Collective behavior of asperities as a model for friction and adhesion

Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one. In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials. We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.

Establishing the C. elegans uterine seam cell (utse) as a novel model for studying cell behavior

The molecular inputs necessary for cell behavior are vital to our understanding of development and disease. Proper cell behavior is necessary for processes ranging from creating one’s face (neural crest migration) to spreading cancer from one tissue to another (invasive metastatic cancers). Identifying the genes and tissues involved in cell behavior not only increases our understanding of biology but also has the potential to create targeted therapies in diseases hallmarked by aberrant cell behavior.

A well-characterized model system is key to determining the molecular and spatial inputs necessary for cell behavior. In this work I present the C. elegans uterine seam cell (utse) as an ideal model for studying cell outgrowth and shape change. The utse is an H-shaped cell within the hermaphrodite uterus that functions in attaching the uterus to the body wall. Over L4 larval stage, the utse grows bidirectionally along the anterior-posterior axis, changing from an ellipsoidal shape to an elongated H-shape. Spatially, the utse requires the presence of the uterine toroid cells, sex muscles, and the anchor cell nucleus in order to properly grow outward. Several gene families are involved in utse development, including Trio, Nav, Rab GTPases, Arp2/3, as well as 54 other genes found from a candidate RNAi screen. The utse can be used as a model system for studying metastatic cancer. Meprin proteases are involved in promoting invasiveness of metastatic cancers and the meprin-likw genes nas-21, nas-22, and toh-1 act similarly within the utse. Studying nas-21 activity has also led to the discovery of novel upstream inhibitors and activators as well as targets of nas-21, some of which have been characterized to affect meprin activity. This illustrates that the utse can be used as an in vivo model for learning more about meprins, as well as various other proteins involved in metastasis.

Response of linear, viscous damped systems to excitations having time-varying frequency

The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time.

The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.

Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.

The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.

It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance.

One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon.

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

SteelConverter and Caltech VirtualShaker: Rapid Nonlinear Cloud-Based Structural Model Conversion and Analysis

STEEL, the Caltech created nonlinear large displacement analysis software, is currently used by a large number of researchers at Caltech. However, due to its complexity, lack of visualization tools (such as pre- and post-processing capabilities) rapid creation and analysis of models using this software was difficult. SteelConverter was created as a means to facilitate model creation through the use of the industry standard finite element solver ETABS. This software allows users to create models in ETABS and intelligently convert model information such as geometry, loading, releases, fixity, etc., into a format that STEEL understands. Models that would take several days to create and verify now take several hours or less. The productivity of the researcher as well as the level of confidence in the model being analyzed is greatly increased.

It has always been a major goal of Caltech to spread the knowledge created here to other universities. However, due to the complexity of STEEL it was difficult for researchers or engineers from other universities to conduct analyses. While SteelConverter did help researchers at Caltech improve their research, sending SteelConverter and its documentation to other universities was less than ideal. Issues of version control, individual computer requirements, and the difficulty of releasing updates made a more centralized solution preferred. This is where the idea for Caltech VirtualShaker was born. Through the creation of a centralized website where users could log in, submit, analyze, and process models in the cloud, all of the major concerns associated with the utilization of SteelConverter were eliminated. Caltech VirtualShaker allows users to create profiles where defaults associated with their most commonly run models are saved, and allows them to submit multiple jobs to an online virtual server to be analyzed and post-processed. The creation of this website not only allowed for more rapid distribution of this tool, but also created a means for engineers and researchers with no access to powerful computer clusters to run computationally intensive analyses without the excessive cost of building and maintaining a computer cluster.

In order to increase confidence in the use of STEEL as an analysis system, as well as verify the conversion tools, a series of comparisons were done between STEEL and ETABS. Six models of increasing complexity, ranging from a cantilever column to a twenty-story moment frame, were analyzed to determine the ability of STEEL to accurately calculate basic model properties such as elastic stiffness and damping through a free vibration analysis as well as more complex structural properties such as overall structural capacity through a pushover analysis. These analyses showed a very strong agreement between the two softwares on every aspect of each analysis. However, these analyses also showed the ability of the STEEL analysis algorithm to converge at significantly larger drifts than ETABS when using the more computationally expensive and structurally realistic fiber hinges. Following the ETABS analysis, it was decided to repeat the comparisons in a software more capable of conducting highly nonlinear analysis, called Perform. These analyses again showed a very strong agreement between the two softwares in every aspect of each analysis through instability. However, due to some limitations in Perform, free vibration analyses for the three story one bay chevron brace frame, two bay chevron brace frame, and twenty story moment frame could not be conducted. With the current trend towards ultimate capacity analysis, the ability to use fiber based models allows engineers to gain a better understanding of a building’s behavior under these extreme load scenarios.

