Nowadays sealing systems are commonly designed by means of hydrodynamic and elastohydrodynamic theories. Although the analytical as well as the computational approaches have improved in meaning full manner since the last decades: For small sealing gaps, in the order of micrometers and below, a discrepancy between experimental investigated and theoretically predicted leakage flows occur. As a cause for the discrepancy a breakdown of the no slip boundary condition is suspected. Since in small sealing gaps the continuum hypothesis is violated and molecular effects have to be considered. One fundamental quantity to take molecular affects into account is the slip length. Within this paper a new measurement apparatus to evaluate the slip length for hydraulic applications is presented. The adjustable gaps between two planar surfaces are in the order of magnitude of 1 μm. In a first step the slip length for the system steel-oil –steel is investigated at three different temperatures: 18°C, 22°C and 25°C. The measured slip lengths are in the order of magnitude of ~100 nm.

Interaction of a liquid droplet and a fiber or layer of fibers is ubiquitous in nature and in a variety of industrial applications. It plays a crucial role in fog harvesting, coalescence filtration, membrane desalination, self-cleaning and fiber based microfluidics, among many others. This work presents a quantitative investigation on the interactions of a droplet with a fiber or layers of fibers. More precisely, the present work is focused on 1) predicting the effects of fiber’s size and material on its ability to withhold a droplet against external forces and on the liquid residue left on the fiber after the droplet detachment, 2) predicting the outcome of two fibers competing to attract the same droplet, and 3) predicting the wetting stability of a droplet deposited on a layer of electrospun fibers. This work is comprised of series of computational and experimental studies for mutual validation and/or calibration. The simulations were conducted using the Surface Evolver code and the experiments were devised using a ferrofluid and a magnet. We also investigated the drag reduction performance of fibrous coatings because of its close connection with droplet-fiber interaction. We started by studying the drag reduction performance of a superhydrophobic granular coating because of its geometrical simplicity. We modeled the flow of water over the granular coating and studied the effects of hydrostatic pressure and microstructural properties on the drag reduction performance of the coating. We then examined the drag reduction performance of a lubricant infused surface with trapped air made of layers of parallel fibers (FLISTA). A mathematical model was developed to predict the shape of the water-lubricant interface and lubricant-air interface under a given hydrostatic pressure. This information was used to solve the flow field over the coating in a Couette configuration to find the effects of hydrostatic pressure and microstructural properties of the coating on its drag reduction performance.

Enhanced mass transport in carbon-based nanoscale conduits (e.g. carbon nanotubes, graphene nanochannels/capillaries, graphene/graphene oxide membranes) has attracted tremendous interest over the last decade due to its significant implications for water desalination/purification, nanofiltration, electronic cooling, battery/fuel cells, and lab-on-a-chip. Further development of carbon-based nanoscale conduits for practical applications relies on understanding fundamental mechanisms of transport through individual conduits, which have not been well studied due to challenges in fabrication and measurement. In this thesis, the construction of two-dimensional planar graphene nanochannel devices and the studies of enhanced water and ion transport inside the graphene nanochannels are reported for the first time. The graphene nanochannels are fabricated by conformally covering high-quality graphene on the surfaces of silica nanochannels. A new fabrication scheme consisting of graphene wet transfer, graphene patterning and vacuum anodic bonding is developed to create such graphene nanochannels with heights ranging from 24 to 124 nm. Using these nanochannels and a new hybrid nanochannel based capillary flow measurement technique, we successfully measured the hydraulic resistance (water permeability) of single graphene nanochannels. Our results demonstrate that the frictionless surface of graphene induces a boundary slip and enhances water flow inside the graphene nanochannel. The measured slip length of graphene in the graphene nanochannels poses a median value around 16 nm, albeit with a large variation from 0 to 200 nm regardless of the channel height. The small-yet-widely-varying values of the graphene slip length are attributed to the surface charge of graphene and the interaction between graphene and underneath silica substrate, which are in good agreement with the prediction of our molecular dynamics (MD) simulation. In addition, we also investigated enhanced ion transport inside the graphene nanochannels. Higher electroosmotic conductance at low electrolyte concentrations (10-6 M~10-2 M) is observed in graphene nanochannels when compared with silica nanochannels with the same geometry. Our results suggest that the enhanced electroosmotic flow is also due to the boundary slip at the graphene/electrolyte interface. Besides, our analysis shows that the surface charge on the graphene, originating from the dissociation of oxygen-containing functional groups, is crucial to the enhanced electroosmotic flow inside nanochannels.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21551号 / 理博第4458号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 准教授 藤 定義, 准教授 荒木 武昭 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Nowadays sealing systems are commonly designed by means of hydrodynamic and elastohydrodynamic theories. Although the analytical as well as the computational approaches have improved in meaning full manner since the last decades: For small sealing gaps, in the order of micrometers and below, a discrepancy between experimental investigated and theoretically predicted leakage flows occur. As a cause for the discrepancy a breakdown of the no slip boundary condition is suspected. Since in small sealing gaps the continuum hypothesis is violated and molecular effects have to be considered. One fundamental quantity to take molecular affects into account is the slip length. Within this paper a new measurement apparatus to evaluate the slip length for hydraulic applications is presented. The adjustable gaps between two planar surfaces are in the order of magnitude of 1 μm. In a first step the slip length for the system steel-oil –steel is investigated at three different temperatures: 18°C, 22°C and 25°C. The measured slip lengths are in the order of magnitude of ~100 nm.

