The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 6, Issue 2, pp 277–292

Modeling film flows down inclined planes

  • C. Ruyer-Quil
  • P. Manneville

DOI: 10.1007/s100510050550

Cite this article as:
Ruyer-Quil, C. & Manneville, P. Eur. Phys. J. B (1998) 6: 277. doi:10.1007/s100510050550


A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable Ƭ that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations.

PACS. 47.20M Interfacial instability - 47.20K Nonlinearity

Copyright information

© EDP Sciences, Springer-Verlag 1998

Authors and Affiliations

  • C. Ruyer-Quil
    • 1
  • P. Manneville
    • 1
  1. 1.Laboratoire d'Hydrodynamique (CNRS UMR no 7646.), École Polytechnique, FranceFR