Bénard convection flows

Journal of Non-Equilibrium Thermodynamics

Volumn 22, Issue 1, 1997, Pages 1-9

  Bragard, J ^a,b   Velarde, M G ^a,b  

^a INSTITUTO PLURIDISCIPLINAR   (Spain)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW PATTERNS; PHASE INTERFACES; SURFACE TENSION; THERMAL GRADIENTS; THERMODYNAMIC STABILITY; TURBULENCE;

LABYRINTHINE CONVECTION FLOWS; MARANGONI NUMBER;

HEAT CONVECTION;

EID: 0030704003     PISSN: 03400204     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (65)

1. Rowlinson, J. S., Widom, B., Molecular theory of capilarity, Clarendon Press, Oxford, 1982.
2. Levich, V. G., Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962.
3. Bénard, H., Les tourbillons cellulaires dans une nappe liquide, Rev. Gén. Sciences Pure Appl., 11 (1990), 1261-1271.
4. Normand, C., Pomeau, Y., Velarde, M. G., Convective instability: A physicist's approach, Rev. Mod. Phys., 49 (1977), 581-624.
5. Velarde, M. G., Normand, C., Convection, Sci. Am., 243 (1980), 92-108.
6. Koschmieder, E. L., Bénard Cells and Taylor V ortices, Cambridge Univ. Press, Cambridge, UK, 1993.
7. Thomson, J., On certain curious motions observale at the surfaces of wine and other alcoholic liquors, Philos. Mag., 10 (1855), 330.
8. Thomson, J., On a changing tessellated structure in certain fluid, Proc. Roy. Phil. Soc. (Glasgow), 13 (1882), 464.
9. Weber, E. H., Mikroskopische Beobachtungen sehr gesetzmässiger Bewegungen, welche die Bildung von Niederschlägen harziger Körper aus Weingeist begleiten. Ann. Phys. (Poggendorf), 94 (1855), 447.
10. Velarde, M. G., Hydrodynamic Instabilities, in: Fluid Dynamics, Eds. R. Balian and J. L. Peube, pages 469-527, Gordon and Breach, New York, 1976.
11. Block, M. J., Surface tension as the cause of Bénard cells and surface deformation in a liquid film, Nature, 178 (1956), 650-651.
12. Lord Rayleigh, On the dynamics of revolving fluids, Proc. R. Soc. London Ser. A, 93 (1916), 148.
13. Velarde, M. G., Castillo, J. L., Transport and reactive phenomena leading to interfacial instability, in: Convective transport and instability phenomena, Eds. J. Zierep and H. Oertel, pages 235-264, Braun-Verlag, Karlsruhe, 1982.
14. Pearson, J. R. A., On convection cells induced by surface tension, J. Fluid Mech., 4 (1958), 489-500.
15. Davis, S. H., Thermocapillary instabilities, Ann. Rev. Fluid Mech., 19 (1987), 403-435.
16. Cross, M. C., Hohenberg, P. C., Pattern formation outside of equilibrium, Rev. Mod. Phys., 65 (1993), 851-1112.
17. Thess, A., Orzag, S. A, Surface-tension-driven Bénard convection at infinite Prandtl number, J. Fluid Mech., 283 (1995), 201-230.
18. Scanlon, J. W., Segel, L. A., Finite amplitude cellular convection induced by surface tension, J. Fluid Mech., 30 (1967), 149-162.
19. Levchenko, E. B., Chernyakov, A. L., Instability of surface waves in a nonuniformly heated liquid, Sov. Phys. JET P, 54 (1981), 102.
20. García-Ybarra, Castillo, P. L., Velarde, M. G., Bénard-Marangoni convection with a deformable interface and poorly conducting boundaries, Phys. Fluids, 30 (1987), 2655-2661.
21. García-Ybarra, J. L., Castillo, P. L., Velarde, M. G., A non-linear evolution equation for Bénard-Marangoni convection with deformable boundary, Phys. Lett. A, 122 (1987), 107-110.
22. Chu, X. L., Velarde, M. G., Transverse and longitudinal waves induced and sustained by surfactant gradients at liquid-liquid interfaces, J. Coll. Int. Sci., 131 (1989), 471-484.
23. Cloot, A., Lebon, G., A non-linear stability analysis of the Bénard-Marangoni problem, J. Fluid Mech., 145 (1984), 447-469.
24. Bragard, J., Lebon, G., Non-linear Marangoni convection in a layer of finite depth Europhys. Lett., 21 (1993), 831-836.
25. Cerisier, P., Jamond, C., Pantaloni, J., Pérez-Garcia, C., Stability of roll and hexagonal patterns in bénard-marangoni convection, Phys. Fluids, 30 (1987), 954-959.
26. Schatz, M. F., VanHook, S. J., McCormick, W. D., Swift, J. B., Swinney, H. L., Onset of surface-tension-driven Bénard convection, Phys. Rev. Lett., 75 (1995), 1938-1947.
27. Davis, S. H., Buoyancy-surface tension instability by the method of energy, J. Fluid. Mech., 39 (1969), 347-359.
28. Davis, S. H., Homsy, G. M., Energy stability theory for free-surface problems: buoyancy-thermocapillary layers, J. Fluid. Mech., 98 (1980), 527.
29. Castillo, J. L., Velarde, M. G., Buoyancy-thermocapillary instability: the role of interfacial deformation in one- and two-component fluid layers heated from below or above, J. Fluid. Mech., 125 (1982), 463.
30. Nitschke, K., Thess, A., Secondary instability in surface tension driven Bénard convection, Phys. Rev. E, 52 (1995), 5772-5775.
31. Bragard, J., Velarde, M. G., Bénard-Marangoni Convection: Planforms and related theoretical predictions, J. Fluid Mech., in print (1996).
