(Cont.) Ferrofluid "negative viscosity" measurements in uniform and non-uniform rotating magnetic fields occur when magnetic field induced flow creates torque that exceeds the torque necessary to drive a viscometer spindle. Numerical simulations of torque and spin-up flow in uniform and non-uniform rotating magnetic fields, including contribution from the spin velocity and spin viscosity terms, are fitted to measurements to estimate the value ranges of relaxation time r - 1.3-30 gs and spin viscosity n' - 1-11.8x109 Nos in waterbased ferrofluid. Based on the ferrohydrodynamic theory and models, theory of the complex magnetic susceptibility tensor is derived, which depends on spin velocity, that can be a key to external magnetic field control of ferrofluid biomedical applications. Preliminary impedance analysis and measurements investigate complex magnetic susceptibility change of ferrofluid in oscillating and rotating uniform magnetic fields and allow calculation of the resulting dissipated power or mechanical work in pumping fluid.

When ferrofluid in a cylindrical container is subjected to a rotating azimuthally directed magnetic field, the fluid "spins up" into an almost rigid-body rotation where ferrofluid nanoparticles have both a linear and an angular "spin" velocity. Flow observations are often limited to the ferrofluid free surface due to the opaque nature of the ferrofluid and the surface flow can spin-up in the same or opposite directions to the direction of the rotating field. The mechanisms governing this flow have been attributed to surface driven flows that depend on the shape of the meniscus formed by the free surface. However, bulk flow experiments using ultrasound velocimetry show that even in the presence of a stationary cover, bulk ferrofluid flows would result when a rotating magnetic field was applied. The mechanisms explaining the bulk flows have been attributed by some authors to being a result of spin diffusion theory while others believe that non-uniform magnetic properties drive the flow, with both theories being rigorously explored in this thesis. This thesis applies ferrohydrodynamic analysis to extended fluid flow equations driven by magnetization forces and torques on the ferrofluid, Maxwell's equations relating magnetization, magnetic field and ferrofluid flow, and a Langevin magnetization relaxation constitutive law including the effects of fluid linear and spin velocities. Some key concepts investigated in this analysis are: (1) Ferrofluid filled cylindrical vessels of finite height placed within a uniform magnetic field result in non-uniform magnetic fields inside the ferrofluid due to demagnetization effects that can drive the flow; (2) A spherical vessel of ferrofluid in a uniform magnetic field has a resulting uniform magnetic field unless there is a spatial variation of magnetic properties, induced in this thesis by an external source of non-uniform magnetic field from a current carrying coil or a permanent magnet; and (3) COMSOL Multiphysics spin-diffusion modeling shows that spin viscosity can also initiate a flow due to spin-velocity boundary conditions which can hinder magnetic nanoparticle rotation near a wall or allow particles to roll along a wall due to flow vorticity. Ferrofluid spin-up flows were investigated that take into account demagnetizing effects associated with the shape of the container. The experiments conducted in this thesis involve using a sphere of ferrofluid in a uniform rotating field since a sphere has uniform and equal demagnetizing factors in all three Cartesian directions. The uniform rotating magnetic field is generated by two orthogonally placed spherical coils, known as "fluxballs" that generate a uniform magnetic field in the horizontal and vertical directions inside the fluxballs and a dipole field outside. By driving the coils with sinusoidal signals that are out of phase in time by 90 degrees a uniform rotating field is generated inside the test chamber containing the sphere of ferrofluid. The test sphere of ferrofluid is placed at the center of the larger surrounding "fluxball" machine. Negligible flows are measured within the ferrofluid filled sphere using ultrasound velocimetry in the "fluxball" machine with a uniform rotating magnetic field. COMSOL simulations using non-zero values of spin-viscosity, with a zero spin-velocity boundary condition at the outer wall, predict measurable flow while simulations setting spin-viscosity to zero result in negligible flow. Previously published values of spin-viscosity measured in cylindrical vessels are much larger than values allowed by kinetic theory because the flows, from which they were determined, are actually due to the demagnetizing field effects and not due to spin-diffusion. Experiments were also performed by partially filling the test sphere with ferrofluid but only 2/3 full, resulting in significant flows due to non-uniform magnetic fields from spatially dependent demagnetizing factors and possibly free surface effects. Ultrasound velocimetry measurements were also performed with a small permanent magnet or a DC/AC excited small coil on top of the ferrofluid filled test sphere, causing a nonuniform DC or AC magnetic field within the ferrofluid filled test sphere in addition to the uniform rotating magnetic field imposed by the fluxball coils. With an imposed non-uniform magnetic field component from magnet or coil, complex measurable flows with strong vortices are obtained. Formation of vortices is also confirmed in COMSOL simulations of an infinitely long cylinder subjected to a uniform rotating field and the field from an infinitely long permanent magnet. These measurements demonstrate that a non-uniform magnetic field or a non-uniform distribution of magnetic properties drive the flow. The spin-up ferrofluid flow in a rotating uniform externally applied field is highly dependent on the shape of the container due to demagnetizing effects. These demagnetizing effects in a finite-height ferrofluid filled cylindrical container create a non-uniform field inside the ferrofluid that drives the flow and is the cause for previously observed flows in the classic cylindrical spin-up flow experiments. COMSOL Multiphysics simulations applied to a cylinder of infinite height filled with ferrofluid show that spin-diffusion theory cannot be the dominant mechanism for spin-up flows as fitting the COMSOL analysis to measurements result in unphysically large values of spin viscosity. The unphysically large values of spin viscosity are obtained by attributing spin-up flow to be due to spin-diffusion alone rather than the correct non-uniform magnetic field effects. In conclusion, this thesis, through experimental results and numerical simulations, proves that non-uniform magnetic properties within the ferrofluid and not spin-diffusion theory is the driving mechanism for the measured flow.