Water is often found adhering to surfaces in droplet form. Droplets can develop as a result of precipitation, condensation, or chemical reactions. Drops are retained or held on a surface due to a retention force exerted on the drop by the surface. This retention force is a function of the surface tension of the liquid, drop geometry, and the contact angle between the drop and the surface. When external or body forces exceed this retention force the drop begins to move. This thesis seeks to understand and quantify the forces present at the point of droplet departure once it begins to move under an applied force. The conditions of drop departure in shear flow are explored for five microstructured superhydrophobic surfaces, one smooth hydrophobic surface, and one carbon nanotube (CNT) surface. Surface solid fractions range from 0.05 - 1.00, and static contact angles range from 121.4 - 160.6°. Droplet volumes of 5, 10, 20, 30, 40 and 50 µL are tested on each surface. For each experiment, a shear airflow is applied to a droplet placed on a surface. Shear air velocities start at zero and are increased at a consistent speed until the droplet departs. Highspeed imaging is used to track the droplets shape and position with respect to time, and a mass flowmeter is used to track bulk air velocity with respect to time. Particle imaging velocimetry (PIV) measurements were carried out to characterize the velocity profile of the shear airflow, and an appropriate velocity profile is calculated for any given flowrate by interpolating/extrapolating within PIV measurements. The condition of drop departure is defined as the point at which a droplet's acceleration no longer oscillates about zero and instead increases monotonically. As the applied shear force increases until drop departure occur, measurements of droplet base length, height, and cross section area (as viewed from the side) indicate that these quantities remain approximately constant throughout the length of the test. Measurements of advancing and receding contact angles are reported at the point of departure, with increasing contact angle hysteresis (difference between advancing and receding contact angles) observed until departure occurs. Contact angle hysteresis is shown to be a good indicator of droplet mobility. Measurements of bulk air velocity upstream of the droplet and measurements of the average air velocity over the height of the droplet are both reported at the point of departure. Bulk air velocity at the point of departure is shown to vary with droplet volume, while the average air velocity over the droplet height at the point of departure is shown to be independent of droplet volume. Both measures of air velocity decrease with decreasing surface solid fraction, and decrease most rapidly at low solid fractions. Retention forces are calculated using a retention force factor and vary from 10 - 64 µN. Retention force is shown to be roughly constant for a given droplet base length. An appropriate coefficient of drag is calculated in the range of 0.55 to 2.66 for droplet Reynolds numbers of 225 - 908. The coefficient of drag is shown to be independent of droplet Reynolds number, and to be approximately constant for a given droplet Bond number.