32. Gunaratne, G. H., Complex spatial patterns on planar continua, Phys. Rev. Lett. 10 (1993), 1367-1370.
33. Golovin, A. A., Nepomnyashchy, Pismen, L. M., Pattern formation in large-scale Marangoni convection with deformable interface, Physica D 81 (1995), 117-147.
34. Hadji, L., Nonlinear analysis of the coupling between interface deflection and hexagonal patterns in Rayleigh-Bénard-Marangoni convection, Phys. Rev. E 53 (1996), 5982-5992.
35. Kubstrup, C., Herrero, H., Pérez Garcia, C., Fronts between hexagons and squares in a generalized Swift-Hohenberg equation, Phys. Rev. E 54 (1996), 1560-1569.
36. Dauby, P. C., Lebon, G., Bénard-Marangoni instability in rigid rectangular containers, J. Fluid Mech. 329 (1996), 25-64.
37. Landau, E. M., On the problem of turbulence, C. R. Acad. Sci. URSS, 44 (1944), 311.
38. Stuart, J. T., On the nonlinear mechanics of hydrodynamic stability, J. Fluid Mech., 4 (1958), 1-21.
39. Newell, A. C, Whitehead, J. A, Finite bandwidth, finite amplitude convection, J. Fluid Mech., 38 (1969), 279-303.
40. Pérez-Cordon, R., Velarde, M. G., On the (non-linear) foundations of Boussinesq approximation applicable to a thin layer of fluid, J. Phys. (Paris), 36 (1975), 591.
41. Velarde, M. G., Pérez-Cordon, R., On the (non-linear) foundations of Boussinesq approximation aplicable to a thin layer of fluid, (ii) viscous dissipation and large cell gap effects, J. Phys. (Paris), 37 (1975), 177-182.
42. Gray, D. D., Giorgini, A., The validity of the Boussinesq approximation for liquids and gases, Int. J. Heat Mass Transfer 19 (1976), 545-551.
43. de Boer, P. T. C., Thermally driven motion of strongly heated fluids, Int. J. Heat Mass Transfer 27 (1984), 2239-2251.
44. de Boer, P. T. C., Thermally driven motion of highly viscous fluids, Int. J. Heat Mass Transfer 29 (1986), 681-688.
45. Bestehorn, M. Phase instabilities for Bénard-Marangoni convection in fluid layers with large aspect ratio, Phys. Rev. E, 48 (1993), 3622-3634.
46. Swift, J., Hohenberg, P. C., Hydrodynamic fluctuations at the convective instability, Phys. Rev. A, 15 (1977), 319-328.
47. Knobloch, E., Pattern selection in long-wavelength convection, Physica D, 41 (1990), 450-479.
48. Zippelius, A., Siggia, E., Stability of finite-amplitude convection, Phys. Fluids, 26 (1983), 2905-2915.
49. Cerisier, P., Pérez-Garcia, C., Jamond, C., Pantaloni, J., Wavelength selection in Bénard-Marangoni convection, Phys. Rev. A, 35 (1987), 1949-1952.
50. White, D. B., The planforms and onset of convection with a temperature-dependent viscosity, J. Fluid Mech., 191 (1988), 247-286.
51. Christov, C. I., Pontes, J. Velarde, M. G., Splitting methods for free-surface viscous fluids subject to thermal Marangoni effects, Comp. Rend. Bulg. Acad. Sci., 39 (1986), 23-26.
52. Koschmieder, E. L., Prahl, S., Surface tension driven Bénard convection in small containers, J. Fluid Mech. 215 (1990), 571-593.
53. Wierschem, A., Cesirier P., Gallet P., Velarde, M. G., Creation and extinction of cells in Bénard convection, J. Non-Equilib. Thermodyn. 21 (1997), No. 2, in print.
54. Caroli, B., Caroli, C., Roulet, B., On the stability of hexagonal interfacial patterns in directional solidification of binary mixtures, J. Crystal Growth, 68 (1984), 677-690.
55. Sushchik, M. M., Tsimring, L. S., The Eckhaus instability in hexagonal patterns, Physica D, 74 (1994), 90-106.
56. Koschmieder, E., The wavelength of supercritical surface tension driven Bénard convection, Eur. J. Mech. B/Fluids, 10 (1991), 233-237.
57. Koschmieder, E., Switzer, D., The wavenumbers of supercritical surface-tension-driven Bénard convection, J. Fluid Mech., 240 (1992), 533-548.
58. Dauzère, C., Sur les changements qu'éprouvent les tourbillons cellulaires lorsque la température s'élève, Compt. Rend., 155 (1912), 394-398.
59. Walgraef, D., Structures Spatiales Loin de l'Equilibre, Masson, Paris, 1988.
60. Tsimring, L. S., Dynamics of penta-hepta defects in hexagonal patterns, Physica D, 89 (1996), 368-380.
61. Assenheimer, M., Steinberg, V., Transition between spiral pattern and target pattern states in Rayleigh-Bénard convection, Nature, 367 (1994), 345.
62. Assenheimer, M., Steinberg, V., Critical phenomena in hydrodynamics, Europhys. News, 27 (1996), 143.
63. Assenheimer, M., Steinberg, V., Observation of coexisting upflow and downflow hexagons in Boussinesq Rayleigh-Bénard convection, Phys. Rev. Lett., 76 (1996), 756-760.
64. Orell, A., Westwater, J. W., Spontaneous interfacial cellular convection accompanying mass transfer, A.I.Ch.E. Journal, 8 (1962), 350.
65. Linde, H., Marangoni instabilities, in: Convective transport and instability phenomena, Eds. J. Zierep and H. Oertel, pages 265-296, Braun-Verlag, Karlsruhe, 1982.