(Cont.) When the order of the applied magnetic fields is reversed, the DC axial magnetic field is applied first causing the ferrofluid droplet to form the labyrinth instability. The rotating magnetic field is then applied creating a spiral formation. Experiments are conducted for varying Hele-Shaw cell separation gap, and rotating magnetic field amplitude and frequency. Measurements were consistent with our model. A cylindrical vessel is filled with a water-based ferrofluid and excited by a uniform rotating magnetic field that induces a counter-rotating circular flow in the vessel. A DC axial magnetic field is slowly raised to change the curvature of the fluid surface and results in a change in the ferrofluid flow direction to co-rotating with the applied magnetic field. Measurements are taken of the threshold axial magnetic field that results in the change of flow direction for varying rotating magnetic field direction, amplitude, and frequency. An analysis is included that describes the change in flow direction due to surface curvature.

A ferrofluid is a collection of nanoscale ferromagnetic particles with a stabilizing surfactant in a liquid to form a colloid. The dynamic behavior of ferrofluids in the presence of magnetic fields has long been an area of research interest. A particular area of interest deals with the "spin-up" mechanisms of ferrofluids, which describe how a container of ferrofluid comes to a steady state of bulk flow when subjected to a uniform rotating external magnetic field. There are two prevailing theories that attempt to explain the spin-up mechanisms of ferrofluids: spin diffusion theory, and the presence of non-uniformities in the magnetic field, due to "demagnetizing factors" introduced by the shape of the container. This research attempts to confirm previous measurements indicating that non-uniformities in the magnetic field are the primary cause of ferrofluid bulk flow. Partial spheres and cylindrical containers of different volumes -- and thus different demagnetizing factors -- were filled with Ferrotec EFH1 oil-based ferrofluid and subjected to an external uniform rotating magnetic field for various parameters of rotation direction and magnetic field. Ferrofluid bulk flow was measured using ultrasound velocimetry, and the magnitudes and shapes of the velocity profiles were compared. Despite the complicated flows observed within the containers, enough of a trend was established to safely conclude that demagnetizing factors are often the primary cause of ferrofluid bulk flow.

(Cont.) Contrary to the commonly held view in the literature, spin-up flows develop in rotating uniform magnetic fields even in the absence of spin diffusion effects. Including the linear and spin velocity terms in the magnetization relaxation equation results in non-zero spin-up flow. Numerical solutions using FEMLAB software are shown for flow profiles with zero and non-zero spin viscosity. Fitting numerical simulations to velocity profile ultrasound measurements allows the estimation of the magnetization relaxation time and the spin viscosity for Ferrotec Corp.'s MSG Wll and EMG705 water-based ferrofluids.