Parametric excitation of an axisymmetric flow of a thin liquid film down a vertical fiber

Abstract

We investigate axisymmetric flow of thin liquid films falling down the outer side of a vertical cylindrical surface oscillating harmonically in the axial direction. A set of two coupled nonlinear partial differential evolution equations in terms of the local instantaneous film thickness and volumetric flow rate is derived using the Galerkin method. A linear stability analysis of the time-periodic thickness-uniform base state is performed using the Floquet theory. We carry out numerical investigation of the nonlinear dynamics of the films in the framework of the set of evolution equations derived here. We find that the film evolution exhibits strange attractor dynamics ranging from coherent to fully irregular regimes. We show that harmonic parametric excitation affects the spatial topological structure of the interfacial wave and may modify its type from depression wave to elevation wave. The harmonic parametric excitation may also result in a significant decrease in the interfacial wave amplitude.