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Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities

  • Marc K. Smith (a1) (a2) and Stephen H. Davis (a1)
Abstract

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations.

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Adler, J. 1970 Combust. Sci. & Tech. 2, 105.
Carruthers, J. R. 1976 J. Crystal Growth 32, 13.
Chun, C.-H. & Wuest, W. 1978a Acta Astronautica 5, 681.
Chun, C.-H. & Wuest, W. 1978b COSPAR: Space Research 18, 523.
Chun, C.-H. & Wuest, W. 1979 Acta Astronautica 6, 1073.
Clark, P. A. & Wilcox, W. R. 1980 J. Crystal Growth 50, 461.
Davis, S. H. & Homsy, G. M. 1980 J. Fluid Mech. 98, 527.
Gumerman, R. J. & Homsy, G. M. 1974 AIChE J. 20, 981.
Kenning, D. B. R. 1968 Appl. Mech. Rev. 21, 1101.
Kölker, H. 1980 J. Crystal Growth 50, 852.
Papazian, J. M., Gutowski, R. & Wilcox, W. R. 1979 AIAA J. 17, 1111.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 489.
Scanlon, J. & Segel, L. A. 1967 J. Fluid Mech. 30, 149.
Schwabe, D., Scharmann, A., Preisser, F. & Oeder, R. 1978 J. Crystal Growth 43, 305.
Schwabe, D. & Scharmann, A. 1979 J. Crystal Growth 46, 125.
Scott, M. R. & Watts, H. A. 1975 Sandia Labs. Rep. SAND75-0198, Albuquerque.
Scott, M. R. & Watts, H. A. 1977 SIAM J. Num. Anal. 14, 40.
Scriven, L. E. & Sternling, C. V. 1960 Nature 187, 186.
Sen, A. K. & Davis, S. H. 1982 J. Fluid Mech. 121, 163.
Sirignano, W. A. 1972 Combust. Sci. & Tech. 6, 95.
Smith, M. K. 1982 Ph.D. disseration, Northwestern University.
Smith, M. K. & Davis, S. H. 1983 J. Fluid Mech. 132, 145.
Subramanian, R. S. 1981 AIChE J. 27, 646.
Wilcox, W. R. 1971 Preparation and Properties of Solid State Materials Vol. 1: Aspects of Crystal Growth, p. 37. Dekker.
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 J. Fluid Mech. 6, 350.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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