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.

Instrumentation for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes.

The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology.

This dissertation presents the development of a KID-based instrument including a portion of the millimeter-wave bandpass filters and all aspects of the readout electronics, which together enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this dissertation has been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a new instrument for the Caltech Submillimeter Observatory (CSO).

Electrocatalytic reduction of dioxygen at chemically modified electrodes

The kinetics of the reduction of O₂ by Ru(NH₃)₆⁺² as catalyzed by cobalt(II) tetrakis(4-N-methylpyridyl)porphyrin are described both in homogeneous solution and when the reactants are confined to Nafion coatings on graphite electrodes. The catalytic mechanism is determined and the factors that can control the total reduction currents at Nafion-coated electrodes are specified. A kinetic zone diagram for analyzing the behavior of catalyst-mediator-substrate systems at polymer coated electrodes is presented and utilized in identifying the current-limiting processes. Good agreement is demonstrated between calculated and measured reduction currents at rotating disk electrodes. The experimental conditions that will yield the optimum performance of coated electrodes are discussed, and a relationship is derived for the optimal coating thickness.

The relation between the reduction potentials of adsorbed and unadsorbed cobalt(III) tetrakis(4-N-methylpyridyl)porphyrin and those where it catalyzes the electroreduction of dioxygen is described. There is an unusually large change in the formal potential of the Co(III) couple upon the adsorption of the porphyrin on the graphite electrode surface. The mechanism in which the (inevitably) adsorbed porphyrin catalyzes the reduction of O₂ is in accord with a general mechanistic scheme proposed for most monomeric cobalt porphyrins.

Four new dimeric metalloporphyrins (prepared in the laboratory of Professor C. K. Chang) have the two porphyrin rings linked by an anthracene bridge attached to meso positions. The electrocatalytic behavior of the diporphyrins towards the reduction of O₂ at graphite electrodes has been examined for the following combination of metal centers: Co-Cu, Co-Fe, Fe-Fe, Fe-H₂. The Co-Cu diporphyrin catalyzes the reduction of O₂ to H₂O₂ but no further. The other three catalysts all exhibit mixed reduction pathways leading to both H₂O₂ and H₂O. However, the pathways that lead to H₂O do not involve H₂O₂ as an intermediate. A possible mechanistic scheme is offered to account for the observed behavior.

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.

The structure specificity of alpha-chymotrypsin. I. Polypeptides as substrates. II. N-acylated peptide esters as substrates. III. Some reactive esters of N-acylated amino acids as substrates

The structural specificity of α-chymotrypsin for polypeptides and denatured proteins has been examined. The primary specificity of the enzyme for these natural substrates is shown to closely correspond to that observed for model substrates. A pattern of secondary specificity is proposed.

A series of N-acetylated peptide esters of varying length have been evaluated as substrates of α-chymotrypsin. The results are interpreted in terms of proposed specificity theories.

The α-chymotrypsin-catalyzed hydrolyses of a number of N-acetylated dipeptide methyl esters were studied. The results are interpreted in terms of the available specificity theories and are compared with results obtained in the study of polypeptide substrates. The importance of non-productive binding in determining the kinetic parameters of these substrates is discussed. A partial model of the locus of the active site which interacts with the R’₁CONH- group of a substrate of the form R’₁CONHCHR₂COR’₃ is proposed.

Finally, some reactive esters of N-acetylated amino acids have been evaluated as substrates of α-chymotrypsin. Their reactivity and stereo-chemical behavior are discussed in terms of the specificity theories available. The importance of a binding interaction between the carboxyl function of the substrate and the enzyme is suggested by the results obtained.

Study of oscillatory behavior of recording process arising from electron-hole competition in strongly oxidized LiNbO3 : Ce : Cu

We have investigated ultraviolet (UV) photorefractive effect of lithium niobate doubly doped with Ce and Cu. It is found the diffraction efficiency shows oscillating behavior Under UV-1ight-recording. A model in which electrons and holes can be excited from impurity centers in the UV region is proposed to study the oscillatory behavior of the diffraction efficiency. Oil the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Phi. And the electron-hole competition may cause the oscillation of the relative spatial phase shift. A switch point from electron grating to hole grating is chosen to realize nonvolatile readout by a red light with high sensitivity (0.4 cm/J). (c) 2005 Elsevier GmbH. All rights reserved.

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.

I. The effect of droplet solidification upon two-phase flow in a rocket nozzle. II. A kinetic theory investigation of some condensation-evaporation phenomena by a moment method

Part I:

The perturbation technique developed by Rannie and Marble is used to study the effect of droplet solidification upon two-phase flow in a rocket nozzle. It is shown that under certain conditions an equilibrium flow exists, where the gas and particle phases have the same velocity and temperature at each section of the nozzle. The flow is divided into three regions: the first region, where the particles are all in the form of liquid droplets; a second region, over which the droplets solidify at constant freezing temperature; and a third region, where the particles are all solid. By a perturbation about the equilibrium flow, a solution is obtained for small particle slip velocities using the Stokes drag law and the corresponding approximation for heat transfer between the particle and gas phases. Singular perturbation procedure is required to handle the problem at points where solidification first starts and where it is complete. The effects of solidification are noticeable.

