<p>In this thesis, a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit is developed for  canonical geometries consisting of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on hydrodynamics, a linear relationship between wall displacement and  hydrodynamic pressure is employed, due to its suitability for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, which is used to relate flow rate  to the pressure gradient (and the tube/wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without \textit{a priori} assumptions on the magnitude of the oscillation frequency (i.e., at arbitrary Womersley number).The PDE is solved numerically to evaluate the pressure distribution as well as the cycle-averaged pressure at several points along the length of the channel and the tube. It is found  that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is also obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. A good agreement is shown  between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number.</p>

<p>Fluids conveyed in deformable conduits are often encountered in  microfluidic applications, which makes fluid--structure interactions (FSIs) an unavoidable phenomenon. In particular, experiments reported the existence of FSI instabilities in compliant microchannels at low Reynolds numbers, Re, well below the established values for rigid conduits. This observation has significant implications for new strategies for mixing at the microscale, which might harness FSI instabilities in the absence of  turbulence. In this thesis, we conduct research on the modeling and stability of microscale FSIs. Understanding the steady response, the dynamics and the stability of these FSIs are the three major objectives. This thesis begins with the analysis of the steady-state scalings and the linear stability of a previously derived mathematical model, through which we emphasize the power of reduced modeling in making the FSI problems tractable. Next, we turn to a more realistic problem regarding FSIs in a common configuration of low-Re flows through long, shallow rectangular three-dimensional microchannels. Through a scaling analysis, which takes advantage of the geometric separation of scales, we find that the flow can be simplified under the lubrication approximation, while the wall deforms like a variable-stiffness Winkler foundation at the leading order. Coupling these dominant effects, we obtain a new fitting-parameter-free flow rate--pressure drop relation for a thick-walled microchannel, which rationalizes previous experiments. Then, we derive a one-dimensional (1D) steady model, at both vanishing and finite Re, by coupling the reduced flow and deformation models. To satisfy the displacement constraints along the channel edges, weak tension is introduced to regularize the underlying Winkler-foundation-like mechanism. This model is then made dynamic by introducing flow unsteadiness and the elastic wall's inertia. We conduct a global stability analysis of this system by perturbing the non-flat steady state with infinitesimal perturbations. We identify the existence of globally unstable modes, typically in the weakly inertial flow regime, whose features are consistent with experimental observations. The unstable eigenmodes oscillate at frequencies close to the natural frequency of the wall, suggesting that the instabilities are resonance phenomena. We also capture the transient energy amplification of perturbations through a linear non-normality analysis of the proposed reduced 1D FSI model.</p>

No description available.

<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>

<p>  </p> <p>High-resolution enclosed channels/fibers are highly demanded by different disciplines such as microfluidic channels for chemical synthesis, bioreactors for drug metabolism, magnetic locomotor for drug delivery, and wearable devices for motion detection. However, the current fabrication techniques for enclosed channels/fibers are restricted to a few millimeters in size. Their manufacturing often involves time and energy-consuming multi-step processes with insufficient resolution. In this work, we demonstrate a novel co-flow-enabled fabrication method to resolve the technological restrictions in the fabrication of high-resolution enclosed channels/fibers with efficient production time, controllable morphologies, and high throughput manner.</p> <p>An epoxy-based enclosed microfluidic channel was first built. A non-reactive paraffin oil and a liquid resin were pumped into a 3D-printed co-flow generator and worked as core and shell fluids, respectively. The epoxy resin was cured by external heat stimulus. As a result, the reaction region was limited between the generator wall surface and the boundary of core flow, eliminating the need for precise control over the curing system. The experiment was successfully conducted to cure build resin channel inside copper and resin tubes with good shell thickness.</p> <p>Conductive hollow hydrogel microfibers were also fabricated by this method. Sodium Alginate and Calcium Chloride were chosen as the shell and core flows, respectively. The ionic crosslinking happens at the boundary of two flows and expands outwards across the radial direction. Thus, the diameter of the hollow channel can be easily adjusted by tuning the flow rate and the size of the core flow injection needle. PEDOT: PSS, a conductive polymer, was mixed with Sodium Alginate to impart fibers with excellent electrical conductivity. The synthesized hollow microfibers have shown their functionality in stretching movement detection by serving as a fundamental building element of motion sensors. </p>

