Wavy regimes of film flow down a fibre

TL;DR

This paper analyzes axisymmetric traveling waves in gravity-driven liquid film flow down a vertical fibre, identifying four distinct regimes based on dominant physical effects through asymptotic and dynamical systems analysis.

Contribution

It introduces a comprehensive analysis of wave regimes on a fibre, revealing complex transitions and a phase diagram of flow behaviors.

Findings

Four physical regimes identified: advection, azimuthal curvature, inertia, viscous dispersion.

Traveling wave solutions exhibit complex transitions between regimes.

A phase diagram maps the regimes in parameter space.

Abstract

We consider axisymmetric traveling waves propagating on the gravity-driven flow of a liquid down a vertical fibre. Our starting point is the two-equation model for the flow derived in the study by Ruyer-Quil \emph{et al.} [\emph{J. Fluid Mech.} {\bf 603}, 431 (2008)]. The speed, amplitude and shape of the traveling waves are obtained for a wide range of parameters by using asymptotic analysis and elements from dynamical systems theory. Four different regimes are identified corresponding to the predominance of four different physical effects: Advection by the flow, azimuthal curvature, inertia and viscous dispersion. Construction of the traveling-wave branches of solutions reveals complex transitions from one regime to another. A phase diagram of the different regimes in the parameter space is oferred.