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.) 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.

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.

The mechanisms that lead to bulk flow within a ferrofluid-filled container subjected to a rotating uniform magnetic field are experimentally studied. There are two prevailing theories: spin diffusion theory and flow due to non-uniformities in magnetic field within the ferrofluid due to nonuniform demagnetizing factors. This research sought to confirm previous measurements that indicated demagnetizing factors are the primary cause of bulk ferrofluid flow. Flattened spherical containers of various volumes, and thus different demagnetizing factors, were filled with EFH1 oil-based ferrofluid and subjected to a uniform rotating magnetic field of varying conditions (rotation direction and field strength). The shapes and magnitudes of the velocity profiles measured by an ultrasound velocimeter system differed between containers, indicating that demagnetizing factors did affect flow. The complicated flows within the flattened spheres that affected both the shape and magnitude of the flow velocity prevented a direct magnitude comparison between profiles but the flows differed enough to safely conclude that spatial non-uniformities within the fluid likely caused the bulk flow of fluid in the uniform rotating magnetic field.

We have obtained analytical solutions for the flow of two layers of immiscible ferrofluids of different thickness between two parallel plates. The flow is mainly driven by the generation of antisymmetric stresses and couple stresses in the ferrofluids due to the application of a uniform rotating magnetic field. The translational velocity ... and spin velocity ... profiles were obtained for the zero spin viscosity and non-zero spin viscosity cases and the effect of applied pressure gradient on the flow was studied. The interfacial linear and internal angular momentum balance equations derived for the airferrofluid interface case are extended for the case when there is a ferrofluid-ferrofluid interface to obtain the velocity profiles. The magnitude of the translational velocity is directly proportional to the frequency of the applied magnetic field and the square of the magnetic field amplitude. The spin velocity is in the direction of the rotating magnetic field and its direction remains the same at lower values of applied pressure gradient. The direction of translational velocity depends on the balance between the magnitudes of vorticity, body torque, spin velocity and diffusion of internal angular momentum, however at higher values of applied pressure gradient, the pressure gradient dominates the flow. This work shows the importance of surface stresses in driving flows in ferrofluids.