  An attractive technique for forming and collecting aggregates of magnetic
material at a liquid--air interface by an applied magnetic field gradient was
recently addressed theoretically and experimentally [Soft Matter, (9) 2013,
8600-8608]: when the magnetic field is weak, the deflection of the liquid--air
interface has a steady shape, while for sufficiently strong fields, the
interface destabilizes and forms a jet that extracts magnetic material.
Motivated by this work, we develop a numerical model for the closely related
problem of solving two-phase Navier--Stokes equations coupled with the static
Maxwell equations. We computationally model the forces generated by a magnetic
field gradient produced by a permanent magnet and so determine the interfacial
deflection of a magnetic fluid (a pure ferrofluid system) and the transition
into a jet. We analyze the shape of the liquid--air interface during the
deformation stage and the critical magnet distance for which the static
interface transitions into a jet. We draw conclusions on the ability of our
numerical model to predict the large interfacial deformation and the consequent
jetting, free of any fitting parameter.
