Magnetocapillary Instability of Non--Conducting Liquid Jets Revisited : Plateau versus Chandrasekhar

TL;DR

This paper revisits the magnetocapillary instability of non-conducting liquid jets, deriving a new dispersion relation and identifying a critical magnetic field that can stabilize jets regardless of their magnetic susceptibility.

Contribution

It introduces a new dispersion relation for magnetocapillary instability that differs from Chandrasekhar's and demonstrates the stabilizing effect of magnetic fields on permeable jets.

Findings

Existence of a critical magnetic field stabilizing jets

New dispersion relation for magnetocapillary instability

Stabilization occurs for both para- and diamagnetic jets

Abstract

The magnetostatic and magnetocapillary instability problems of isothermal incompressible and inviscid non--conducting liquid jets in a uniform magnetic field, is considered. The equivalence between static and dynamic approaches at the onset of instability and cut--off wavelength is shown. It is established that in the absence of electric currents the stability of permeable jets can be changed by the magnetic field. A new dispersion relation for magnetocapillary instability in such jets is derived. This relation differs from that given by Chandrasekhar. The existence of critical magnetic field which stabilizes jets with finite susceptibility is established. It is shown that the jet is stabilized by the field irrespective of its being para-- or diamagnetic, but the extent of stabilization is different.