No abstract / Submitted to Bulletin of the Society of Rheology, May 2005

This thesis presents a study of two basic modes of deformation of a thin sheet: wrinkling and crumpling, viewed primarily in the context of an elastic sheet confined by capillary forces on a drop of liquid. First, it provides a brief conceptual background in the relevant physics of thin sheet mechanics and capillarity and introduces the general principles of wrinkling and crumpling. The problem of confining a circular sheet on an increasingly curved spherical drop is presented as a vehicle to explore these principles. At finite curvature, the sheet is seen to wrinkle around its outer edge. At large confinement, characteristic features of crumpling gradually dominate the pattern. The experimental observations in both regimes are analyzed separately. Analysis of images of the sheet in the wrinkled regime yield data for the number and length of the wrinkled zone, as a function of the experimental control parameter, the pressure. The length of the wrinkles is correctly described by a far-from-threshold theory, which describes a limiting regime in thin-sheet mechanics, distinguished by high 'bendability'. The validity of this theory is verified by the data for highly bendable, ultrathin sheets for the first time. The theory is based on the assumption that the wrinkles completely relax compressive stresses and therefore preserve the cylindrical symmetry of the stress field. The emergence of crumpling from the wrinkled shape is explored via evolution of visible features in the sheet as well as gaussian curvature measurements obtained by analyzing height maps from optical profilometry. The emergence of several length scales, increasing asymmetry in curvature distribution, the failure of wrinkle extent prediction and formation of d-cones associated with crumpling are all measured to locate the transition to a crumpled state. The value of gaussian curvature at the center of the sheet appears to follow the cylindrically symmetric prediction over the whole range of the experiment, suggesting that the onset of crumpling events does not affect the global shape of the sheet. Finally, analogous wrinkling and crumpling behavior of particle-laden interfaces is discussed. The spontaneous formation of conical defects in a curved 2D crystal is compared to the crumpling of a sheet on a drop, and insight from thin sheet mechanics is applied to the mysterious wrinkling of particle rafts. Some future directions for measuring wrinkling of sheets on negative curvature surfaces and deformations of fluid interfaces are proposed.

