Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-30T07:35:00.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical investigation of the interfacial stability of inviscid fluids in motion, considering surface tension

Published online by Cambridge University Press:  29 March 2006

Jan Berghmans
Jan Berghmans
Affiliation:
The University of Wisconsin, Madison
Get access Rights & Permissions [Opens in a new window]

Abstract

The present work is an analytical study of the stability of interfaces between fluids in motion, special attention being given to the role of surface tension without consideration of viscous effects. A variational approach based upon the principle of minimum free energy, which was first formulated for stagnant fluids, is applied to fluids in motion. This generalization is possible if viscous and inertia effects are unimportant as far as stability is concerned. One stability problem is studied in detail: a gas jet impinging on a free liquid. The analytical results obtained by this variational technique lie within the range of accuracy (15%) of the experimental results for this gas-jet problem. The method is very general and therefore can be applied to quite a number of interface stability problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 1 , 11 July 1972 , pp. 129 - 141
Copyright
© 1972 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

Banks, R. B. & Chandbasekhara, D. V. 1962 Experimental investigation of the penetration of a high-velocity gas jet through a liquid surface J. Fluid Mech. 15, 13.Google Scholar
Bellman, R. & Pennington, R. H. 1954 Effects of surface tension, and viscosity on Taylor instability Quart. Appl. Mech. 12, 151.Google Scholar
Berghmans, J. 1970 Theoretical investigation of the interfacial stability of inviscid fluids in motion, considering surface tension. Ph.D. thesis, University of Wisconsin, Madison.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Cheslak, F. R., Nicholls, J. A. & Sichel, M. 1969 Cavities formed on liquid surfaces by impinging gaseous jets J. Fluid Mech. 36, 55.Google Scholar
Collatz, L. 1966 The Numerical Treatment of Differential Equations, p. 69. Springer.
Collins, R. D. & Lubanska, H. 1954 The depression of liquid surfaces by gaseous jets J. Appl. Phys. 5, 22.Google Scholar
Gauss, F. 1906 Gesammelte Werke, vol. 5, p. 29. Göttingen.
Gibbs, J. W. 1876 On the equilibrium of heterogeneous substances Trans. Conn. Acad. 3, 108.Google Scholar
Gibbs, J. W. 1878 On the equilibrium of heterogeneous substances Trans. Conn. Acad. 3, 343.Google Scholar
Gibson, A. 1934 Hydraulics and Its Applications. London: Constable.
Lamb, H. 1932 Hydrodynamics. Dover.
Landau, L. & Lifschitz, E. 1959 Fluid Mechanics, p. 232. Addison-Wesley.
Laplace, P. S. 1806 Mécanique Céleste, vol 4, p. 471. Paris: Imprimerie Royale.
Mathieu, F. 1960 Contribution à l'étude de l'action d'un jet gazeux sur la surface libre d'un liquide en repos Rev. Univ. des Mines, 16, 309.Google Scholar
Mathieu, F. 1962 Nouvelles recherches sur l'action d'un jet gazeux sur la surface libre d'un liquide en repos Rev. Univ. des Mines, 18, 482.Google Scholar
Milne-Thomson, L. M. 1952 Theoretical Hydrodynamics, Chap. XIV. Macmillan.
Poreh, M. & Chermak, J. 1959 Flow characteristics of a circular submerged jet impinging normally on a smooth boundary. 6th Midwestern Conference on Fluid Mechanics, p. 616.Google Scholar
Rajappa, N. R. & Chang, I. D. 1966 Interfacial instability of a liquid with constant shear Phys. Fluids, 9, 616.Google Scholar
Rosler, R. & Stewart, G. 1968 Impingement of gas jets on liquid surfaces J. Fluid Mech. 31, 163.Google Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. Roy. Soc. A 201, 192.Google Scholar
Turkdogan, T. E. 1966 Fluid mechanics of gas jets impinging on surfaces of liquids Chem. Eng. Sci. 21, 1133.Google Scholar
Tyuptsov, A. D. 1966 Hydrostatics in weak force fields – stability of equilibrium forms of a surface liquid Fluid Dyn. 1, 51. (See also Mekhanika Zhidkosti i Gaza, 1, 78.)Google Scholar