Travelling wave solutions on an axisymmetric ferrofluid jet

Abstract

We consider a potential flow model of axisymmetric waves travelling on a ferrofluid jet. The ferrofluid coats a copper wire, through which an electric current is run. The induced azimuthal magnetic field magnetises the ferrofluid, which in turn stabilises the well known Plateau–Rayleigh instability seen in axisymmetric capillary jets. This model is of interest because the stabilising mechanism allows for axisymmetric magnetohydrodynamical solitary waves. A numerical scheme capable of computing steady periodic, solitary and generalised solitary wave solutions is presented. It is found that the solution space for the model is very similar to that of the classical problem of two-dimensional gravity–capillary waves.

Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl

“…If the reservoir is contaminated, the wave field is moved up the jet and a so‐called “fluid pipe” with a quiescent surface is formed at the base. We also note that in recent years, there has been increased interest in waves on jets in other physical contexts, such as electrohydrodynamic flows 22 and ferrofluids 23–25 …”

“…We also note that in recent years, there has been increased interest in waves on jets in other physical contexts, such as electrohydrodynamic flows 22 and ferrofluids. [23][24][25] In this paper, we consider liquid jets with both vorticity and swirl. A motivation for this is that a viscous boundary layer in a pipe typically gives rise to vorticity, which may have a significant effect on the jet flowing out of the pipe.…”

Linear stability of a ferrofluid centred around a current-carrying wire

“…Moreover, Canu & Renoult (2021) highlight the importance of having a surrounding liquid to mirror experimental conditions and for drug targeting applications. Blyth & Parau (2014) and Doak & Vanden-Broeck (2019) also consider the effect of a non-magnetic fluid surrounding the jet, but in the inviscid limit. Korovin (2004) considers the surrounding liquid being a ferrofluid, filling a cuvette, rather than an infinite domain.…”

“…(2010), who show the existence of axisymmetric periodic and solitary waves at the interface of a ferrofluid jet in a cylindrical domain. Doak & Vanden-Broeck (2019), as well as studying the linear stability, use a numerical model to find stable travelling wave solutions on a ferrofluid jet. Cornish (2018) uses weakly nonlinear stability theory and long wave theory for both a highly viscous and an inviscid axisymmetric jet, studying the resultant drop formation.…”

“…Blyth & Parau (2014) use a fully nonlinear numerical model to show that axisymmetric solitary waves propagate at the surface of an inviscid column of ferrofluid, and compare their results with the experimental work by Bourdin et al (2010), who show the existence of axisymmetric periodic and solitary waves at the interface of a ferrofluid jet in a cylindrical domain. Doak & Vanden-Broeck (2019), as well as studying the linear stability, use a numerical model to find stable travelling wave solutions on a ferrofluid jet. Cornish (2018) uses weakly nonlinear stability theory and long wave theory for both a highly viscous and an inviscid axisymmetric jet, studying the resultant drop formation.…”