The earliest man-made irrigation systems in recorded history date back to the ancient Egypt and Mesopotamia era. After thousands of years of experience, exploration, and experimenting, mankind have learned how to construct canals and dams and use pipes and pumps to direct and control water flow, but till this day, there are still some behaviors of water and other simple fluids that surprise us. One such example is the lotus effect: a surface-tension effect which allows raindrops to roll freely on a lotus leaf as if they were drops of mercury. One of the key factors that determine how a fluid system behave is the size-scale. Fluids flow at small scales very differently than they do at large scales. The standard comparing to which small and large are defined is the capillary length. A number of surface-tension related phenomena are unfamiliar because they are only noticeable at length-scales of a few millimeters or below, and they look nothing like what we would expect fluids to behave when dominated by gravity. As fascinating as many of them may seem at first glance, surface-tension phenomena are actually not that far away from our daily lives. Surface tension is everywhere because it costs energy to create areas of surfaces and interfaces, just like it costs energy to deform a solid (resulting in elasticity) or to elevate a weight (resulting in gravity). To minimize energy, a surface or an interface has the tendency to contract, and this tendency generates surface tension. The size of a system significantly affects the relative strengths of surface-tension effects comparing to effects of body forces, most commonly gravity. By equating the estimated magnitudes of surface tension and gravitational forces of a system, a length scale, know as the capillary length, can be defined. The capillary length of water on earth is about 2.7 mm. At the length scale of everyday objects, which is usually above the capillary length, surface-tension effects are not always prominent, because at those scales the competing force, gravity, is often much stronger. That is why the surface of a glass of water is more or less flat. However, as the size-scale decreases, surface tension decreases a lot slower than gravity, so when the size of a fluid system gets down to below the capillary length, surface tension takes over. One of the defining characteristics of this moment in human history, is the tremendous efforts we are putting into the research and engineering of micro- and nano-scale materials and structures − systems where surface tension is often the predominant force. It is important to study surface-tension effects so that we can use them to our advantage. In this Ph.D. dissertation, we have investigated some important surface-tension phenomena including capillarity, wetting, and wicking. We mainly focus on the geometric aspects of these problems, and to learn about how structures affect properties. Understanding these phenomena can help develop fabrication methods (Chapter 2), study surface properties (Chapter 3), and design useful devices (Chapter 4) at scales below the capillary length. In the first project (Chapter 2), we used numerical simulations and experiments to study the meniscus of a fluid confined in capillaries with complicated cross-sectional geometries. In the simulations, we computed the three-dimensional shapes of the menisci formed in polygonal and star-shaped capillaries with sharp or rounded corners. Height variations across the menisci were used to quantify the effect of surface tension. Analytical solutions were derived for all the cases where the cross-sectional geometry was a regular polygon or a regular star-shape. Power indices that characterize the effects of corner rounding were extracted from simulation results. These findings can serve as guide for fabrications of unconventional three-dimensional structures in Capillary Force Lithography experiments [J. Feng (2011) (a)]. Experimental demonstrations of the working principle was also performed. Although quantitative matching between simulation and experimental results was not achieved due to the limitation of material properties, clear qualitative trends were observed and interesting three-dimensional nano-structures were produced. A second project (Chapter 3) focused on developing techniques to produce three-dimensional hierarchically structured superhydrophobic surfaces with high aspect ratios. We experimented with two different high-throughput electron-beam-lithography processes featuring single and dual electron-beam exposures. After a surface modification procedure with a hydrophobic silane, the structured surfaces exhibited two distinct superhydrophobic behaviors − high and low adhesion. While both types of superhydrophobic surfaces exhibited very high (approximately 160_) water advancing contact angles, the water receding contact angles on these two different types of surfaces differed by about 50_ _ 60_, with the low-adhesion surfaces at about 120_ _ 130_ and the high-adhesion surfaces at about 70_ _ 80_. Characterizations of both the microscopic structures and macroscopic wetting properties of these product surfaces allowed us to pinpoint the structural features responsible for specific wetting properties. It is found that the advancing contact angle was mainly determined by the primary structures while the receding contact angle is largely affected by the side-wall slope of the secondary features. This study established a platform for further exploration of the structure aspects of surface wettability [J. Feng (2011) (b)]. In the third and final project (Chapter 4), we demonstrated a new type of microfluidic channel that enable asymmetric wicking of wetting fluids based on structure-induced direction-dependent surface-tension effect. By decorating the side-walls of open microfluidic channels with tilted fins, we were able to experimentally demonstrate preferential wicking behaviors of various IPA-water mixtures with a range of contact angles in these channels. A simplified 2D model was established to explain the wicking asymmetry, and a complete 3D model was developed to provide more accurate quantitative predictions. The design principles developed in this study provide an additional scheme for controlling the spreading of fluids [J. Feng (2012)]. The research presented in this dissertation spreads out across a wide range of physical phenomena (wicking, wetting, and capillarity), and involves a number of computational and experimental techniques, yet all of these projects are intrinsically united under a common theme: we want to better understand how simple fluids respond to small-scale complex surface structures as manifestations of surface-tension effects. We hope our findings can serve as building blocks for a larger scale endeavor of scientific research and engineering development. After all, the pursue of knowledge is most meaningful if the results improve the well-being of the society and the advancement of humanity.

The chromatographic properties of various silicone stationary phases for capillary gas chromatography have been extensively studied, yet the properties of nonsilicone phases have not been so well investigated. The most popular nonsilicone phases are the high molecular weight polyethylene glycols (HMW PEG) which are commercially available in a wide range of molecular weights, cross-linkable and uncross-linkable (Carbowax 2OM and 4OM, the Superox series, etc.). Their most outstanding features are their unique polarity and selectivity; for this reason these phases are widely used in the analysis of aqueous solutions, essential oils, and perfumes. Unfortunately HMW-PEG's are very sensitive to slight differences in preparation and handling procedures which can cause analyses to differ with each laboratory, each column, and even each use. HMWâ PEG's also suffer from low temperature stability, a high minimum allowable operating temperature, and have lower diffusion coefficients than silicone phases. This study examines the efficiency differences of eight columns differing only in immobilization procedure and added functional groups. Comparison is made using HETP versus u and separation number (TZ) versus u curves. These curves offer important information, in particular, the effect of carrier gas, u, column operating temperature, degree of cross-linking, and cross-linking temperature on chromatographic efficiency and separation number. In addition, the contributions of the CL (resistance to mass transfer in the liquid phase) and DL (diffusion coefficient in the liquid phase) terms in the Golay equation are calculated [1]. Solids at room temperature, PEG stationary phases undergo a solid-liquid phase transition within their useful temperature range. The effect of this transition on the chromatographic properties is investigated using efficiency, separation number, capacity ratio, and retention index versus temperature curves. Four more columns, in addition to the eight mentioned above, demonstrate the influence of end-groups and the molecular weight of the stationary phase on the phase transition temperature range. / Master of Science

