Typescript (photocopy). / Digitized by Kansas Correctional Industries

A model is developed for the dynamics of an acoustically driven bubble in a channel. The bubble is assumed to be smaller than the transverse dimension of the channel and spherical in shape. The channels considered are infinite in length and formed by either parallel planes or tubes with triangular, rectangular, or hexagonal cross sections. For surfaces that are rigid or pressure release, the boundary conditions on the channel walls in each of these geometries can be satisfied using the method of images. Effects due to confinement by the channel walls are thus determined by an analysis of coupled bubble interactions in line and plane arrays. An existing model for the coupled dynamics of spherical bubbles provides the basis for the model. Liquid compressibility is an essential feature of the model, both in terms of radiation damping and the finite propagation speed of acoustic waves radiated by the bubble. Solutions for the frequency response are obtained analytically by perturbation for low drive amplitudes and weak nonlinearity, and by numerical solution for high drive amplitudes and strong nonlinearity. The perturbation solutions for the radial motion at the drive frequency and its second harmonic are obtained in closed form for a bubble between parallel planes. The response of a bubble between rigid parallel planes is found to be mass controlled, whereas for a rigid tube it is found to be radiation damping controlled. The dynamics of a bubble located near the center of a tube are found to depend on the area but not the specific geometry of the cross section. At drive amplitudes below which subharmonic generation occurs, the numerical solutions for high drive amplitudes reveal the same general properties as the perturbation solutions for low drive amplitudes. All of the solutions can be extended to tubes with arbitrary wall impedance if the radiation impedance on the bubble is known, for example calculated by normal mode expansion. / text

Bibliography: leaves 315-326 / xxv, 370 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Faculty of Engineering, 1993

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

The goal of this doctoral work was to observe and analyze the stability and dynamics of phospholipid-encapsulated microbubbles, and in particular the reaction to sudden submersion in a multi-gas medium. To accomplish this goal, first an experimental technique was developed to observe a microbubble in a single-gas environment suddenly immersed in a multi-gas environment, without perturbing the microbubble position. A modified Epstein-Plesset model was concurrently developed to account for the multiple gas species in the bulk solution. The model was used to analyze previous data for the effect of anesthesia carrier gas on microbubble ultrasound contrast agent in vivo circulation persistence. The focus of the experiments then shifted to microbubbles of different sizes encapsulated with a homologous series of saturated diacyl-chain lipid surfactants and emulsifiers. Constitutive models for the elastic and gas permeation properties of the lipid encapsulation were developed to elucidate the unique behaviors observed during the experiments. The experimental techniques employed were: (1) transmission bright field optical microscopy to obtain real-time, digital videos of microbubbles growing and dissolving in response to perturbations in the local gas environment and (2) the Langmuir trough film balance to determine the elasticity of the phospholipid monolayers during compression, expansion, and expansive relaxation. The modeling techniques employed was (1) a forward-wind finite difference method to discretize a series of non-linear differential equations and (2) a Newton-Raphson method to solve the diameter of a microbubble from the mechanical stress balance. These modeling techniques were used to determine the behavior of a microbubble a priori, whereas the fitting models implemented the iterative methods to solve for parameters without a Newton-Raphson method. Results showed that microbubbles coated with soluble surfactants and dissolving in a single gas solution could be predicted by the original Epstein-Plesset model. When subjected to a multi-gas medium, the modified Epstein-Plesset model accurately predicted microbubble growth and dissolution. The model was used to analyze the increase in microbubble circulation lifetime observed by others in anesthetized rats inhaling air rather than oxygen as the anesthesia carrier gas. The predictive capabilities of the model broke down, however, if the gas-core was encapsulated with a phospholipid monolayer. A typical, large (>40 µm diameter) lipid-coated microbubble displayed stunted growth, followed by three anomalous dissolution regimes: (1) rapid dissolution back to the initial resting diameter followed by (2) slow, steady dissolution and finally (3) stabilization, where the apparent surface tension approached a near-zero value. The model was modified to allow fitting of the radius-time curve by varying the surface tension. The analysis showed that the surface tension is dynamic, and suggested that a "break up" tension allowed for rapid expansion of the microbubble beyond the initial resting diameter. Lipid jamming was proposed as the mechanism eventually halting dissolution. Further observations of smaller microbubbles (<20 µm diameter) coated with a homologous series of saturated diacyl chain lipids gave significantly different results. Initially the microbubbles grew, but growth was severely subdued, if not eliminated, for more solid encapsulations below a threshold size (~10 µm diameter). Following growth, most microbubbles rapidly dissolved back to their original size. The microbubbles then experienced an anomalous lag time before spontaneously dissolving again. The lag times were highly variable and shown to correlate to the reduced temperature of the encapsulation, rather than the initial microbubble size. Most of the microbubbles stabilized again at a diameter of 1-2 µm, and this "stable diameter" appeared to be universal and independent of both the initial microbubble size and the rigidness of the encapsulation. Constitutive models were developed to describe these physical phenomena in the early growth and dissolution stages which were verified with independent monolayer relaxation studies.

