Eur. Phys. J. B 6, 277-292 (1998)
https://doi.org/10.1007/s100510050550

Modeling film flows down inclined planes

Laboratoire d'Hydrodynamique (CNRS UMR n.) , École Polytechnique, 91128 Palaiseau, France

Corresponding authors: ^a ruyer@ladhyx.polytechnique.fr - ^b pops@ladhyx.polytechnique.fr

Received: 16 April 1998
Revised: 29 June 1998
Accepted: 2 July 1998
Published online: 15 November 1998

Abstract

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 τ 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.