Methods of co-optimizing resolution and detection in Capillary Zone Electrophoresis (CZE) and Micellar Electrokinetic Chromatography (MEKC) are examined by deriving mathematical expressions which illustrate the relative importance of various experimental parameters. For CZE, expressions are derived to show the interrelationship between efficiency, capillary dimensions and sample size. The interrelationship shows that resolution and detectability cannot be optimized simultaneously. Efficiency and, therefore, resolution are maximized when small sample sizes and capillaries with small internal diameters are employed. Detection is more favorable when large sample sizes and capillaries with large internal diameters are used. To achieve a favorable compromise between resolution and detection, the Influence of pH, electrolyte concentration and forced air convection are examined. A decrease in pH or an increase in electrolyte concentration reduces electroosmotic flow. This increases the relative velocity difference between two zones and, thereby, minimizes the efficiency required for unit resolution. Forced air convection minimizes the loss in efficiency observed as capillaries with larger internal diameters are employed. In MEKC, the importance of efficiency is minimized by employing a micellar phase which provides adequate selectivity for the separation. The separation of ASTM test mix LC-79-2 obtained in sodium dodecyl sulfate, sodium decyl sulfate, and sodium dodecyl sulfate modified with Brij 35 indicates that selectivity is governed by the nature of the surfactant's polar head group. Beyond selectivity optimization, resolution may be improved by increasing efficiency or decreasing electroosmotic flow. Of these approaches, increasing capillary length, to improve efficiency, is more time effective. Using the guidelines described herein, several practical applications were developed. The methods are examined with respect to migration time and quantitative reproducibility. / Ph. D.

Les milieux poreux sont omniprésents dans le quotidien des hommes du 21ème siècle que ce soit par hasard ou par nécessité. Certains permettent le transport d’une ou plusieurs phases fluides immiscibles, une situation à la fois courante et critique dans de nombreuses applications industrielles. Le transport d’une phase mouillante, l’imbibition, a été largement étudiée mais un certain nombre de problèmes restent ouverts. Dans cette thèse, nous nous sommes concentrés sur trois d’entre eux. La fragmentation de phase induite par la gravité dans une jonction asymétrique a été étudiée. La dynamique et un critère d’apparition ont été prédits analytiquement puis confirmés expérimentalement. Ensuite, l’évolution de l’épaisseur d’un front d’imbibition dans un réseau de capillaires a été simulée numériquement. Les résultats ont permis de lever une controverse de la littérature. Enfin, l’imbibition dans un milieu constitué de lames flexibles déformables a été explorée numériquement et expérimentalement. Il a été montré que la déformabilité des lames induit leur coalescence et agit sur la dynamique de l'imbibition. / Porous media are ubiquitous in today’s society due to chance or necessity. Some of them allow the transportation of one or several immiscible fluid phases simultaneously. This property is both usual and critical in many industrial processes. The transport of a wetting phase, imbibition, has been widely studied but lots of issues remain opened. In this manuscript, three of them are addressed. Gravity induced phase fragmentation has been studied in an asymmetric pore junction. Fragmentation criterion and dynamic are predicted analytically and confirmed experimentally. Then, the broadening of an imbibition front in a capillary network has been investigated numerically. Results resolved a controversy in the literature. Finally, imbibition in a medium made of flexible sheets has been studied both numerically and experimentally. It showed that sheets flexibility induces their clustering and influences the imbibition dynamic.

The contact angle defined by Young's equation depends on the ratio between solid and liquid surface energies. Young's contact angle is constant for a given system, and cannot explain the stability of fluid droplets in capillary tubes. Within this framework, large variations in contact angle and explained aassuming surface roughness, heterogeneity or contamination. This research explores the static and dynamic behavior of fluid droplets within capillary tubes and the variations in contact angle among interacting menisci. Various cases are considered including wetting and non-wetting gluids, droplets in inclined capillary tubes or subjected to a pressure difference, within one-dimensional and three-dimensional capillary systems, and under static or dynamic conditions (either harmonic fluid pressure or tube oscillation). The research approach is based on complementary analytical modeling (total energy formulation) and experimental techniques (microscopic observations). The evolution of meniscus curvatures and droplet displacements are studied in all cases. Analytical and experimental results show that droplets can be stable within capillary tubes even under the influence of an external force, the resulting contact angles are not constant, and bariations from Young's contact angle aare extensively justified as menisci interaction. Menisci introduce stiffness, therefore two immiscible Newtonian fluids behave as a Maxwellian fluid, and droplets can exhibit resonance or relaxation spectral features.

