Drop formation in a magnetic fluid coating a horizontal cylinder carrying an axial electric current

We consider the effect of a magnetic field generated by a current flowing in the axial direction, in a cylindrical conducting medium on the evolution of a thin magnetic liquid film coating the outside of the cylinder. We first derive the new governing equations when a body force, due to the interaction of the magnetic dipoles in the liquid with the magnetic field due to the current in the cylinder, is included with surface tension and gravitational forces. The equations are discretized and solved numerically using an alternating direction implicit algorithm. Simulations demonstrate that the transition from a uniform coating to the formation of undulations to a final configuration of distinct drops follows a similar evolution for a wide range of cylinder radii and magnetic field strengths. Magnetic forces generally oppose the effects of gravity, and consequently the drainage toward the bottom of the cylinder is slowed, the characteristic time for drop formation is delayed, and the final coating is not confined to the cylinder bottom, but can wrap around the entire circumference of cylinder for sufficiently large magnetic fields. The range of dimensionless parameters considered are limited by the physicochemical properties of an ester ferrofluid, the maximum current density and radius of the conducting cylinder, and the susceptibility chi, where there is a linear relationship between H and M. Thus the results are applicable to actual physical situations. Published by AIP Publishing.