This dissertation focuses on the effects of heating on superhydrophobic (SHPo) surfaces. The work is divided into two main categories: heat transfer without mass transfer and heat transfer in conjunction with mass transfer. Numerical methods are used to explore the prior while experimental methods are utilized for the latter. The numerical work explores convective heat transfer in SHPo parallel plate microchannels and is separated into two stand-alone chapters that have been published archivally. The first considers surfaces with a rib/cavity structure and the second considers surfaces patterned with a square lattice of square posts. Laminar, fully developed, steady flow with constant fluid properties is considered where the tops of the ribs and posts are maintained at a constant heat flux boundary condition and the gas/liquid interfaces are assumed to be adiabatic. For both surface configurations the overall convective heat transfer is reduced. Results are presented in the form of average Nusselt number as well as apparent temperature jump length (thermal slip length). The heat transfer reduction is magnified by increasing cavity fraction, decreasing Peclet number, and decreasing channel size relative to the micro-structure spacing. Axial fluid conduction is found to be substantial at high Peclet numbers where it is classically neglected. The parameter regimes where prior analytical works found in the literature are valid are delineated. The experimental work is divided into two stand-alone chapters with one considering channel flow and the other a pool scenario. The channel work considers high aspect ratio microchannels with one heated SHPo wall. If water saturated with dissolved air is used, the air-filled cavities of SHPo surfaces act as nucleation sites for mass transfer. As the water heats it becomes supersaturated and air can effervesce onto the SHPo surface forming bubbles that align to the underlying micro-structure if the cavities are comprised of closed cells. The large bubbles increase drag in the channel and reduce heat transfer. Once the bubbles grow large enough, they are expelled from the channel and the nucleation and growth cycle begins again. The pool work considers submerged, heated SHPo surfaces such that the nucleation behavior can be explored in the absence of forced fluid flow. The surface is maintained at a constant temperature and a range of temperatures (40 - 90 °C) are explored. Similar nucleation behavior to that of the microchannels is observed, however, the bubbles are not expelled. Natural convection coefficients are computed. The surfaces with the greatest amount of nucleation show a significant reduction in convection coefficient, relative to a smooth hydrophilic surface, due to the insulating bubble layer.

In this work, we develop an interface-preserving level-set method in the finite-element framework for interfacial flows with moving contact lines. In our method, the contact line is advected naturally by the flow field. Contact angle hysteresis can be easily implemented without explicit calculation of the contact angle or the contact line velocity, and meshindependent results can be obtained following a simple computational strategy. We have implemented the method in three dimensions and provide numerical studies that compare well with analytical solutions to verify our algorithm. We first develop a high-order numerical method for interface-preserving level-set reinitialization. Within the interface cells, the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. For the non-interface cells, we compute the gradient of the level set function by solving a Hamilton-Jacobi equation as a conservation law system using the discontinuous Galerkin method. This follows the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660-690]. The missing constant for these cells is recovered using the continuity of the level set function while taking into account the characteristics. To treat highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax-Friedrichs flux and a penalty flux. Our method is accurate for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N + 1)th order accuracy in the interface cells and Nth order accuracy in the whole domain are observed for smooth solutions when Nth degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We then develop a level-set method in the finite-element framework. The contact line singularity is removed by the slip boundary condition proposed by Ren and E [Phys. Fluids, vol. 19, p. 022101, 2007], which has two friction coefficients: βN that controls the slip between the bulk fluids and the solid wall and βCL that controls the deviation of the microscopic dynamic contact angle from the static one. The predicted contact line dynamics from our method matches the Cox theory very well. We further find that the same slip length in the Cox theory can be reproduced by different combinations of (βN; βCL). This combination leads to a computational strategy for mesh-independent results that can match the experiments. There is no need to impose the contact angle condition geometrically, and the dynamic contact angle automatically emerges as part of the numerical solution. With a little modification, our method can also be used to compute contact angle hysteresis, where the tendency of contact line motion is readily available from the level-set function. Different test cases, including code validation and mesh-convergence study, are provided to demonstrate the efficiency and capability of our method. Lastly, we extend our method to three-dimensional simulations, where an extension equation is solved on the wall boundary to obtain the boundary condition for level-set reinitializaiton with contact lines. Reinitialization of ellipsoidal interfaces is presented to show the accuracy and stability of our method. In addition, simulations of a drop on an inclined wall are presented that are in agreement with theoretical results. / Doctor of Philosophy / When a liquid droplet is sliding along a solid surface, a moving contact line is formed at the intersection of the three phases: liquid, air and solid. This work develops a numerical method to study problems with moving contact lines. The partial differential equations describing the problem are solved by finite element methods. Our numerical method is validated against experiments and theories. Furthermore, we have implemented our method in three-dimensional problems.

