MODELING THIN FLUID FILM ON A ROTARY BELL

A component of the mission in the Institute of Research for Technology Development at the University of Kentucky is advancing research and development and bringing it to the factory floor for continuous improvement. This dissertation delves into the art and science of rotational fluid mechanics in the context of rotary bell atomizers. One outcome proves that an approximation for calculating fluid film thicknesses on high-speed spinning surfaces inferred while working in cylindrical and spherical coordinate systems can be applied to an arbitrary bell profile. However, the analytical limits of this approximation were not investigated. In all cases, a restriction exists that the bell profile curvature is much greater than the fluid film thickness. The validity of this approximation was supported by findings in publications employing curvilinear coordinates created by axisymmetric revolution of a planar curve. This validation enabled rigorous analyses of bell profiles beyond the common cylindrical or spherical profiles. A curvilinear system containing a coordinate of arc length along the bell profile is the arbitrary case, and the most reduced high-speed case collapses to an approximation from an observed pattern in simpler coordinate systems. The jump to varying curvature curvilinear coordinates requires additional mathematics to calculate metric tensor coefficients and spatial derivatives of directional unit vectors, and to develop lengthy vector invariants. Another outcome was to explain the underlying symmetry in the reduced order solution for a coupled rotary system that included centrifugal and Coriolis effects on a conical rotary bell

Energetics and thermodynamics of α-iron from first-principles and machine-learning potentials

Iron is a material of fundamental importance in the industrial and economic processes of our society as it is the major constituent of steels. With advances in computational science, much progress has been made in the understanding of the microscopic mechanisms that determine the macroscopic properties of such material at ordinary or extreme conditions. Ab initio quantum mechanical calculations based on density-functional theory (DFT), in particular, proved to be a unique tool for this purpose. Nevertheless, in order to study large enough systems up to length- and time-scales comparable with those accessible in experiments, interatomic potentials are needed. These are typically based on functional forms driven by physical intuition and fitted on experimental data at zero/low temperature and/or on available first-principles data. Despite their vast success, however, their low flexibility limits their systematic improvement upon database extension. Moreover, their accuracy at intermediate and high temperature remains questionable. In this thesis, we first survey a selection of embedded atom method (EAM) potentials to understand their strengths and limitations in reproducing experimental thermodynamic, vibrational and elastic properties of bcc iron at finite temperature. Our calculations show that, on average, all the potentials rapidly deviate from experiments as temperature is increased. At the same time, they suggest that, despite an anomalous rapid softening of its $C_{44}$ shear constant, the Mendelev03 parameterization is the most accurate among those considered in this work. As a second step, we compute the same finite-temperature properties from DFT. We verify our plane-wave spin-polarized pseudopotential implementation against selected zero temperature all-electron calculations, thus highlighting the difficulties of the semi-local generalized gradient approximation exchange and correlation functional in describing the electronic properties of iron. On the other hand, we demonstrate that after accounting for the vibrational degrees of freedom, DFT provides a good description of the thermal behavior of thermodynamic and elastic properties of $\alpha$-iron up to a good fraction of the Curie temperature without the explicit inclusion of magnetic transverse degrees of freedom. Electronic entropy effects are also analyzed and shown to be of secondary importance. Finally, we attempt at generating a set of highly flexible Gaussian approximation potentials (GAP) for bcc iron that retain ab initio accuracy both at zero and finite temperature. To this end, we use a non-linear, non-parametric Gaussian-process regression, and construct a training database of total energies, stresses and forces taken from first-principles molecular dynamics simulations. We cover approximately $10^5$ local atomic environments including pristine and defected bulk systems, and surfaces with different crystallographic orientations. We then validate the different GAP models against DFT data not directly included in the dataset, focusing on the prediction of thermodynamic, vibrational, and elastic properties and of the energetics of bulk defects

An Experimental Technique for Developing Intermediate Strain Rates in Ductile Metals

Quantifying the strain-rate sensitive dynamic properties of structural materials is an important area of research in the solid mechanics field. Property evaluation is typically accomplished using dynamic tests which involve rapid loading or impact of specimens. In these tests, inertial forces and wave propagation make it difficult to accurately record the material response to a loading condition at an equivalent location. Furthermore, these tests typically generate high strain rates (in excess of 103 s−1) and an experimental method for generating rates of strain in the intermediate strain rate regime which is relatively simple, low cost, and reliable is still lacking. This research effort develops an experimental technique for generating tensile plastic strain rates up to 102 s−1 in ductile metals. The technique relies on an impact from a load cell instrumented drop weight machine capable of delivering a suitable impact velocity and energy to globally deform a slotted beam specimen. At impact, a state of plastic uniaxial tensile stress is created in the ligament underneath a slot. The ligament is instrumented with an electrical-resistance strain gauge, and the strain history from the gauge is measured and stored in a digital oscilloscope. The Johnson-Cook constitutive equation is assumed to reflect the material behavior and its parameters are determined through a matching of the experimental strain history with a finite element simulation

