Floquet analysis on a viscous cylindrical fluid surface subject to a time-periodic radial acceleration

TL;DR

This paper uses Floquet analysis to study how viscosity affects the stability and pattern formation of a viscous cylindrical fluid surface under periodic radial acceleration, revealing different effects based on azimuthal wavenumber.

Contribution

It provides a linear stability analysis of a viscous cylindrical fluid surface under periodic forcing, highlighting viscosity's role in pattern onset and dispersion relations.

Findings

Viscosity significantly influences the critical forcing amplitude.

Viscosity affects the dispersion relation of non-axis symmetric patterns.

Different dependencies of viscosity effects are observed for azimuthal wavenumber m=1 versus m>1.

Abstract

Parametrically excited standing waves are observed on a cylindrical fluid filament. These are the cylindrical analog of Faraday instability in a flat surface or spherical droplet. Using the Floquet technique, linear stability analysis has been investigated on a viscous cylindrical fluid surface, which is subjected to a time-periodic radial acceleration. Viscosity has a significant impact on the critical forcing amplitude as well as the dispersion relation of the non-axis symmetric patterns. The effect of viscosity on onset parameters of the pattern with azimuthal wavenumber, $m=1$, has shown different dependency from $m>1$. The effect of viscosity increases with an increasing $m$ is also observed.