The mixing of compounds in a highly viscous medium is important in many industrial settings; from food processing to the manufacturing of rocket fuel and drugs. Experts in mixing have long been aware of how things become mixed in a nonturbulent flow, but there has been little quantitative analysis of such mixing processes. As recent developments in chaos theory have found their way into the engineering literature, there have been some attempts to apply these ideas toward numerically quantifying nonturbulent mixing processes. Chaos theory is a new name for an old subject in mathematics, dynamical systems theory which includes ergodic theory. By examining the older literature of ergodic theory, one can determine what is necessary to quantify nonturbulent mixing processes. This has led to the methods which are suggested in this dissertation. After discussing some principles of ergodic theory, the design of a bladeless mixer is presented. The philosophy of this design is to adopt an abstract mathematically mixing system around which to design and build an actual machine. Ergodic theory is then used to develop methods for quantifying nonturbulent mixing processes by both experimental and numerical means. These methods are then applied to the bladeless mixer.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 192-199).

Thesis (MS)--Montana State University--Bozeman, 2009. / Typescript. Chairperson, Graduate Committee: David A. Miller. Includes bibliographical references (leaves 114-117).

This work focuses on understanding the buckling deformation mechanisms of bending, wrinkling, and folding that occur on the surfaces and interfaces of polymer systems. We gained fundamental insight into the formation mechanism of these buckled structures for thin glassy films placed on an elastomeric substrate. By taking advantage of geometric confinement, we demonstrated new strategies in controlling wrinkling morphologies. We were able to achieve surfaces with controlled patterned structures which will have a broad impact in optical, adhesive, microelectronics, and microfluidics applications. Wrinkles and strain localized features, such as delaminations and folds, are observed in many natural systems and are useful for a wide range of patterning applications. However, the transition from sinusoidal wrinkles to more complex strain localized structures is not well understood. We investigated the onset of wrinkling and strain localizations under uniaxial strain. We show that careful measurement of feature amplitude allowed not only the determination of wrinkle, fold, or delamination onset, but also allowed clear distinction between each feature. The folds observed in this experiment have an outward morphology from the surface in contrast to folds that form into the plane, as observed in a film floating on a liquid substrate. A critical strain map was constructed, where the critical strain was measured experimentally for wrinkling, folding, and delamination with varying film thickness and modulus. Wrinkle morphologies, i.e. amplitude and wavelength of wrinkles, affect properties such as electron transport in stretchable electronics and adhesion properties of smart surfaces. To gain an understanding of how the wrinkle morphology can be controlled, we introduced a geometrical confinement in the form of rigid boundaries. Upon straining, we found that wrinkles started near the rigid boundaries where maximum local strain occurred and propagated towards the middle as more global strain was applied. In contrast to homogeneous wrinkling with constant amplitude that is observed for an unconfined system, the wrinkling observed here had varying amplitude as a function of distance from the rigid boundaries. We demonstrated that the number of wrinkles can be tuned by controlling the distance between the rigid boundaries. Location of wrinkles was also controlled by introducing local stress distributions via patterning the elastomeric substrate. Two distinct wrinkled regions were achieved on a surface where the film is free-standing over a circular hole pattern and where the film is supported by the substrate. The hoe diameter and applied strain affected the wavelength and amplitude of the free-standing membrane. Using discontinuous dewetting, a one-step fabrication method was developed to selectively deposit a small volume of liquid in patterned microwells and encapsulate it with a polymeric film. The pull-out velocity, a velocity at which the sample is removed from a bath of liquid, was controlled to observe how encapsulation process is affected. The polymeric film was observed to wrinkle at low pull-out velocity due to no encapsulation of liquid; whereas the film bent at medium pull-out velocity due to capillary effect as the liquid evaporated through the film. To quantify the amount of liquid encapsulated, we mixed salt in water and measured the size of the deposited salt crystals. The salt crystal size, and hence the amount of liquid encapsulated, was controlled by varying either the encapsulation velocity or the size of the patterned microwells. In addition, we showed that the deposited salt crystals are protected by the laminated film until the film is removed, providing advantageous control for delivery and release. Yeast cells were also captured in the microwells to show the versatility. This encapsulation method is useful for wide range of applications, such as trapping single cells for biological studies, growing microcrystals for optical and magnetic applications, and single-use sensor technologies.