Surface Modifications in Adhesion and Wetting

Advances in surface modification are changing the world. Changing surface properties of bulk materials with nanometer scale coatings enables inventions ranging from the familiar non-stick frying pan to advanced composite aircraft. Nanometer or monolayer coatings used to modify a surface affect the macro-scale properties of a system; for example, composite adhesive joints between the fuselage and internal frame of Boeing\u27s 787 Dreamliner play a vital role in the structural stability of the aircraft. This dissertation focuses on a collection of surface modification techniques that are used in the areas of adhesion and wetting. Adhesive joints are rapidly replacing the familiar bolt and rivet assemblies used by the aerospace and automotive industries. This transition is fueled by the incorporation of composite materials into aircraft and high performance road vehicles. Adhesive joints have several advantages over the traditional rivet, including, significant weight reduction and efficient stress transfer between bonded materials. As fuel costs continue to rise, the weight reduction is accelerating this transition. Traditional surface pretreatments designed to improve the adhesion of polymeric materials to metallic surfaces are extremely toxic. Replacement adhesive technologies must be compatible with the environment without sacrificing adhesive performance. Silane-coupling agents have emerged as ideal surface modifications for improving composite joint strength. As these coatings are generally applied as very thin layers (\u3c50 nm), it is challenging to characterize their material properties for correlation to adhesive performance. We circumvent this problem by estimating the elastic modulus of the silane-based coatings using the buckling instability formed between two materials of a large elastic mismatch. The elastic modulus is found to effectively predict the joint strength of an epoxy/aluminum joint that has been reinforced with silane coupling agents. This buckling technique is extended to investigate the effects of chemical composition on the elastic modulus. Finally, the effect of macro-scale roughness on silane-reinforced joints is investigated within the framework of the unresolved problem of how to best characterize rough surfaces. Initially, the fractal dimension is used to characterize grit-blasted and sanded surfaces. It is found that, contrary to what has been suggested in the literature, the fractal dimension is independent of the roughening mechanism. Instead, the use of an anomalous diffusion coefficient is proposed as a more effective way to characterize a rough surface. Surface modification by preparation of surface energy gradients is then investigated. Materials with gradients in surface energy are useful in the areas of microfluidics, heat transfer and protein adsorption, to name a few. Gradients are prepared by vapor deposition of a reactive silane from a filter paper source. The technique gives control over the size and shape of the gradient. This surface modification is then used to induce droplet motion through repeated stretching and compression of a water drop between two gradient surfaces. This inchworm type motion is studied in detail and offers an alternative method to surface vibration for moving drops in microfluidic devices. The final surface modification considered is the application of a thin layer of rubber to a rigid surface. While this technique has many practical uses, such as easy release coatings in marine environments, it is applied herein to enable spontaneous healing between a rubber surface and a glass cover slip. Study of the diffusion controlled healing of a blister can be made by trapping an air filled blister between a glass cover slip and a rubber film. Through this study we find evidence for an interfacial diffusion process. This mechanism of diffusion is likely to be important in many biological systems

Behavior of Turbulent Structures within a Mach 5 Mechanically Distorted Boundary Layer

High-resolution particle image velocimetry (PIV) is employed to resolve the velocity fields within a Mach 4.9 mechanically distorted turbulent boundary layer (Reθ ≈ 40,000). The goal of this study is to directly observe the mechanisms responsible for the modified turbulent stresses present in mechanically distorted boundary layers. This is achieved by measuring the effects of the mechanical distortions upon the distribution, population, size, orientation, and energy content of the turbulent structures, and how the perturbed state of these structures is manifested within the ensemble-averaged turbulent stresses. The two mechanical distortions under investigation are 1) streamline curvature-induced favorable pressure gradients (Ip = {-0.08; -0.49}), and 2) periodic arrays of diamond roughness elements (k/δ ≈ 0.07). A smooth-wall, flat-plate boundary layer is also included to establish the unperturbed state of the turbulent structures. The response of the mean turbulence statistics is investigated through ensemble-averaged profiles of Reynolds stresses, indicating the respective influences of pressure gradient effects and surface roughness upon the turbulent statistics. The distortion and reorientation of the large-scale coherent motions is quantified through the determination of the integral length scale and local structure angle from two-point correlations. Detection of individual vortices through the swirling strength criterion λci allows the population distribution of the turbulent eddies to be examined, along with the conditionally averaged hairpin structure. The baseline and rough-wall stresses showed good agreement when scaled by the smooth-wall friction velocity. Two-point correlations indicate that the reorientation of the large-scale [i.e. O(δ)] coherent structures, coupled with the modified wall-normal fluctuations, is primarily responsible for the modification of the rough-wall Reynolds stresses. The reduced Reynolds stresses observed in the favorable pressure gradients is partially due to the attenuation of the local flowfield around the near-wall hairpin structures, mitigating the mechanism for “producing” turbulence. The rotational rate of the hairpin vortices, measured through the mean prograde swirling strength, was reduced for the favorable pressure gradient models

Complexity, Language, and Life: Mathematical Approaches

In May 1984 the Swedish Council for Scientific Research convened a small group of investigators at the scientific research station at Abisko, Sweden, for the purpose of examining various conceptual and mathematical views of the evolution of complex systems. The stated theme of the meeting was deliberately kept vague, with only the purpose of discussing alternative mathematically based approaches to the modeling of evolving processes being given as a guideline to the participants. In order to limit the scope to some degree, it was decided to emphasize living rather than nonliving processes and to invite participants from a range of disciplinary specialities spanning the spectrum from pure and applied mathematics to geography and analytic philosophy. The results of the meeting were quite extraordinary; while there was no intent to focus the papers and discussion into predefined channels, an immediate self-organizing effect took place and the deliberations quickly oriented themselves into three main streams: conceptual and formal structures for characterizing system complexity; evolutionary processes in biology and ecology; the emergence of complexity through evolution in natural languages. The chapters presented in this volume are not the proceedings of the meeting. Following the meeting, the organizers felt that the ideas and spirit of the gathering should be preserved in some written form, so the participants were each requested to produce a chapter, explicating the views they presented at Abisko, written specifically for this volume. The results of this exercise are contained in this book