Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-02-11T16:29:46.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers

Published online by Cambridge University Press:  26 April 2006

S. W. Joo ,
S. H. Davis  and
S. G. Bankoff
S. W. Joo
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
S. H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
S. G. Bankoff
Affiliation:
Department of Chemical Engineering, Northwestern University, Evanston, IL 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A layer of volatile viscous liquid drains down a uniformly heated inclined plate. Long-wave instabilities of the uniform film are studied by deriving an evolution equation for two-dimensional disturbances. This equation incorporates viscosity, gravity, surface tension, thermocapillarity, and evaporation eifects. The linear theory derived from this describes the competition among the instabilities. Numerical solution of the evolution equation describes the finite-amplitude behaviour that determines the propensity for dryout of the film. Among the phenomena that appear are the tendency to wave breaking, the creation of secondary structures, and the preemption of dryout by mean flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 117 - 146
Copyright
© 1991 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

Atherton, R. W. & Homsy, G. M. 1976 On the derivation of evolution equations for interfacial waves. Chem. Engng Commun. 2, 57–77.Google Scholar
Bankoff, S. G. 1971 Stability of liquid flow down a heated inclined plane. Intl J. Heat Mass Transfer. 14, 377–385.Google Scholar
Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554–574.Google Scholar
Benney, D. J. 1966 Long waves on liquid films. J. Math. & Phys. 45, 150–155.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Chang, H. -C. 1989 Onset of nonlinear waves of falling films. Phys. Fluids A l, 1314–1327.Google Scholar
Davis, S. H. 1983 Rupture of thin liquid films. In Waves in Fluid Interfaces. (ed. R. E. Meyer), pp. 291–302. Academic.
Gjevik, B. 1970 Occurrence of finite-amplitude surface waves on falling liquid films. Phys. Fluids. 13, 1918–1925.Google Scholar
Goussis, D. A. & Kelly, R. E. 1990 On the thermocapillary instabilities in a liquid layer heated from below. Intl J. Heat Mass Transfer. 33, 2237–2245.Google Scholar
Kapitza, P. L. & Kapitza, S. P. 1949 Wave flow of thin layers of a viscous fluidZh. Ek. Teor.Fiz. 19, 105; also in Collected Works, pp. 690–709. Pergamon (1965).Google Scholar
Kelly, R. E., Davis, S. H. & Goussis, D. A. 1986 On the instability of heated film flow with variable surface tension. Proc. 8th Intl Heat Transfer Conf., vol. 4, pp. 1937–1942. (ed C. L. Tien, V. P. Carey and J. K. Ferrell). Hemisphere.
Krantz, W. B. & Goren, S. L. 1971 Stability of thin liquid films flowing down a plane. Indust. Engng Chem. Fund. 10, 91–101.Google Scholar
Lin, S.-P. 1974 Finite amplitude side-band stability of a viscous film. J. Fluid Mech. 63, 417–429.Google Scholar
Lin, S.-P. & Wang, C.-Y. 1985 Modeling wavy film flows. In Encyclopedia of Fluid Mechanics. vol.1, pp. 931 951. Gulf Publishing Co.Google Scholar
Palmer, H. J. 1976 The hydrodynamic stability of rapidly evaporating liquids at reduced pressure. J. Fluid Mech. 75, 487–511.Google Scholar
Pearson, J. R. A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.Google Scholar
Pumir, A., Manneville, P. & Pomeau, Y. 1983 On solitary waves running down an inclined plane. J. Fluid Mech. 135, 27–50.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc Faraday Trans. II 70, 132–147.Google Scholar
Spindler, B. 1982 Linear stability of liquid films with interfacial phase change. Intl J. Heat MassTransfer. 25, 161–173.Google Scholar
Spindler, B., Solesio, J. N. & Delhaye, J. M. 1978 On the equations describing the instabilities of liquid films with interfacial phase change. In Two-Phase Momentum, Heat and Mass Transfer in Chemical Process and Energy Engineering Systems. (ed. F. Durst, G. V. Tsiklauri & N. H. Afgan), vol. 1, pp. 339–344. Hemisphere.
Sreenivasan, S. & Lin, S.-P. 1978 Surface tension driven instability of a liquid film flow down a heated incline. Intl J. Heat Mass Transfer. 21, 1517–1526.Google Scholar
Tougou, H. 1981 Deformation of supercritical stable waves on a viscous liquid film down an inclined plane wall with the decrease of wave number. J. Phys. Soc. Japan. 50, 1017–1024.Google Scholar
Williams, M. B. & Davis, S. H. 1982 Nonlinear theory of film rupture. J. Colloid Interface Sci. 90, 220–228.Google Scholar
Yiantsios, S. G. & Higgins, B. G. 1989 Rayleigh-Taylor instability in thin viscous films. Phys.Fluids. A1, 1484–1501.Google Scholar
Yih, C.-S. 1955 Stability of parallel laminar flow with a free surface. Proc. 2nd US Congr. Appl. Mech., pp. 623–628.Google Scholar
Asme. Yih, C.-S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids. 6, 321–334.Google Scholar