Part II:

When a liquid surface, in contact with only its pure vapor, is not in the thermodynamic equilibrium with it, a net condensation or evaporation of fluid occurs. This phenomenon is studied from a kinetic theory viewpoint by means of moment method developed by Lees. The evaporation-condensation rate is calculated for a spherical droplet and for a liquid sheet, when the temperatures and pressures are not too far removed from their equilibrium values. The solutions are valid for the whole range of Knudsen numbers from the free molecule to the continuum limit. In the continuum limit, the mass flux rate is proportional to the pressure difference alone.

A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

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.

Chemical and electrochemical investigations of cobalt cyanide and ruthenium ammine complexes

Part I.

The stoichiometry and kinetics of the reaction between Co(CN₅H^3- and HgX₂ (X = CN, OH) have been investigated. The products of the reaction are two new complexes, [(NC)₅Co-HgX]^3- and [(NC)₅Co-Hg-Co(CN)₅]^6-, whose spectra are reported. The kinetic measurements produced a value for the forward rate constant of the reaction Co(CN)₅H^3- + OH^- k₁/k_-1 Co(CN)₅^4- +H₂O, k1 = (9.7 ± 0.8) x 10^-2 M^-1 sec^-1 at 24°C, and an equilibrium constant for the reaction K = 10^-6 M^-1.

Part II.

Unusually large and sharp "adsorption waves" appear in cyclic voltammograms of Co(CN)₅^3- and several cobalt(III) pentacyano complexes at stationary mercury electrodes. The nature of the adsorbed species and the reasons for the absence of the adsorption waves in polarograms taken with a d.m.e. have been examined. The data are compatible with the adsorption, in all cases, of a coordinatively unsaturated cobalt(II) complex, Co(CN)₄^2-, by means of a cobalt-mercury bond. When the resulting adsorbed complex is reduced, a series of subsequent chemical and electrode reactions is initiated in which three faradays of charge are consumed for each mole of adsorbed complex. The adsorption of the anionic complex strongly retards the reduction of other negatively charged complexes.

Part III.

A number of formal redox potentials for Ru^III (NH₃)₅L + e = Ru^II (NH₃)₅L and Ru^III(NH₃)₄L₂ + e = Ru^II (NH₃)₄L₂ (where L is various ligands) has been measured by cyclic voltammetry, potentiometry, and polarography and are discussed in terms of the properties of the ligands, such as π-accepting capability. Reduction of coordinated pyrazine in the complexes, Ru(NH₃)₅ Pz²⁺, cis- and trans-Ru(NH₃)₄Pz₂²⁺, on a mercury electrode has been observed. The behavior of this reduction in various acidity of the solution as well as the reoxidation of the reduction products are discussed.

Behavior ecology of the Humboldt squid, Dosidicus gigas: insights from an animal-borne video and data logging system

Dosidicus gigas is a large pelagic cephalopod of the eastern Pacific that has recently undergone an unexpected, significant range expansion up the coast of North America. The impact that such a range expansion is expected to have on local fisheries and marine ecosystems has motivated a thorough study of this top predator, a squid whose lifestyle has been quite mysterious until recently. Unfortunately, Dosidicus spends daylight hours at depths prohibitive to making observations without significant artificial interference. Observations of this squid‟s natural behaviors have thus far been considerably limited by the bright illumination and loud noises of remotely-operated-vehicles, or else the presence of humans from boats or with SCUBA. However, recent technological innovations have allowed for observations to take place in the absence of humans, or significant human intrusion, through the use of animal-borne devices such as National Geographic‟s CRITTERCAM. Utilizing the advanced video recording and data logging technology of this device, this study seeks to characterize unknown components of Dosidicus gigas behavior at depth. Data from two successful CRITTERCAM deployments reveal an assortment of new observations concerning Dosidicus lifestyle. Tri-axial accelerometers enable a confident description of Dosidicus orientation during ascents, descents, and depth maintenance behavior - previously not possible with simple depth tags. Video documentation of intraspecific interactions between Dosidicus permits the identification of ten chromatic components, a previously undescribed basal chromatic behavior, and multiple distinct body postures. And finally, based on visualizations of spermatophore release by D. gigas and repetitive behavior patterns between squid pairs, this thesis proposes the existence of a new mating behavior in Dosidicus. This study intends to provide the first glimpse into the natural behavior of Dosidicus, establishing the groundwork for a comprehensive ethogram to be supported with data from future CRITTERCAM deployments. Cataloguing these behaviors will be useful in accounting for Dosidicus‟ current range expansion in the northeast Pacific, as well as to inform public interest in the impacts this expansion will have on local fisheries and marine ecosystems.