Ferrofluids are comprised of subdomain particles of magnetite or iron oxide material that can become magnetized in the presence of a magnetic field. These unique liquids are being incorporated into many new applications due to the ability to control them at a distance using magnetic fields. However, although our understanding of the dynamics of ferrofluids has evolved, many aspects of ferrohydrodynamics remain largely unexplored, especially experimentally. This study is the first to characterize the stability and internal dynamics of accumulating or dispersing ferrofluid aggregates spanning the stable, low Reynolds number behavior to unstable, higher Reynolds numbers. The dynamics of ferrofluid aggregates are governed by the interaction between the bulk flow shear stresses acting to wash away the aggregate and magnetic body forces acting to retain them at the magnet location. This interaction results in different aggregate dynamics, including the stretching and coagulation of the aggregate to Kelvin-Helmholtz shedding from the aggregate interface as identified by focused shadowgraphs. Using TRDPIV, the first time-resolved flow field measurements conducted in ferrofluids reveal the presence of a three-stage process by which the ferrofluid interacts with a pulsatile bulk flow. An expanded parametric study of the effect of Reynolds number, magnetic field strength, and flow unsteadiness reveals that the increased field results can result in the lifting and wash away of the aggregate by means of vortex strengthening. In pulsatile flow, different forms of the three-stage interaction occur based on magnetic field, flow rate, and Reynolds number. / Ph. D.

<p>Ferrofluids are remarkable materials composed of magnetic nanoparticles dispersed in a carrier liquid. These suspensions exhibit fluid-like behavior in the absence of a magnetic field, but when exposed to a magnetic field, they can respond and deform into a variety of patterns. This responsive behavior of ferrofluids makes them an excellent material for applications such as drug delivery for targeted therapies and soft robots. In this thesis, we will focus on the interfacial dynamics of ferrofluids in Hele-Shaw cells. The three major objectives of this thesis are: understanding the pattern evolution, unraveling the underlying nonlinear dynamics, and ultimately achieving passive control of ferrofluid interfaces. First, we introduce a novel static magnetic field setup, under which a confined circular ferrofluid droplet will deform and spin steadily like a `gear’, driven by interfacial traveling waves. This study combines sharp-interface numerical simulations with weakly nonlinear theory to explain the wave propagation. Then, to better understand these interfacial traveling waves, we derive a long-wave equation for a ferrofluid thin film subject to an angled magnetic field. Interestingly, the long-wave equation derived, which is a new type of generalized Kuramoto--Sivashinsky equation (KSE), exhibits nonlinear periodic waves as dissipative solitons and reveals fascinating issues about linearly unstable but nonlinearly stable structures, such as transitions between different nonlinear periodic wave states. Next, inspired by the low-dimensional property of the KSE, we simplify the original 2D nonlocal droplet problem using the center manifold method, reducing the shape evolution to an amplitude equation (a single local ODE). We show that the formation of the rotating `gear’ arises from a Hopf bifurcation, which further inspires our work on time-dependent control. By introducing a slowly time-varying magnetic field, we propose strategies to effectively control a ferrofluid droplet's evolution into a targeted shape at a targeted time. The final chapter of this thesis concerns our ongoing research into the interfacial dynamics under the influence of a fast time-varying and rotating magnetic field, which induces a nonsymmetric viscous stress tensor in the ferrofluid, requiring the balance of the angular momentum equation. As a consequence, wave propagation on a ferrofluid interface can be now triggered by magnetic torque. A new thin-film long-wave equation is consistently derived taking magnetic torque into account.</p>

Made available in DSpace on 2014-07-29T15:07:10Z (GMT). No. of bitstreams: 1 Dissertacao nelio.pdf: 402379 bytes, checksum: 978793fda386f5ccef16f94380d52b6f (MD5) Previous issue date: 2008-04-05 / In this work we investigated the problem of Rayleigh-Bénard for a magnetic binary fluid, i.e., a magnetic fluid, which consist of magnetic nanopartilces stably dispersed in a liquid carrier. The theoretical calculations were performed based on a Lorenz-like model, which transforms a system of partial differential equations into ordinary differential ones. The analysis of the magnetic binary fluid problem used the Navier-Stokes, thermal conduction and mass diffusion equations. The magnetic body force was obtained using the Cowley- Rosensweig tensor as well as the Maxwell equations. The mass flux had included the difusive contribution, associated to Fick s law, and also the thermal diffusion term, due to the Soret effect. Our model consist of a system of eight ordinary differential equations, which were shown to mantain the same mathematical form as the ones obtained earlier by Cross for a non-magnetic binary fluid. However, as expected, our coefficients depend on the magnetic field. According to our investigation on the site www.isiknowledge.com this is the first time in the literature that those equations are obtained, which we named the Lorenz-Cross equations on Ferrohydrodynamics. The validity of our system of equations were, also, checked in the limit of a simple fluid, where our model returns to the Lorenz equations. The only difference is the existence of an effective Rayleigh number, represented by the sum of the Rayleigh number and the magnetic Rayleigh one. Finally, the efect of magnetophoresis in the system of equations had also been discussed. / Neste trabalho investigamos o problema de Rayleigh-Bénard para um fluido binário magnético, ou seja, um fluido magnético, que consiste de nanopartículas magnéticas dispersas em um líqüido carreador.Os cálculos teóricos foram baseados na construção de um modelo tipo Lorenz, pelo qual transformamos um sistema de equações diferenciais parciais em equações diferenciais ordinárias. O sistema de equações para o fluido binário utilizou as equações de Navier-Stokes, condução de calor e difusão de massa.A força magnética foi obtida, usando o tensor eletromagnético de Cowley-Rosensweig, levando em conta as equações de Maxwell. O fluxo de massa considerou o termo difusivo, associado a Lei de Fick, e a contribuição termodifusiva, devido ao efeito de Soret.Nosso modelo consiste de um sistema de 8 equações diferenciais ordinárias, e manteve a mesma forma matemática daquelas obtidas anteriormente por Cross para um sistema binário não-magnético. Entretanto, possui contribuições dependentes do campo magnético. De acordo com nosso levantamento bibliográfico essa é a primeira vez na literatura que essas equações são obtidas, as quais denominamos de equações de Lorenz-Cross na Ferrohidrodinâmica.A validade do nosso sistema de equações foi verificada, também, no limite de um fluido simples, no qual nosso sistema retorna ao modelo tradicional de Lorenz com a diferença da contribuição de um número de Rayleigh efetivo, que representa a soma do número de Rayleigh tradicional com um Rayleigh magnético. A contribuição do efeito magnetoforético para o sistema de equações também foi discutida.