This Thesis explores physical phenomena characteristic for thin liquid films and small droplets of simple and complex liquids on solid substrates for which wettability and capillarity control their statical and dynamical properties. We start by discussing the general concepts of wettability and capillarity and introduce the common mathematical framework of the lubrication approximation for studies of thin liquid films and small contact angle drops. We demonstrate the derivation of the generic equation describing the evolution of a film of simple liquid from the Navier-Stokes equations. We show how this model can be further extended to incorporate various effects relevant to the case of complex liquids. The results described in the Thesis comprise three projects with the common main theme of the influence of wettability and capillarity on the statics and dynamics of the studied systems, namely (i) Evaporating sessile droplets fed through the solid substrate - a geometry that allows us to discuss steady states of the system and their role in the time evolution of freely evaporating droplets without influx in an isothermal case; (ii) The influence of a solute--dependent wettability on the stability, static and dynamical properties of thin films and drops of non-volatile mixtures, suspensions and solutions; (iii) A parameter-passing scheme between particle-based Molecular Dynamics simulations and the continuum lubrication model which allows us to discuss equilibrium properties of small polymeric droplets. We present the physical questions arising in the three systems and discuss approaches and results as well as possible extensions.

Brazing and soldering, as advanced manufacturing processes, are of significant importance to industrial applications. It is widely accepted that joining by brazing or soldering is possible if a liquid metal wets the solids to be joined. Wetting, hence spreading and capillary action of liquid metal (often called filler) is of significant importance. Good wetting is required to distribute liquid metal over/between the substrate materials for a successful bonding. Topographically altered surfaces have been used to exploit novel wetting phenomena and associated capillary actions, such as imbibitions (a penetration of a liquid front over/through a rough, patterned surface). Modification of surface roughness may be considered as a venue to tune and control the spreading behavior of the liquids. Modeling of spreading of liquids on rough surface, in particular liquid metals is to a large extent unexplored and constitutes a cutting edge research topic. In this dissertation the imbibitions of liquid metal has been considered as pertained to the metal bonding processes involving brazing and soldering fillers. First, a detailed review of fundamentals and the recent progress in studies of non-reactive and reactive wetting/capillary phenomena has been provided. An imbibition phenomenon has been experimentally achieved for organic liquids and molten metals during spreading over topographically modified intermetallic surfaces. It is demonstrated that the kinetics of such an imbibition over rough surfaces follows the Washburn-type law during the main spreading stage. The Washburn-type theoretical modeling framework has been established for both isotropic and anisotropic non-reactive imbibition of liquid systems over rough surfaces. The rough surface domain is considered as a porous-like medium and the associated surface topographical features have been characterized either theoretically or experimentally through corresponding permeability, porosity and tortuosity. Phenomenological records and empirical data have been utilized to verify the constructed model. The agreement between predictions and empirical evidence appears to be good. Moreover, a reactive wetting in a high temperature brazing process has been studied for both polished and rough surfaces. A linear relation between the propagating triple line and the time has been established, with spreading dominated by a strong chemical reaction.

Flying insects face challenging conditions such as rainfall, fog, and dew. In this theoretical and experimental thesis, we investigate the survival mechanisms of the mosquito, Anopheles, through particles of various size. Large particles such as falling raindrops can weigh up to fifty times a mosquito. Mosquitoes survive such impacts by virtue of their low mass and strong exoskeleton. Smaller particle sizes, as present in fog and insecticide, pose the greatest danger. Mosquitoes cannot fly through seemingly innocuous household humidifier fog or other gases with twice the density of air. Upon landing, fog accumulates on the mosquito body and wings, which in small quantities can be shaken off in the manner of a wet dog. Large amounts of dew on the wings create a coalescence cascade ultimately folding the wings into taco shapes, which are difficult to dry. The insights gained in this study will inform the nascent field of flapping micro-aerial vehicles.