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Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

Published online by Cambridge University Press:  20 April 2006

F. Preisser ,
D. Schwabe  and
A. Scharmann
F. Preisser
Affiliation:
I. Physikalisches Institut, Justus Liebig-Universität, Heinrich-Buff-Ring 16, D-6300 Giessen, W. Germany
D. Schwabe
Affiliation:
I. Physikalisches Institut, Justus Liebig-Universität, Heinrich-Buff-Ring 16, D-6300 Giessen, W. Germany
A. Scharmann
Affiliation:
I. Physikalisches Institut, Justus Liebig-Universität, Heinrich-Buff-Ring 16, D-6300 Giessen, W. Germany
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Abstract

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.

The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.

The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 126 , January 1983 , pp. 545 - 567
Copyright
© 1983 Cambridge University Press

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References

Babskiy, V. G., Sklovskaya, J. S. & Sklovskiy, Y. B. 1975 In Space Studies in the Ukraine. no. 1 (ed. E. Pisarenko). Kiev: Naukova Domka. Available as NASA Tech. Transl. F 15, p. 535.
Birikh, R. V. 1966 Thermocapillary convection in a horizontal layer of liquid J. Appl. Mech. Tech. Phys. 3, 43.Google Scholar
Block, M. J. 1956 Surface tension as the cause of Bénard cells and surface deformation in a liquid film Nature 178, 650.Google Scholar
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid J. Fluid Mech. 52, 97.Google Scholar
Chang, CH. E. & Wilcox, W. R. 1976 Analysis of surface tension driven flow in floating zone melting Int. J. Heat Mass Transfer 19, 355.Google Scholar
Chang, CH. E., Wilcox, W. R. & Lefever, R. A. 1979 Thermocapillary convection in floating zone melting: influence of zone geometry and Prandtl number at zero gravity. Mat. Res. Bull. 14, 527.Google Scholar
Chun, C.-H. & Wuest, W. 1978 A microgravity simulation of the Marangoni convection Acta Astronautica 5, 681.Google Scholar
Chun, C. H. & Wuest, W. 1979 Experiments on the transition from steady to oscillatory Marangoni convection in a floating zone under reduced gravity effect Acta Astronautica 6, 1073.Google Scholar
Clark, P. A. & Wilcox, W. R. 1980 Influence of gravity on thermocapillary convection in floating zone melting of silicon J. Cryst. Growth 50, 461.Google Scholar
Clever, R. M. & Busse, F. H. 1974 Transition to time dependent convection J. Fluid Mech. 65, 625.Google Scholar
D'ANS-LAX 1964 Taschenbuch für Chemiker und Physiker, vol. II. Springer.
Grodzka, P. G. & Bannister, T. C. 1975 Heat flow and convection experiments aboard Apollo 17 Science 187, 165.Google Scholar
Heywang, W. 1956 Zur Stabilität senkrechter Schmelzzonen. Z. Naturforsch. 11 A, 238.Google Scholar
Janz, G. J. 1967 Molten Salts Handbook. Academic.
LANDOLT-BöRNSTEIN 1969 Zahlenwerte und Funktionen, vol. 2, part 5A. Springer.
LANDOLT-BöRNSTEIN 1971 Zahlenwerte und Funktionen, vol. 2, part 1. Springer.
Langlois, W. E. 1980 Digital simulation of Czochralski bulk flow in microgravity J. Cryst. Growth 48, 25.Google Scholar
Langlois, W. E. 1981 Conservative differencing procedures for rotationally symmetric flow with swirl Comp. Meth. in Appl. Mech. & Engng 25, 315.Google Scholar
Levich, B. G. 1962 Physico-Chemical Hydrodynamics. Prentice-Hall.
Nield, D. A. 1964 Surface tension and buoyancy effects in cellular convection J. Fluid Mech. 19, 341.Google Scholar
Ostrach, S. 1977 Motion induced by capillarity. In Proc. Int. Conf. on Physico-Chemical Hydrodynamics (Levich Conferenece 1977). St Peter Port, Guernsey, U.K.: Advance Publications.
Pearson, J. R. A. 1958 On convection cells induced by surface tension J. Fluid. Mech. 4, 489.Google Scholar
Preisser, F. 1981 Die thermische Marangonikonvektion in zylindrischen Schmelzzonen. Thesis, Justus-Liebig-Universität Giessen.
Schwabe, D. 1981a Marangoni effects in crystal growth melts. Physicochem. Hydrodyn. 2, 263.Google Scholar
Schwabe, D. 1981b Marangonikonvektion in Schmelzen. Habilitationsschrift, Justus-Liebig-Universität Giessen.
Schwabe, D., Preisser, F. & Scharmann, A. 1982 Verification of the oscillatory state of thermocapillary convection in a floating zone under low gravity. Acta Astronautica 9 (in the press).Google Scholar
Schwabe, D. & Scharmann, A. 1979 Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts J. Cryst. Growth 46, 125.CrossRefGoogle Scholar
Schwabe, D. & Scharmann, A. 1980 Thermocapillary convection in crystal growth melts Lett. Heat Mass Transfer 7, 283.Google Scholar
Schwabe, D. & Scharmann, A. 1981 Marangoni convection in open boat and crucible J. Cryst. Growth 52, 435.Google Scholar
Schwabe, D., Scharmann, A. & Preisser, F. 1979 Steady and oscillatory Marangoni convection in floating zones under 1-g. ESA SP-142, 327.
Schwabe, D., Scharmann, A. & Preisser, F. 1980 Konvektion in einer floating zone ohne Rotation. DGLR-Bericht 80–02, p. 323.Google Scholar
Schwabe, D., Scharmann, A. & Preisser, F. 1982 Studies of Marangoni convection in floating zones Acta Astronautica 9, 183.Google Scholar
Schwabe, D., Scharmann, A., Preisser, F. & Oeder, R. 1978 Surface tension driven flow in floating zone melting J. Cryst. Growth 43, 305.Google Scholar
Scriven, L. E. & Sternling, C. V. 1964 On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321.CrossRefGoogle Scholar
Smith, K. A. 1966 On convection instability induced by surface-tension gradients J. Fluid Mech. 24, 401.Google Scholar
Smith, M. K. & Davis, S. H. 1981 Instability of a thermocapillary shear flow. European Mechanics Colloquium 138, Karlsruhe, 9–11 March, 1981, abstracts pp. 129–130.Google Scholar
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection J. Fluid Mech. 44, 661.Google Scholar