title: Self-similarity of solitary waves on inertia-dominated falling liquid films.
abstract: We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20-120 and surface tension coefficients σ=0.0512-0.072 N m(-1) on substrates with inclination angles β=19°-90°. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.
authors.affiliation: Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Fabian
authors.initials: F
authors.lastname: Denner
authors.affiliation: Department of Mathematics and Statistics, The Open University, Milton Keynes MK7 6AA, United Kingdom.|Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Marc
authors.initials: M
authors.lastname: Pradas
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Alexandros
authors.initials: A
authors.lastname: Charogiannis
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Christos N
authors.initials: CN
authors.lastname: Markides
authors.affiliation: Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Berend G M
authors.initials: BG
authors.lastname: van Wachem
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: Serafim
authors.initials: S
authors.lastname: Kalliadasis