Eddies driven by eddy currents: Magnetokinetic flow in a conducting drop due to an oscillating magnetic field

Department of Chemical Engineering, Indian Institute of Science - Bangalore 560012, India

Received: 10 August 2024
Accepted: 3 December 2024

Abstract

An oscillating magnetic field of amplitude H₀ and angular frequency ω is applied across an electrically conducting non-magnetic drop of conductivity κ, viscosity η and radius R. The oscillating magnetic field generates an oscillating electric field due to Faraday's law, , where E and H are the electric and magnetic field, and μ₀ is the magnetic permeability. This generates a current density, . The non-linear interaction between the oscillating current and magnetic field results in a time-independent body force density, due to Ampere's circuital law. This drives a pair of axisymmetric circulation rolls in the two hemispheres of the drop in the viscous limit where inertia is neglected. The characteristic circulation velocity is times a function of the dimensionless parameter , the square root of the ratio of the magnetic field frequency and the eddy current relaxation rate. The velocity increases proportional to for , has a maximum at , and decreases proportional to for . Large strain rates in the range are generated in a metal drop of radius 0.1–1 mm for magnetic flux density as low as , provided relatively high frequencies of oscillation in the range are used. Joule heating could increase the drop temperature by tens of degrees Kelvin in comparison to the ambient.