Understanding Ferrofluid Spin-Up Flows in Rotating Uniform Magnetic Fields
A fully filled sphere of ferrofluid has constant demagnetizing factors in all three Cartesian directions such that when subjected to a uniform external rotating magnetic field the internal field is also uniform, and ultrasound measurements give no observable flow. Non-uniform magnetic fields or a non-uniform distribution of susceptibility are necessary conditions for ferrofluid spin-up flows in the absence of a free surface. The effect of the non-uniform distribution of the internal momentum of particles is negligible and is represented by setting the spin-viscosity term to zero.
COMSOL Multiphysics models of ferrofluid in an infinitely tall cylinder and fully filled sphere can be shown to give negligible flow with zero spin-viscosity . COMSOL models of an infinitely long ferrofluid filled cylinder, with zero spin-viscosity, subjected to a non-uniform field imposed by an infinitely long permanent magnet in addition to a uniform rotating magnetic field results in significant flow. These flows are also observed experimentally when subjecting a ferrofluid filled sphere to a non-uniform field imposed by a permanent magnet/solenoidal coil and the uniform rotating magnetic field.
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