Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-08T04:44:27.583Z Has data issue: false hasContentIssue false

Buoyancy-thermocapillary instability: the role of interfacial deformation in one- and two-component fluid layers heated from below or above

Published online by Cambridge University Press:  20 April 2006

J. L. Castillo
Affiliation:
Departamento Física Fundamental – U.N.E.D., Apdo Correos 50487. Madrid, Spain
M. G. Velarde
Affiliation:
Departamento Física Fundamental – U.N.E.D., Apdo Correos 50487. Madrid, Spain

Abstract

Energy stability theory has been used to study BBnard convection in one- and two-component horizontal fluid layers heated from below or above when there is a deformable upper surface. To a first approximation in the crispation number, we provide sufficient conditions for stability of the motionless state of the layer, and delineate regions of possible subcritical instability.

Type
Research Article
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Block, M. 1956 Surface tension as the cause of Bénard cells and surface deformation in a liquid film. Nature, 178, 650.Google Scholar
Bourgeois, S. V. & Brashears, M. R. 1977 Fluid dynamics and kinematics of molten metals in the low-gravity environment of Skylab. Prog. Astro. Aero. 52, 189.Google Scholar
Castillo, J. L. & Velarde, M. G. 1980 Microgravity and the thermoconvective stability of a binary liquid layer open to the ambient air. J. Non-Equilib. Thermodyn. 5, 111.Google Scholar
Coriell, S. R., Cordes, M. R., Boettinger, W. J. & Sekerka, R. F. 1980 Convective and interfacial instabilities during unidirectional solidification of a binary alloy. J. Crystal Growth 49, 13.Google Scholar
Coulet, A. L., Billia, B. & Capella, I. 1981 Cell size of dilute binary alloys. J. Crystal Growth 51, 106.Google Scholar
Davis, S. H. 1969 Buoyancy-surface tension instability by the method of energy. J. Fluid Mech. 39, 347.Google Scholar
Davis, S. H. & Homsy, G. M. 1980 Energy stability theory for free-surface problems: buoyancythermocapillary layers. J. Fluid Mech. 98, 527.Google Scholar
Fisher, D. J. & Kurz, W. 1980 Interface stability as a measure of material purity. J. Crystal Growth 49, 204.Google Scholar
Guyon, E. & Pantaloni, J. 1980 Effect de tension superficielle sur la convection de Rayleigh-Bénard. C. R. Acad. Sci. Paris 290 B, 301.Google Scholar
Hurle, D. T. J. 1977 Hydrodynamics in crystal growth. In Crystal Growth and Materials (ed. E. Kaldis & H. J. Scheet), p. 549. North-Holland.
Joseph, D. D. 1965 On the stability of the Boussinesq equations, Arch. Rat. Mech. Anal. 20, 59.Google Scholar
Joseph, D. D. 1976 Stability of Fluid Motions, vol. I. Springer.
Lebon, G. & Pérez-García, C. 1980 Study of surface tension effects in thermal convection by variational methods. Bull. Acad. R. Belg. Cl. Sci. 66, 520.Google Scholar
Malméjac, Y., Bewersdorff, A., Da Riva, I. & Napolitano, L. G. 1981 Challenges and prospectives of microgravity research in space. European Space Agency Rep. BR-05 (Paris).Google Scholar
Nield, D. 1964 Surface tension and buoyancy effects in cellular convection. J. Fluid Mech. 19, 341.Google Scholar
Normand, C., Pomeau, Y. & Velarde, M. G. 1977 Convective instability: a physicist's approach. Rev. Mod. Phys. 49, 581.Google Scholar
Pérez-Cordón, R. & Velarde, M. G. 1975 On the (non linear) foundations of Boussinesq approximation applicable to a thin layer of fluid. J. Phys. (Paris) 36, 591.Google Scholar
Schechter, R. S., Velarde, M. G. & Platten, J. K. 1974 The two-component Bénard problem. Adv. Chem. Phys. 26, 265.Google Scholar
Schwabe, D. 1981 Marangoni effects in crystal growth melts. Physicochem. Hydrodyn. 2, 263.Google Scholar
Scriben, 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.Google Scholar
Shir, C. C. & Joseph, D. D. 1968 Convective instability in a temperature and concentration field. Arch. Rat. Mech. Anal. 30, 38.Google Scholar
Smith, K. A. 1966 On convective instability induced by surface-tension gradients. J. Fluid Mech. 24, 401.Google Scholar
Sørensen, T. S. (ed.) 1979 Dynamics and Instability of Fluid Interfaces. Lecture Notes in Physics, vol. 105. Springer.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Velarde, M. G. 1977 Hydrodynamic Instabilities (in isotropic fluids). In Fluid Dynamics: Les Houches, 1973 (ed. R. Balian & J. L. Peube), p. 469. Gordon & Breach.
Velarde, M. G. & Normand, C. 1980 Convection. Sci. Am. 243, 92.Google Scholar
Velarde, M. G. & Pérez-Cordón, R. 1976 On the (non linear) foundations of Boussinesq approximation applicable to a thin layer of fluid. II. Viscous dissipation and large cell gap effects. J. Phys. (Paris) 37, 177.Google Scholar