The fully three-dimensional start-up deformations and accelerations of initially spherical magnetically susceptable linearly magnetizable ferrofluid droplets, driven by a rotating uniform magnetic field, are investigated through the use of coupled finite element/boundary element computer simulations. For given magnetic susceptability, a critical viscosity is suggested, proportional to both magnetic field strength and rotation speed, below which the deformations of the initially spherical droplet inevitably lead to breakup, but above which a simple persistent spheroidal solid body rotation is attained.
K E Y W O R D Sdroplet deformations, ferrofluids, finite/boundary elements, rotating magnetic field
INTRODUCTIONA ferrofluid is a non-electrically conducting, stable colloidal suspension of magnetic particles in a Newtonian carrier liquid that makes the latter sensitive to the presence of a magnetic field. 1 Such "ferrohydrodynamics" (FHD) are distinguishable from the "magnetohydrodynamics" (MHD) of electrically conducting fluids by the complete absence of electric currents and the Lorentz forces they might otherwise induce. The particles typically have sizes of about 10 nm and are often coated with a stabilizing dispersing agent (surfactant) to avoid particle agglomeration 2 -even in the presence of strong magnetic field gradients. Additionally, if the particles are also "magnetically soft," with a magnetization relaxation time of the order 10 −7 seconds, then hysteresis effects may also be neglected, as will be done here.Finally, a ferrofluid in droplet form gives a rich and varied phenomenology of physical behavior through the competition between magnetic and surface tension forces on the surface, in an analogous manner to that seen between electric and surface tension forces in electrohydrodynamics. [3][4][5] There have been many experimental 6-8 and numerical [8][9][10][11][12] studies of the simple axisymmetric prolate spheroid equilibrium shapes ferrodrops achieve inside static uniform applied magnetic fields analogous to those of dielectric drops in an electric field, [13][14][15][16] where the prolate elongation from a sphere aligns with the applied field direction and assumes a stable equilibrium configuration directly proportional to the field strength.However, if the external magnetic field rotates, then two distinct classes of behavior emerge, dependent on the rotation speed.