Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

DESIGN, MODELING, AND FABRICATION OF MICROROBOT LEGS

This dissertation presents work done in the design, modeling, and fabrication of magnetically actuated microrobot legs. Novel fabrication processes for manufacturing multi-material compliant mechanisms have been used to fabricate effective legged robots at both the meso and micro scales, where the meso scale refers to the transition between macro and micro scales. This work discusses the development of a novel mesoscale manufacturing process, Laser Cut Elastomer Refill (LaCER), for prototyping millimeter-scale multi-material compliant mechanisms with elastomer hinges. Additionally discussed is an extension of previous work on the development of a microscale manufacturing process for fabricating micrometer-sale multi-material compliant mechanisms with elastomer hinges, with the added contribution of a method for incorporating magnetic materials for mechanism actuation using externally applied fields. As both of the fabrication processes outlined make significant use of highly compliant elastomer hinges, a fast, accurate modeling method for these hinges was desired for mechanism characterization and design. An analytical model was developed for this purpose, making use of the pseudo rigid-body (PRB) model and extending its utility to hinges with significant stretch component, such as those fabricated from elastomer materials. This model includes 3 springs with stiffnesses relating to material stiffness and hinge geometry, with additional correction factors for aspects particular to common multi-material hinge geometry. This model has been verified against a finite element analysis model (FEA), which in turn was matched to experimental data on mesoscale hinges manufactured using LaCER. These modeling methods have additionally been verified against experimental data from microscale hinges manufactured using the Si/elastomer/magnetics MEMS process. The development of several mechanisms is also discussed: including a mesoscale LaCER-fabricated hexapedal millirobot capable of walking at 2.4 body lengths per second; prototyped mesoscale LaCER-fabricated underactuated legs with asymmetrical features for improved performance; 1 centimeter cubed LaCER-fabricated magnetically-actuated hexapods which use the best-performing underactuated leg design to locomote at up to 10.6 body lengths per second; five microfabricated magnetically actuated single-hinge mechanisms; a 14-hinge, 11-link microfabricated gripper mechanism; a microfabricated robot leg mechansim demonstrated clearing a step height of 100 micrometers; and a 4 mm x 4 mm x 5 mm, 25 mg microfabricated magnetically-actuated hexapod, demonstrated walking at up to 2.25 body lengths per second.

TWO-PHASE HEAT TRANSFER MECHANISMS WITHIN PLATE HEAT EXCHANGERS: EXPERIMENTS AND MODELING

Two-phase flow heat exchangers have been shown to have very high efficiencies, but the lack of a dependable model and data precludes them from use in many cases. Herein a new method for the measurement of local convective heat transfer coefficients from the outside of a heat transferring wall has been developed, which results in accurate local measurements of heat flux during two-phase flow. This novel technique uses a chevron-pattern corrugated plate heat exchanger consisting of a specially machined Calcium Fluoride plate and the refrigerant HFE7100, with heat flux values up to 1 W cm-2 and flow rates up to 300 kg m-2s-1. As Calcium Fluoride is largely transparent to infra-red radiation, the measurement of the surface temperature of PHE that is in direct contact with the liquid is accomplished through use of a mid-range (3.0-5.1 µm) infra-red camera. The objective of this study is to develop, validate, and use a unique infrared thermometry method to quantify the heat transfer characteristics of flow boiling within different Plate Heat Exchanger geometries. This new method allows high spatial and temporal resolution measurements. Furthermore quasi-local pressure measurements enable us to characterize the performance of each geometry. Validation of this technique will be demonstrated by comparison to accepted single and two-phase data. The results can be used to come up with new heat transfer correlations and optimization tools for heat exchanger designers. The scientific contribution of this thesis is, to give PHE developers further tools to allow them to identify the heat transfer and pressure drop performance of any corrugated plate pattern directly without the need to account for typical error sources due to inlet and outlet distribution systems. Furthermore, the designers will now gain information on the local heat transfer distribution within one plate heat exchanger cell which will help to choose the correct corrugation geometry for a given task.

