematic diagram of the floating half zone convection
Figure 2

The schematic diagram of the floating half zone convection

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+The critical Marangoni number depending on the volume of liquid bridge
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The critical Marangoni number depending on the volume of liquid bridge
Figure 3

The critical Marangoni number depending on the volume of liquid bridge

Grahic Jump Location
+The PIV measurement system in two cross sections of a liquid bridge
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The PIV measurement system in two cross sections of a liquid bridge
Figure 4

The PIV measurement system in two cross sections of a liquid bridge

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+The onset of oscillatory processes on the coordinated measurements of temperature and free surface radii during a heating rate 0.14°C∕s in a liquid bridge
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The onset of oscillatory processes on the coordinated measurements of temperature and free surface radii during a heating rate 0.14°C∕s in a liquid bridge
Figure 5

The onset of oscillatory processes on the coordinated measurements of temperature and free surface radii during a heating rate 0.14°C∕s in a liquid bridge

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+The measurement results of free surface waves of oscillatory thermocapillary convection in a liquid bridge of floating half zone
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The measurement results of free surface waves of oscillatory thermocapillary convection in a liquid bridge of floating half zone
Figure 6

The measurement results of free surface waves of oscillatory thermocapillary convection in a liquid bridge of floating half zone

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+The spectrum of surface temperature at z=0.16mm given by a numerical simulation result
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The spectrum of surface temperature at z=0.16mm given by a numerical simulation result
Figure 7

The spectrum of surface temperature at z=0.16mm given by a numerical simulation result

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+The measured temperature distributions (above), spectra (middle), and applied temperature differences (lower) given by the experimental results. The subharmonic bifurcations appear at (a), f0=(36.55±0.05)°C, (b) f2=(48.01±0.05)°C, (c) f4=(61.65±0.05)°C, (d) f8=(64.56±0.05)°C, and (e) f16=(65.15±0.05)°C, respectively.
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The measured temperature distributions (above), spectra (middle), and applied temperature differences (lower) given by the experimental results. The subharmonic bifurcations appear at (a), f0=(36.55±0.05)°C, (b) f2=(48.01±0.05)°C, (c) f4=(61.65±0.05)°C, (d) f8=(64.56±0.05)°C, and (e) f16=(65.15±0.05)°C, respectively.
Figure 8

The measured temperature distributions (above), spectra (middle), and applied temperature differences (lower) given by the experimental results. The subharmonic bifurcations appear at (a), f0=(36.55±0.05)°C, (b) f2=(48.01±0.05)°C, (c) f4=(61.65±0.05)°C, (d) f8=(64.56±0.05)°C, and (e) f16=(65.15±0.05)°C, respectively.

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