Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-09T22:17:06.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-isothermal spreading of a thin liquid film on an inclined plane

Published online by Cambridge University Press:  26 April 2006

P. Gilberto López ,
S. George Bankoff  and
Michael J. Miksis
P. Gilberto López
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
S. George Bankoff
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
Michael J. Miksis
Affiliation:
McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A thin layer of liquid advancing over a dry, heated, inclined plate is studied. A lubrication model with contact line motion is derived. The plate is at constant temperature, and the surface Biot number is specified. The steady-state solution is obtained numerically. In addition, the steady-state solution is studied analytically in the neighbourhood of the contact line. A linear stability analysis about the steady state is then performed. The effects of gravity, thermocapillarity and contact line motion are discussed. In particular, we determine a band of unstable wavenumbers, and the maximum growth rate as a function of these parameters.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 324 , 10 October 1996 , pp. 261 - 286
Copyright
© 1996 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

Bruyn, J. R. de 1992 Growth of fingers at a driven three-phase contact line. Phys. Rev. A 46, R4500–R4503.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Stability of evaporating condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
Cazabat, A. M. 1991 Wetting films. Adv. Colloid Interface Sci. 34, 72–88.Google Scholar
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665–684.Google Scholar
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: Static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371–400.Google Scholar
Dussan, V. E. B. & Davis, S. H. 1974 On the motion of a fluid—fluid interface along a solid surface. J. Fluid Mech. 65, 71–96.Google Scholar
Ehrhard, P. 1993 Experiments on isothermal and non-isothermal spreading. J. Fluid Mech. 257, 463–483.Google Scholar
Ehrhard, P. & Davis, S. H. 1991 Non-isothermal spreading of liquid drops on horizontal plates. J. Fluid Mech. 229, 365–388.Google Scholar
Gennes, P. G. de 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 828–861.Google Scholar
Goodwin, R. & Homsy, G. M. 1991 Viscous flow down a slope in the vicinity of a contact line. Phys. Fluids A 3, 515–528.Google Scholar
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125–143.Google Scholar
Haley, P. J. & Miksis, M. J. 1991 The effect of the contact line on droplet spreading. J. Fluid Mech. 223, 57–81.Google Scholar
Hocking, L. M. 1990 Spreading and instability of a viscous fluid sheet. J. Fluid Mech. 211, 373–392.Google Scholar
Hocking, L. M. 1992 Rival contact-angle models and the spreading of drops. J. Fluid Mech. 239, 671–681.Google Scholar
Hocking, L. M. & Miksis, M. J. 1993 Stability of a ridge of fluid. J. Fluid Mech. 247, 157–177.Google Scholar
Huppert, H. E. 1982 Flow and Instability of viscous gravity currents down a slope. Nature 300, 427–429.Google Scholar
Joo, S. W., Davis, S. H. & Bankoff, S. G. 1991 Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers. J. Fluid Mech. 230, 117–146.Google Scholar
Kelley, R. E., Davis, S. H. & Goussis, D. A. 1986 On the instability of heated film flow with variable surface tension. In Heat Transfer 1986. Proc. 9th Intl Heat Transfer Conference, San Francisco, vol. 4, pp. 1936–1942.
Lin, S. P. 1975 Stability of liquid flow down a heated inclined plane. Lett. Heat Mass. Transfer 2, 361–370.Google Scholar
Renk, F., Wayner, P. C. Jr & Homsy, G. M. 1978 On the transition between a wetting film and a capillary meniscus. J. Colloid Interface Sci. 67, 408–414.Google Scholar
Schwartz, A. M. & Tejeda, S. B. 1972 Studies of dynamic contact angles on solids. J. Colloid Interface Sci. 38, 359–375.Google Scholar
Schwartz, L. W. 1989 Viscous flows down an inclined plane: Instability and finger formation. Phys. Fluids A 3, 443–445.Google Scholar
Silvi, N. & Dussan, V. E. B. 1985 On the rewetting of an inclined solid surface by a liquid. Phys. Fluids 28, 5–7.Google Scholar
Smith, B. T. 1976 Matrix Eigensystem Routines: Eispack Guide. Springer.
Sreenivasan, S. & Lin, S. P. 1978 Surface tension driven instability of a liquid film down a heated incline. Intl J. Heat Mass Transfer 21, 1517–1526.Google Scholar
Troian, S. M., Herbolzheimer, E., Safran, S. A. & Joanny, J. F. 1989 Fingering instabilities of driven spreading films. Europhys. Lett. 10, 25–30.Google Scholar
Troung, J. C. & Wayner, P. C. Jr 1987 Effects of capillary and van der Waals dispersion forces on the equilibrium profile of a wetting liquid: theory and experiment. J. Chem. Phys. 87, 4180–4188.Google Scholar
Wayner, P. C. Jr 1993 Spreading of a finite liquid film with a finite apparent contact angle by the evaporation/condensation process. Langmuir 9, 294–299.Google Scholar
Williams, R. 1977 The advancing front of a spreading liquid. Nature 266, 153–154.Google Scholar