Magnetization, multiparticle interactions, and chain dynamics in magnetic fluids under rapidly rotating external fields

This dissertation investigates multiparticle interactions in magnetic fluids, specifically colloidal ferrofluids, under non-equilibrium conditions. Colloidal ferrofluids are suspensions of tiny ($\sim$100 Å in diameter) magnetic particles in a non-magnetic Newtonian carrier fluid. In the absence of an external magnetic field, Brownian effects cause the ferrofluid to have no net magnetization, but when a magnetic field is applied, the fluid becomes strongly magnetized. The magnetic particles, or any suspended non-magnetic chain-forming particles, are sufficiently small that the fluid flow in their vicinity is well within the low-Reynolds number Stokes flow regime.; The thesis first addresses the problem of proper formulation for the magnetization of a ferrofluid under non-equilibrium conditions. At equilibrium, when the applied field is stationary or varies quasistatically, the magnetization of the ferrofluid is well understood and given by the so-called Langevin function. But the commonly used model for non-equilibrium situations, the Shliomis relaxation model, is phenomenological in origin and has certain short-comings when the magnetic effects are large compared to Brownian effects or when the field is rapidly varying. This thesis begins with a simple deterministic model and moves on to a stochastic approach, based upon the complete solution to the Fokker-Planck convective-diffusion equation for the orientation-space probability density of the dipolar particles. It then compares the predictions of all three models and proposes modifications to the common Shliomis relaxation model which increase its range of applicability.; Secondly the dissertation addresses the problem of modeling the dynamics of pairs and chains of non-magnetic particles suspended in a ferrofluid, when subjected to a rotating external field. Such non-magnetic particles develop induced dipole moments which interact with each other magnetically and hydrodynamically, forming chains and clusters which rotate with the external field, break up, and re-form. The suspending ferrofluid can be treated as a magnetized continuum; however the multitude of spinning dipoles impart antisymmetric stresses to the suspension which manifest themselves as torques exerted upon the larger non-magnetic particles in the suspension. These torques must be taken into account when modeling the behavior of chains and clusters, providing the primary driving force for the unusual dynamics of the chains. To incorporate hydrodynamic interactions for two particles, exact mobility and resistance tensors are available. We also develop an approximate pairwise-additive treatment of hydrodynamic interactions among three or more particles in order to achieve simulations of larger chains and clusters of non-magnetic particles.