On travelling waves of a control-volume model for liquid films flowing down a fibre

Abstract

This paper analytically investigates the solutions to a control-volume model for liquid films flowing down a vertical fibre. The dynamic evolution of the free surface is governed by a coupled degenerate nonlinear PDE system for the fluid film radius and the axial velocity. We prove the existence of weak solutions to the coupled system based on the application of a priori estimates derived for energy-entropy functionals. Existence of travelling wave solutions to the system is also established. Numerical studies are presented to illustrate the derived analytical results for both the dynamic PDE solutions and the travelling wave structures.