Following this, a final study was done on Hall’s U20 structure [1] where the structure was analyzed in all three softwares and their results compared. The pushover curves from each software were compared and the differences caused by variations in software implementation explained. From this, conclusions can be drawn on the effectiveness of each analysis tool when attempting to analyze structures through the point of geometric instability. The analyses show that while ETABS was capable of accurately determining the elastic stiffness of the model, following the onset of inelastic behavior the analysis tool failed to converge. However, for the small number of time steps the ETABS analysis was converging, its results exactly matched those of STEEL, leading to the conclusion that ETABS is not an appropriate analysis package for analyzing a structure through the point of collapse when using fiber elements throughout the model. The analyses also showed that while Perform was capable of calculating the response of the structure accurately, restrictions in the material model resulted in a pushover curve that did not match that of STEEL exactly, particularly post collapse. However, such problems could be alleviated by choosing a more simplistic material model.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes.

Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.

The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² ˂ n_e ˂ 10¹⁵ particles/cm³, 3500 ˂ T ˂ 11000 °K, and 200 ˂ v_z ˂ 1200 cm/sec.

The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.

Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions.

In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 ˂ x_NO ˂ 0.0055. The temperatures were measured pyrometrically and varied between 1300 ˂ T ˂ 1750°K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.

Chemical and Electrochemical Behavior of Graphene-Covered Silicon Photoanodes

This dissertation describes efforts over the last five years to develop protective layers for semiconductor photoelectrodes based on monolayer or few-layer graphene sheets. Graphene is an attractive candidate for a protective layer because of its known chemical inertness, transparency, ease of deposition, and limited number of electronic states. Monolayer graphene was found to effectively inhibit loss of photocurrent over 1000 seconds at n-Si/aqueous electrolyte interfaces that exhibit total loss over photocurrent over 100 seconds. Further, the presence of graphene was found to effect only partial Fermi level pinning at the Si/graphene interface with respect to a range of nonaqueous electrolytes. Fluorination of graphene was found to extend the stability imparted on n-Si by the monolayer sheet in aqueous Fe(CN)₆^3-/4- electrolyte to over 100,000 seconds. It was demonstrated that the stability of the photocurrent of n-Si/fluorinated graphene/aqueous electrolyte interfaces relative to n-Si/aqueous electrolyte interfaces is likely attributable to the inhibition of oxidation of the silicon surface.

This dissertation also relates efforts to describe and define terminology relevant to the field of photoelectrochemistry and solar fuels production. Terminology describing varying interfaces employed in electrochemical solar fuels devices are defined, and the research challenges associated with each are discussed. Methods for determining the efficiency of varying photoelectrochemical and solar-fuel-producing cells from the current-voltage behavior of the individual components of such a device without requiring the device be constructed are described, and a range of commonly employed performance metrics are explored.

A singular perturbation method of calculating the behavior of supercavitating hydrofoils with rounded noses

A simple, direct and accurate method to predict the pressure distribution on supercavitating hydrofoils with rounded noses is presented. The thickness of body and cavity is assumed to be small. The method adopted in the present work is that of singular perturbation theory. Far from the leading edge linearized free streamline theory is applied. Near the leading edge, however, where singularities of the linearized theory occur, a non-linear local solution is employed. The two unknown parameters which characterize this local solution are determined by a matching procedure. A uniformly valid solution is then constructed with the aid of the singular perturbation approach.

The present work is divided into two parts. In Part I isolated supercavitating hydrofoils of arbitrary profile shape with parabolic noses are investigated by the present method and its results are compared with the new computational results made with Wu and Wang's exact "functional iterative" method. The agreement is very good. In Part II this method is applied to a linear cascade of such hydrofoils with elliptic noses. A number of cases are worked out over a range of cascade parameters from which a good idea of the behavior of this type of important flow configuration is obtained.

Some of the computational aspects of Wu and Wang's functional iterative method heretofore not successfully applied to this type of problem are described in an appendix.