Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder

TL;DR

This paper demonstrates that radial oscillatory forcing can dynamically stabilize Rayleigh-Plateau modes on a viscous liquid cylinder, with theoretical predictions aligning well with numerical simulations.

Contribution

It introduces a Floquet stability analysis and a generalized Mathieu equation for viscous fluids, advancing understanding of mode stabilization under oscillatory forcing.

Findings

RP unstable modes can be stabilized with radial forcing.

Viscosity significantly influences stabilization effectiveness.

Theoretical predictions match numerical simulations closely.

Abstract

We demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force. Viscosity is found to play a crucial role in this stabilisation. Linear stability predictions are obtained via Floquet analysis demonstrating that RP unstable modes can be stabilised using radial forcing. We also solve the linearised, viscous initial-value problem for free-surface deformation obtaining an equation governing the amplitude of a three-dimensional Fourier mode. This equation generalises the Mathieu equation governing Faraday waves on a cylinder derived earlier in Patankar et al. (2018), is non-local in time and represents the cylindrical analogue of its Cartesian counterpart (Beyer & Friedrich 1995). The memory term in this equation is physically interpreted and it is shown that for highly viscous fluids, its contribution can be sizeable. Predictions from the numerical solution to this equation demonstrates RP mode stabilisation upto several hundred forcing cycles and is in excellent agreement with numerical simulations of the incompressible, Navier-Stokes equations.