Doctor of Philosophy / Department of Physics / Bruce M. Law / Three diverse first author surfaces science experiments conducted by Sean P. McBride 1-3 will be discussed in detail and supplemented by secondary co-author projects by Sean P. McBride, 4-7 all of which rely heavily on the use of an atomic force microscope (AFM). First, the slip length parameter, b of liquids is investigated using colloidal probe AFM. The slip length describes how easily a fluid flows over an interface. The slip length, with its exact origin unknown and dependencies not overwhelming decided upon by the scientific community, remains a controversial topic. Colloidal probe AFM uses a spherical probe attached to a standard AFM imaging tip driven through a liquid. With the force on this colloidal AFM probe known, and using the simplest homologous series of test liquids, many of the suspected causes and dependencies of the slip length demonstrated in the literature can be suppressed or eliminated. This leaves the measurable trends in the slip length attributed only to the systematically varying physical properties of the different liquids. When conducting these experiments, it was realized that the spring constant, k, of the system depends upon the cantilever geometry of the experiment and therefore should be measured in-situ. This means that the k calibration needs to be performed in the same viscous liquid in which the slip experiments are performed. Current in-situ calibrations in viscous fluids are very limited, thus a new in-situ k calibration method was developed for use in viscous fluids. This new method is based upon the residuals, namely, the difference between experimental force-distance data and Vinogradova slip theory. Next, the AFM’s ability to acquire accurate sub nanometer height profiles of structures on interfaces was used to develop a novel experimental technique to measure the line tension parameter, τ, of isolated nanoparticles at the three phase interface in a solid-liquid-vapor system. The τ parameter is a result of excess energy caused by the imbalance of the complex intermolecular forces experienced at the three phase contact line. Many differences in the sign and magnitude of the τ parameter exist in the current literature, resulting in τ being a controversial topic.

Ce travail de thèse, constitué de deux parties apparemment très différentes, a pour objectif commun de modéliser et simuler certaines interfaces non classiques en mécanique des fluides et en mécanique des solides. Dans la première partie qu'est la partie principale du travail, l'écoulement de Stokes d'un fluide dans un canal encadré par deux parois solides parallèles est étudié. La surface d'une paroi étant supposée lisse, la condition d'adhérence parfaite classique est adoptée pour l'interface fluide-solide homogène correspondante. La surface de l'autre paroi étant supposée rugueuse et capable de piéger de petites poches d'air, l'interface liquide-solide correspondante est donc hétérogène. La première partie de ce travail consiste à homogénéiser l'interface liquide-solide hétérogène de façon à remplacer cette dernière par une interface fluide-solide homogène imparfaite caractérisée par une longueur de glissement effective. Le problème essentiel de déterminer la longueur de glissement effective est résolu par le développement : (i) d'une approche semi-analytique dans le cas où la surface rugueuse est périodique; (ii) d'une approche basée sur la méthode de solution fondamentale dans le cas où la surface rugueuse est aléatoire. Les résultats obtenus par les approches développées sont systématiquement comparés avec ceux délivrés par la méthode des éléments finis. La deuxième partie du travail est de déterminer les modules élastiques effectifs d'un composite fibreux dans lequel les interfaces entre la matrice et les fibres sont imparfaites et décrites par le modèle membranaire. Une méthode numérique efficace basée sur la transformée de Fourier est ainsi développée et implantée pour traiter le cas général où la section d'une fibre peut avoir une forme quelconque / The present work, consisting of two seemingly very different parties, aims at modeling and simulating some non-classical interfaces in fluid mechanics and solid mechanics. In the first part which is the main part of the work, the Stokes flow of a fluid in a channel bounded by two parallel solid walls is studied. The surface of a solid wall being assumed to be smooth, the classic perfect adherence condition is adopted for the corresponding homogeneous fluid-solid interface. The surface of the other wall being taken to be rough and capable of trapping small pockets of air, the corresponding liquid-solid interface is heterogeneous. The first part of this work is to homogenize the heterogeneous liquid-solid interface so as to replace it by an imperfect homogeneous fluid-solid interface characterized by an effective slip length. The essential underlying problem of determining the effective slip length is achieved by developing: (i) a semi-analytical approach when the rough surface is periodic; (ii) an approach based on the fundamental solution method when the surface is randomly rough. The results obtained by the developed approaches are systematically compared with those issued from the finite element method. The second part of the work is to determine the effective elastic moduli of a fiber composite in which the interfaces between the matrix and fibers are imperfect and described by the membrane model. An efficient numerical method based on the fast Fourier transform is developed and implemented to treat the general case where the section of a fiber can be of any shape