Ferrohydrodynamic pumping in spatially uniform sinusoidally time-varying magnetic fields

Past work has analyzed ferrofluid pumping in a planar duct driven by spatially non-uniform traveling wave magnetic fields. Here we examine a much simpler case where the applied magnetic fields along and transverse to the duct axis are spatially uniform and varying sinusoidally with time. In the uniform magnetic field the magnetization characteristic depends on particle spin but does not depend on fluid velocity. The magnetization force density along the duct axis is zero while the magnetic torque density is non-zero as M and H are not collinear due to a magnetic relaxation time constant as well as due to spatially varying particle spin. The governing linear and angular momentum conservation equations are numerically integrated to solve for flow and spin velocity distributions for zero and non-zero spin viscosities as a function of magnetic field strength, phase, frequency, and direction along and transverse to the duct axis, and as a function of pressure gradient along the duct, vortex viscosity, dynamic viscosity, and ferrofluid magnetic susceptibility. Analytical solutions for simple limiting cases are also given including an effective viscosity that depends on magnetic field strength which can be made zero or negative.