Aviation and aerospace structural components made of composite laminates due to their internal structure and manufacturing methods contain a number of inter- and intracomponent defects, which size, dispersion and interaction alter significantly the critical compression strain level. While there are a plethora of theoretical and experimental work on the problems stability loss and fracture of composites with internal defects in the scope of classic problems of fracture mechanics, there are few theoretical and numerical analyses available for the nonclassical problems of fracture mechanics of composites compressed along layers with interface cracks. These analyses usually have been considered the simplest problems, where the composite material with pronounced microstructure and interface defects (cracks, delaminations) have been analysed as two-dimensional (2-D) continuum in the condition of plane strain state. In the scope of these analyses only parallel defects have been considered, allowing for the interpenetration of the stress-free crack faces, or assuming so-called interfacial cracks with connected edges. This thesis broadens knowledge in the area of non-classical problems of fracture mechanics. It investigates the effect of interfacial cracks interaction on the critical buckling strain in layered and fibrous composite materials under compressive static loading. The behaviour of composite is analysed on several length-scales, starting from a ply and laminate levels (in 2-D approximation), down to a single-fibre level (a full 3-D model). The statements of the problems are based on the model of piecewise-homogeneous medium model, the most accurate within the framework of the mechanics of deformable bodies as applied to composite materials with pronounced microstructure. All composite constituents are modelled as linear-elastic material, where both isotropic and anisotropic materials are considered depending on the length-scale. It is assumed that the moment of stability loss in the microstructure of materials is treated as the onset of the fracture process. Besides that, the critical strain that corresponds to loss of stability in the microstructure of the composite, either surface or internal instability, must be smaller than the critical strain that corresponds to loss of stability of the entire composite. This project involves parameterised variables, such as the crack size, the crack spacing, the layer volume fraction and the fibre volume fraction. At each length-scale two types of cracks are analysed, namely, cracks with stress-free crack faces and cracks with frictionless Hertzian contact of the crack faces. A number of finite-element models for each length-scale are developed, and are validated analytically and numerically. The models' ability to simulate practical composite structures to a useful degree of accuracy with suitable material properties is discussed. A number of parameters, which quantifies the interfacial crack interaction and crack faces contact interaction phenomena, are introduced and discussed. Qualitative discussion on the crack faces contact zones, post-critical behaviour of composites and crack propagation are presented and discussed. Finally, the subject areas for the future work are outlined.

Thesis (Ph. D.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2004. / Dr. Zureick, Abdul-Hamid, Committee Member; Dr. White, Donald, Committee Member; Dr. Saxena, Ashok, Committee Member; Dr. Jacobs, Laurence, Committee Member; Dr. Haj-Ali, Rami, Committee Chair; Dr. Armanios, Erian, Committee Member. Vita. Includes bibliographical references (leaves 164-172).

Lic.-avh. Luleå : Luleå tekniska universitet, 2009.

<p>Continuous-fiber ceramic matrix composites (CMCs) are of interest as hot-section components in gas turbine engines due to their refractoriness and low density relative to metallic alloys. In service, CMCs will be subjected to spatially inhomogeneous temperature and stress fields. Robust tools that enable prediction of deformation and fracture under these conditions are therefore required for component design and analysis. Such tools are presently lacking. The present work helps to address this deficiency by developing models for CMC mechanical behavior at two length scales: that of the constituents and that of the components. Problems of interest are further divided into two categories: &lsquo;1-D loadings,&rsquo; in which the stresses are aligned with the fiber axes, and &lsquo;2-D loadings,&rsquo; in which the stress state is more general. </p><p> For the former class of problems, the major outstanding issue is material fracture, not deformation. A fracture criterion based on the attainment of a global load maximum is developed, which yields results for pure bending of CMCs in reasonable agreement with available experimental data. For the latter class of problems, the understanding of both the micro-scale and macro-scale behavior is relatively immature. An approach based upon analysis of a unit cell (a single fiber surrounded by a matrix jacket) is pursued. Stress fields in the constituents of the composite are estimated using analytical models, the accuracy of which is confirmed using finite element analysis. As part of a fracture mechanics analysis, these fields enable estimation of the steady-state matrix cracking stress for arbitrary in-plane loading of a unidirectional ply. While insightful at the micro-scale, unit cell models are difficult to extend to coarser scales. Instead, material deformation is typically predicted using phenomenological constitutive models. One such model for CMC laminates is investigated and found to predict material instability where none should exist. Remedies to the model to correct this deficiency are proposed; the remediated model is subsequently utilized in conjunction with an analytical model to probe stress fields adjacent to holes and notches in CMC panels. However, even the revised model is incapable of capturing the range of experimental behavior reported for CMCs with both stiff and compliant matrices. To ameliorate this deficiency, a new elastic-plastic constitutive model is developed. It extends the deformation theory of plasticity from metals to CMCs, and its predictions of near-notch strain fields in an open-hole tension test compare favorably to strains measured using digital image correlation. Based on these developments, future experimental and modeling work is proposed. With respect to the latter, cohesive interface simulations seem particularly suited for capturing multiple interacting damage mechanisms at multiple length scales in a physically sensible manner. In principle, they can function as virtual tests, guiding both engineering design and materials development. </p>

Thesis (Ph. D.)--Lehigh University, 1997. / Includes vita. Includes bibliographical references (leaves 253-260).

Thesis (Ph. D.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 173-184).