Multi-Scale Dynamic Study of Secondary Impact During Drop Testing of Surface Mount Packages

This dissertation focuses on design challenges caused by secondary impacts to printed wiring assemblies (PWAs) within hand-held electronics due to accidental drop or impact loading. The continuing increase of functionality, miniaturization and affordability has resulted in a decrease in the size and weight of handheld electronic products. As a result, PWAs have become thinner and the clearances between surrounding structures have decreased. The resulting increase in flexibility of the PWAs in combination with the reduced clearances requires new design rules to minimize and survive possible internal collisions impacts between PWAs and surrounding structures. Such collisions are being termed ‘secondary impact’ in this study. The effect of secondary impact on board-level drop reliability of printed wiring boards (PWBs) assembled with MEMS microphone components, is investigated using a combination of testing, response and stress analysis, and damage modeling. The response analysis is conducted using a combination of numerical finite element modeling and simplified analytic models for additional parametric sensitivity studies.

AIR SIDE HEAT TRANSFER ENHANCEMENT IN HEAT EXCHANGERS UTILIZING INNOVATIVE DESIGNS AND THE ADDITIVE MANUFACTURING TECHNIQUE

Over the last decade, rapid development of additive manufacturing techniques has allowed the fabrication of innovative and complex designs. One field that can benefit from such technology is heat exchanger fabrication, as heat exchanger design has become more and more complex due to the demand for higher performance particularly on the air side of the heat exchanger. By employing the additive manufacturing, a heat exchanger design was successfully realized, which otherwise would have been very difficult to fabricate using conventional fabrication technologies. In this dissertation, additive manufacturing technique was implemented to fabricate an advanced design which focused on a combination of heat transfer surface and fluid distribution system. Although the application selected in this dissertation is focused on power plant dry cooling applications, the results of this study can directly and indirectly benefit other sectors as well, as the air-side is often the limiting side for in liquid or single phase cooling applications. Two heat exchanger designs were studied. One was an advanced metallic heat exchanger based on manifold-microchannel technology and the other was a polymer heat exchanger based on utilization of prime surface technology. Polymer heat exchangers offer several advantages over metals such as antifouling, anticorrosion, lightweight and often less expensive than comparable metallic heat exchangers. A numerical modeling and optimization were performed to calculate a design that yield an optimum performance. The optimization results show that significant performance enhancement is noted compared to the conventional heat exchangers like wavy fins and plain plate fins. Thereafter, both heat exchangers were scaled down and fabricated using additive manufacturing and experimentally tested. The manifold-micro channel design demonstrated that despite some fabrication inaccuracies, compared to a conventional wavy-fin surface, 15% - 50% increase in heat transfer coefficient was possible for the same pressure drop value. In addition, if the fabrication inaccuracy can be eliminated, an even larger performance enhancement is predicted. Since metal based additive manufacturing is still in the developmental stage, it is anticipated that with further refinement of the manufacturing process in future designs, the fabrication accuracy can be improved. For the polymer heat exchanger, by fabricating a very thin wall heat exchanger (150μm), the wall thermal resistance, which usually becomes the limiting side for polymer heat exchanger, was calculated to account for only up to 3% of the total thermal resistance. A comparison of air-side heat transfer coefficient of the polymer heat exchanger with some of the commercially available plain plate fin surface heat exchangers show that polymer heat exchanger performance is equal or superior to plain plate fin surfaces. This shows the promising potential for polymer heat exchangers to compete with conventional metallic heat exchangers when an additive manufacturing-enabled fabrication is utilized. Major contributions of this study are as follows: (1) For the first time demonstrated the potential of additive manufacturing in metal printing of heat exchangers that benefit from a sophisticated design to yield a performance substantially above the respective conventional systems. Such heat exchangers cannot be fabricated with the conventional fabrication techniques. (2) For the first time demonstrated the potential of additive manufacturing to produce polymer heat exchangers that by design minimize the role of thermal conductivity and deliver a thermal performance equal or better that their respective metallic heat exchangers. In addition of other advantages of polymer over metal like antifouling, anticorrosion, and lightweight. Details of the work are documented in respective chapters of this thesis.