Kelvin-Helmholtz and Buckling Instabilities for a Viscoelastic Liquid

TL;DR

This study investigates the complex interplay of Kelvin-Helmholtz and buckling instabilities in Newtonian and viscoelastic jets, revealing how viscoelasticity suppresses instability growth and introduces new modes at different wave-numbers.

Contribution

It provides new insights into how viscoelasticity influences jet stability and the development of instabilities, combining experimental visualization with analysis of nonlinear dynamics.

Findings

High wave-number perturbations grow linearly with jet remaining straight.

Low wave-number instabilities cause jet buckling and chevron modes.

Viscoelasticity significantly inhibits instability growth and alters mode development.

Abstract

In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the Kelvin-Helmholtz instability for both Newtonian and viscoelastic jets. The nonlinear dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of perturbation frequencies. Our results show that at high wave-numbers the imposed perturbations initially grow linearly with time and the jet axis remains straight while the Kelvin-Helmholtz wave amplitude grows and rolls up into bags that encapsulate the central jet within themselves. At low wave-numbers (long wave-lengths) the jet axis buckles under the action of viscous stresses and a coupling between the Kelvin-Helmholtz instability and bending of the jet leads to new concertina or chevron modes which grow with time as they move downstream. Addition of viscoelasticity to the jet leads to the pronounced inhibition of the Kelvin-Helmholtz instability as the jet perturbation amplitude grows and large elongational stresses in the fluid become important. For long waves, the initially-relaxed viscoelastic jet first buckles in a manner similar to the Newtonian solvent but once again the viscoelastic effects suppress the instability growth as they are convected downstream.