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On competition between modes at the onset of Bénard-Marangoni convection in a layer of fluid

Published online by Cambridge University Press:  17 February 2009

Ishak Hashim
Ishak Hashim
Affiliation:
Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia, 43600 Bangi Selangor, Malaysia.
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Abstract

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In this paper we use classical linear stability theory to analyse the onset of steady and oscillatory Bénard-Marangoni convection in a horizontal layer of fluid in the more physically-relevant case when both the non-dimensional Rayleigh and Marangoni numbers are linearly dependent. We present examples of situations in which there is competition between modes at the onset of convection when the layer is heated from below.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 3 , January 2002 , pp. 387 - 395
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Benguria, R. D. and Depassier, M. C., “On the linear stability theory of Bénard-Marangoni convection”, Phys. Fluids A 1 (7) (1989) 1123–1127.CrossRefGoogle Scholar
[2]Davis, S. H. and Homsy, G. M., “Energy stability theory for free surface problems: Buoyancythermocapillary layers”, J. Fluid Mech. 98 (3) (1980) 527–553.CrossRefGoogle Scholar
[3]Golovin, A. A., Nepomnyashchy, A. A. and Pismen, L. M., “Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid-gas system with deformable interface”, J. Fluid Mech. 341 (1997) 317–341.CrossRefGoogle Scholar
[4]Hashim, I., “Theoretical analysis of the onset of Bénard-Marangoni convection”, Ph. D. Thesis, University of Strathclyde, UK, 1998.Google Scholar
[5]Hashim, I. and Wilson, S. K., “The onset of Bénard-Marangoni convection in a horizontal layer of fluid”, Int. J. Engng Sci. 37 (5) (1999) 643–662.CrossRefGoogle Scholar
[6]Hurle, D. T. J., “Surface aspects of crystal growth from the melt”, Adv. in Colloid Interface Sci. 15 (1981) 101–130.CrossRefGoogle Scholar
[7]Johnson, D. and Narayanan, R., “Experimental observation of dynamic mode switching in interfacial-tension-driven convection near a codimension-two point”, Phys. Rev. E 54 (4)(1996) 3102–3104.CrossRefGoogle Scholar
[8]Mills, K. C. and Keene, B. J., “Factors affecting variable weld penetration”, Int. Materials Rev. 35 (4) (1990) 185–216.CrossRefGoogle Scholar
[9]Nield, D. A., “Surface tension and buoyancy effects in cellular convection”, J. Fluid Mech. 19 (1964) 341–352.CrossRefGoogle Scholar
[10]Ostrach, S., “Fluid mechanics in crystal growth—The 1982 Freeman Scholar Lecture”, J. Fluids Engng 105 (1983) 5–20.CrossRefGoogle Scholar
[11]Pearson, J. R. A., “On convection cells induced by surface tension”, J. Fluid Mech. 4 (1958) 489–500.CrossRefGoogle Scholar
[12]Pérez-García, C. and Carneiro, G., “Linear stability analysis of Bénard-Marangoni convection in fluids with a deformable free surface”, Phys. Fluids A 3 (2) (1991) 292–298.CrossRefGoogle Scholar
[13]Powell, M. J. D., “A hybrid method for nonlinear equations”, in Numerical methods for nonlinear algebraic equations (ed. Rabinowitz, P.), (Gordon and Breach, London, 1970) 87–114.Google Scholar
[14]Rayleigh, Lord, “On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side”, Phil. Mag. 32 (6) (1916) 529–546.CrossRefGoogle Scholar
[15]Schwabe, D., “Surface-tension-driven flow in crystal growth melts”, Crystals 11 (1988) 75–112.CrossRefGoogle Scholar
[16]Takashima, M., “Nature of the neutral state in convective instability induced by surface tension and buoyancy”, J. Phys. Soc. Japan 28 (4) (1970) 810.CrossRefGoogle Scholar
[17]VanHook, S. J., Schatz, M. F., McCormick, W. D., Swift, J. B. and Swinney, H. L., “Long-wavelength instability in surface-tension-driven Bénard convection”, Phys. Rev. Lett. 75 (24) (1995) 4397–4400.CrossRefGoogle ScholarPubMed
[18]Zierep, J. and Oertel, H. Jr., Convective transport and instability phenomena (G. Braun, Karlsruhe, 1982).Google Scholar