Reviews of topical problems

The Benard-Marangoni thermocapillary-instability problem

Universite des Sciences et Technologies de Lille1, Mathematiques Pures et Appliquees, Department de Mecanique Fondamentale, Batiment M 3, Villeneuve d’Ascq Cedex, 59655, France

Physically, there are two main mechanisms responsible for driving the instability in the coupled buoyancy (Benard) and thermocapillary (Marangoni) convection problem for a weakly expansible viscous liquid layer bounded from below by a heated solid surface and on the top by a free surface subject to a temperature-dependent surface tension. The first mechanism is density variation generated by the thermal expansion of the liquid; the second results from the surface-tension gradients due to temperature fluctuations along the upper free-surface. In the present paper we consider only the second effect as in the Benard experiments [the so-called Benard-Marangoni (BM) problem]. Indeed, for a thin layer we show that it is not consistent to consider both effects simultaneously, and we formulate an alternative concerning the role of buoyancy. In fact, it is necessary to consider two fundamentally distinct problems: the classical shallow-convection problem for a non-deformable upper surface with partial account of the Marangoni effect (the RBM problem), and the full BM problem for a deformable free surface without the buoyancy effect. We shall be mostly concerned with the thermocapillary BM instabilities problem on a free-falling vertical film, since most experiments and theories have focused on this (in fact, wave dynamics on an inclined plane is quite analogous). For a thin film we consider three main situations in relation to the magnitude of the characteristic Reynolds number (Re) and we derive various model equations. These model equations are analyzed from various points of view but the central intent of this paper is to elucidate the role of the Marangoni number on the evolution of the free surface in space and time. Finally, some recent numerical results are presented.

Fulltext is available at IOP
PACS: 44.25.+f, 44.30.+v, 47.10.+g, 47.27.+i (all)
DOI: 10.1070/PU1998v041n03ABEH000374
Citation: Zeytounian R Kh "The Benard-Marangoni thermocapillary-instability problem" Phys. Usp. 41 241–267 (1998)
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Оригинал: Зейтунян Р Х «Проблема термокапиллярной неустойчивости Бенара-Марангони» УФН 168 259–286 (1998); DOI: 10.3367/UFNr.0168.199803b.0259

References (85) Cited by (39) Similar articles (17) ↓

  1. A.V. Getling “Formation of spatial structures in Rayleigh—Bénard convection34 (9) 737–776 (1991)
  2. L.Kh. Ingel, M.V. Kalashnik “Nontrivial features in the hydrodynamics of seawater and other stratified solutions55 356–381 (2012)
  3. A.N. Vulfson, O.O. Borodin “The system of convective thermals as a generalized ensemble of Brownian particles59 109–120 (2016)
  4. A.M. Fridman “Prediction and discovery of extremely strong hydrodynamic instabilities due to a velocity jump: theory and experiments51 213–229 (2008)
  5. L.A. Bol’shov, P.S. Kondratenko, V.F. Strizhov “Natural convection in heat-generating fluids44 999–1016 (2001)
  6. V.A. Bednyakov, E.V. Khramov “Search for Supersymmetry with R-parity violation at the ATLAS”, accepted
  7. L.T. Adzhemyan, N.V. Antonov, A.N. Vasil’ev “Quantum field renormalization group in the theory of fully developed turbulence39 1193–1219 (1996)
  8. I.A. Vasil’eva “Stationary radiation of objects with scattering media44 1255–1282 (2001)
  9. E.D. Eidel’man “Excitation of an electric instability by heating38 1231–1246 (1995)
  10. S.K. Betyaev “Hydrodynamics: problems and paradoxes38 287–316 (1995)
  11. M.F. Sarry “Theoretical calculation of equations of state: analytical results42 991–1015 (1999)
  12. F.Kh. Mirzoev, V.Ya. Panchenko, L.A. Shelepin “Laser control processes in solids39 1–29 (1996)
  13. M.A. Liberman, B. Johansson “Properties of matter in ultrahigh magnetic fields and the structure of the surface of neutron stars38 117–136 (1995)
  14. M.V. Kuznetsov, A.S. Razinkin, A.L. Ivanovskii “Oxide nanostructures on a Nb surface and related systems: experiments and ab initio calculations53 995–1014 (2010)
  15. Yu.L. Klimontovich “Kinetic equations for nonideal gas and nonideal plasma16 512–528 (1974)
  16. N.P. Kovalenko, I.Z. Fisher “Method of integral equations in statistical theory of liquids15 592–607 (1973)
  17. A.F. Andreev “Interaction of conduction electrons with a Metal surface14 609–615 (1972)

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