This dissertation begins with a review of Calabi-Yau manifolds and their moduli spaces, flux compactification largely tailored to the case of type IIb supergravity, and Coleman-De Luccia vacuum decay. The three chapters that follow present the results of novel research conducted as a graduate student. Our first project is concerned with bubble collisions in single scalar field theories with multiple vacua. Lorentz boosted solitons traveling in one spatial dimension are used as a proxy to the colliding 3-dimensional spherical bubble walls. Recent work found that at sufficiently high impact velocities collisions between such bubble vacua are governed by "free passage" dynamics in which field interactions can be ignored during the collision, providing a systematic process for populating local minima without quantum nucleation. We focus on the time period that follows the bubble collision and provide evidence that, for certain potentials, interactions can drive significant deviations from the free passage bubble profile, thwarting the production of a new patch with different field value. However, for simple polynomial potentials a fine-tuning of vacuum locations is required to reverse the free passage kick enough that the field in the collision region returns to the original bubble vacuum. Hence we deem classical transitions mediated by free passage robust. Our second project continues with soliton collisions in the limit of relativistic impact velocity, but with the new feature of nontrivial field space curvature. We establish a simple geometrical interpretation of such collisions in terms of a double family of field profiles whose tangent vector fields stand in mutual parallel transport. This provides a generalization of the well-known limit in flat field space (free passage). We investigate the limits of this approximation and illustrate our analytical results with numerical simulations. In our third and final project we investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIb string theory compactified on the mirror quintic. For a large collection of these models, we numerically determine the distribution of Taylor coefficients in a polynomial expansion of each model's scalar potential to fourth order. We provide an analytic explanation of the proncounced hierarchies exhibited by the random sample of masses and couplings generated numerically. The analytic argument is based on the structure of masses in no scale supergravity and the divergence of the Yukawa coupling at the conifold point in the moduli space of the mirror quintic. Our results cast the superpotential vev as a random element whose capacity to cloud structure vanishes as the conifold is approached.

Frothers are used in flotation to aid generation of small bubbles, but little is known about the mechanisms that take place in the flotation machine to produce such an effect. Coalescence prevention is the common explanation, although the exact mechanism is obscure and almost no attention has been paid to a frother effect on bubble break-up, the other possible mechanism. This thesis presents a technique to study the effect of frothers on bubble coalescence at the generation stage (at a capillary tube) and a technique to study the effect of frothers on bubble coalescence and break-up in a turbulent field. The first technique is based on the sound bubbles emit when they form and coalesce. The sound signal was linked to bubble formation and coalescence events using high-speed cinematography. The technique has a resolution capable of detecting coalescence events that occur within 1-2 ms. The second technique allows discriminating between coalescence and break-up and is based on the exposure of a mono-size distribution of bubbles to a turbulent field generated by a three-bladed axial flow impeller. Analysis of bubble size distributions after contact with the turbulent field gives the coalescence and break-up fraction. The results show frothers reduce coalescence and alter the bubble size distribution of bubbles generated by break-up. / In the course of high-speed imaging an effect of frother on bubble shape and motion after formation was detected. Analysis of this forms the third major component of the work. A dependence of velocity on bubble aspect ratio is shown, which is in line with recent literature.

