Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studiedwithin a sphere subjected to a uniform rotatingmagnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 901 phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1–14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1–4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniformmagnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1–20 mm/s) when the field ismade non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a nonuniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-upflow in ferrofluidswith no free surface,while tangentialmagnetic surface stress contributes to flow in the presence of a free surface. Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity Z0 10 8 10 12 N s than those obtained from theoretical spin diffusion analysis where Z0r10 18 N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity Z0 10 8 10 12 N swith a zero spin-velocity boundary condition at the outerwall predictsmeasureable flow, while simulations setting spin viscosity to zero (Z0 1⁄40) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (Z0 1⁄40). & 2010 Elsevier B.V. All rights reserved.