<p>Particle suspensions in viscoelastic fluids (e.g., polymeric fluids, liquid crystalline solutions, gels) are ubiquitous in industrial processes and in biology. In such fluids, particles often acquire lift forces that push them to preferential streamlines in the flow domain. This lift force depends greatly on the fluid’s rheology, and plays a vital role in many applications such as particle separations in microfluidic devices, particle rinsing on silicon wafers, and particle resuspension in enhanced oil recovery. Previous studies have provided understanding on how fluid rheology affects the motion of spherical particles in simple viscoelastic fluid flows such as shear flows. However, the combined effect of more complex flow profiles and particle shape is still under-explored. The main contribution of this thesis is to: (a) provide understanding on the migration and rotation dynamics of an arbitrary-shaped particle in complex flows of a viscoelastic fluid, and (b) develop guidelines for designing such suspensions for general applications.</p> <p><br></p> <p>In the first part of the thesis, we develop theories based on the second-order fluid (SOF) constitutive model to provide solutions for the polymeric force and torque on an arbitrary-shaped solid particle under a general quadratic flow field. When the first and second normal stress coefficients satisfy  <strong>Ψ</strong>₁  = −2 <strong>Ψ</strong> ₂ (corotational limit), the fluid viscoelasticity modifies only the fluid pressure and we provide exact solutions to the polymer force and torque on the particle. For a general SOF with  <strong>Ψ</strong> ₁ ≠  −2 <strong>Ψ</strong> ₂, fluid viscoelasticity modifies the shear stresses, and we provide a procedure for numerical solutions. General scaling laws are also identified to quantify the polymeric lift based on different particle shapes and orientation. We find that the particle migration speed is directly proportional to the length the particle spans in the shear gradient direction (L_sg), and that polymeric torques lead to unique orientation behavior under flow.</p> <p><br></p> <p>Secondly, we investigate the migration and rotational behavior of prolate and oblate spheroids in various viscoelastic, pressure-driven flows. In a 2-D slit flow, fluid viscoelasticity causes prolate particles to transition to a log-rolling motion where the particles orient perpendicular to the flow-flow gradient plane. This behavior leads to a slower overall migration speed (i.e., lift) of prolate particles towards the flow centerline compared to spherical particles of the same volume. In a circular tube flow, prolate particles align their long axis along the flow direction due to the extra polymer torque generated by the velocity curvature in all radial directions. Again, this effect causes prolate particles to migrate slower to the flow centerline than spheres of the same volume. For oblate particles, we quantify their long-time orientation and find that they migrate slower than spheres of the same volume, but exhibit larger migration speeds than prolate particles. Lastly, we examine the effect of normal stress ratio ? <strong>α</strong>  = <strong>Ψ</strong> ₂ /<strong>Ψ</strong>₁on the particle motion and find that this parameter only quantitatively impacts the particle migration velocity but has negligible effect on the rotational dynamics. We therefore can utilize the exact solution derived under the corotational limit (?<strong>α</strong> = −1/2) for a quick and reasonable prediction on the particle dynamics.</p> <p><br></p> <p>We next experimentally investigate the migration behavior of spheroidal particles in microfluidic systems and draw comparisons to our theoretical predictions. A dilute suspension of prolate/oblate microparticles in a density-matched 8% aqueous polyvinylpyrrolidone (PVP) solution is used as the model suspension system. Using brightfield microscopy, we qualitatively confirm our theoretical predictions for flow Deborah numbers 0 < De < 0.1 – i.e., that spherical particles show faster migration speed than prolate and oblate particles of the same volume in tube flows.</p> <p><br></p> <p>We finally design a holographic imaging method to capture the 3-D position and orientation of dynamic microparticles in microfluidic flow. We adopt in-line holography setup and propose a straightforward hologram reconstruction method to extract the 3-D position and orientation of a non-spherical particle. The method utilizes image moment to locate the particle and localize the detection region. We detect the particle position in the depth direction by quantifying the image sharpness at different depth position, and uses principal component analysis (PCA) to detect the orientation of the particle. For a semi-transparent particle that produces complex diffraction patterns, a mask based on the image moment information can be utilized during the image sharpness process to better resolve the particle position.</p> <p><br></p> <p>In the last part of this thesis, we conclude our work and discuss the future research perspectives. We also comment on the possible application of current work to various fields of research and industrial processes.</p> <p><br></p>