No description available.

The Lagrangian formalism utilized by Ilinskii, Hamilton and Zabolotskaya [J. Acoust. Soc. Am. 121, 786-795 (2007)] to derive equations for the radial and translational motion of interacting bubbles is extended here to obtain a model for the dynamics of interacting bubbles and elastic particles. The bubbles and particles are assumed to be spherical but are otherwise free to pulsate and translate. The model is accurate to fifth order in terms of a nondimensional expansion parameter R/d, where R is a characteristic radius and d is a characteristic distance between neighboring bubbles or particles. The bubbles and particles may be of nonuniform size, the particles elastic or rigid, and external acoustic sources are included to an order consistent with the accuracy of the model. Although the liquid is assumed initially to be incompressible, corrections accounting for finite liquid compressibility are developed to first order in the acoustic Mach number for a cluster of bubbles and particles, and to second order in the acoustic Mach number for a single bubble. For a bubble-particle pair consideration is also given to truncation of the model at fifth order in R/d via automated derivation of the model equations to arbitrary order. Numerical simulation results are presented to demonstrate the effects of key parameters such as particle density and size, liquid compressibility, particle elasticity and model order on the dynamics of single bubbles, pairs of bubbles, bubble-particle pairs and clusters of bubbles and particles under both free response conditions and sinusoidal or shock wave excitation. / text

Formation of gas bubbles in complex fluids and their subsequent rise due to buoyancy is a very important fundamental phenomenon both in nature and industry. Bubble size and bubble velocity are critical parameters which govern the interfacial transport phenomena and play an important role in gas-solid contact. These characteristics affect the operating parameters as well as the design of equipment in industrial applications. Non-Newtonian, Shear-thickening fluids have been studied extensively due to their immense potential for commercial use in shock absorbing and force damping applications, such as liquid body armor, sports and personal protection. Furthermore, a better understanding of shear-thickening fluid is pertinent to industrial processing for enhancing flow, preventing the breakage or clogging of mixing equipment, and preventing clogging in narrow orifices. Despite their significance, many aspects of the flow of these non-Newtonian fluids remain poorly understood. In the first part of this dissertation, we study the dynamics of rising bubbles in three dimensional fluidized beds using computational fluid dynamics-discrete element method (CFD-DEM) to shed light on the physics underpinning phenomena uncovered previously using magnetic resonance imaging (MRI). We were able to understand the underlying mechanism behind the anomalous collapse of a bubble in side-by-side injection as well as an alternating asynchronous pinch-off pattern due to jet interaction in a fluidized bed by looking into the gas streamlines and the drag force on the particles. In the second part of this dissertation, we study dynamics of rising bubbles in Newtonian fluids and non-Newtonian cornstarch-water suspensions experimentally using optical imaging. We were able to identify that Capillary number (Ca) is a key dimensionless parameter governing the regimes of interacting jets in water. We also observed a periodic coalescence of bubbles at the same points in space in cornstarch-water suspensions and attributed this behavior to leading bubbles entering a shear thickening regime. Further, we identified the key dimensionless parameters for wobbling behavior of single bubbles in cornstarch suspensions to be Bond (Bo), and Reynolds (Re) number, regardless of the bubble being in a Newtonian or a shear-thinning regime. We believe our findings can be applied in industry to optimize the mass transport and liquid mixing for a range of applications.