Wavy film flows down an inclined plane. Part I: Perturbation theory and general evolution equation for the film thickness

1997/12/15 by Alexander Frenkel, Alexander L. Frenkel, Frenkel, Alexander L. +3
Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics and Thin Films #Fluid Dynamics and Turbulent Flows #Nanofluid Flow and Heat Transfer #Pattern Formation and Solitons (nlin.PS) #nlin.PS #patt-sol

paper · pdf · doi:10.48550/arxiv.patt-sol/9712005

arxiv created 1997/12/15 · openalex publication_date 1997/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of 3D waves in inclined films are pointed out.

Citations

• Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium

Related

• A Mathematical Justification of a Thin Film Approximation for the Flow down an Inclined Plane
• Uniform Estimates for the Flow of a Viscous Incompressible Fluid down an Inclined Plane in the Thin Film Regime
• Formation and evolution of roll waves in a shallow free surface flow of\n a power-law fluid down an inclined plane
• Hydrodynamic instability of shear imposed falling film over a uniformly heated inclined undulated substrate
• Periodic-coefficient damping estimates, and stability of large-amplitude roll waves in inclined thin film flow