Wavelength measurements of Rosensweig instabilities in a ferrofluid in a non-uniform magnetic field

Abstract

A suitably strong electric field, applied at the free surface of a conducting or even dielectric fluid, will exert electrostatic traction on the fluid surface that can stretch the meniscus into a pointed conical shape. 1 Electrospray results when the field is strong enough to cause the tip of this 'Taylor cone' to exhaust a jet of charged droplets or ions. 2 By exact analogy with electrostatically stressed dielectric fluids, magnetic fields can distort magnetizable fluids into identical pointed geometries, 3,4 however magnetostatic jetting is never observed. 5 It is believed, yet not completely understood, that electrostatic jetting is a result of finite charge conductivity, a phenomenon which has no parallel in the magnetic fluid. Recently Meyer and King have shown that it is possible to induce hybrid electromagnetostatic jets by exciting surface instabilities in a novel electrically conductive superparamagnetic liquid. 6,7 When this fluid is subjected to simultaneous magnetic and electric fields a self-assembling array of discrete and stable cone-shaped emitters forms spontaneously in the fluid surface. While electrohydrodynamic flows, ferrohydrodynamic flows, and magnetohydrodynamic flows have long been studied separately, the ionic liquid ferrofluid described by Meyer and King is the first liquid to simultaneously respond strongly to electrostatic, magnetostatic, and Lorentz stresses, requiring a unification of EHD/FHD/MHD fluid physics. The purpose of this paper is to begin an analytic description of the fluid mechanics encountered when electromagnetically stimulating a highly conductive ferrofluid to produce spray. A potential energy analysis is used to describe the formation of the emitting cone. A linear stability analysis is performed on the resulting jet, showing that magnetic effects can radically shift the stability bounds of an electrospray.