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We construct classical stochastic mass transport processes for stationary states which are chosen to factorize over pairs of sites of an undirected, connected, but otherwise arbitrary graph. For the special topology of a ring we derive static properties such as the critical point of the transition between the liquid and the condensed phase, the shape of the condensate and its scaling with the system size. It turns out that the shape is not universal, but determined by the interplay of local and ultralocal interactions. In two dimensions the effect of anisotropic interactions of hopping rates can be treated analytically, since the partition function allows a dimensional reduction to an effective one-dimensional zero-range process. Here we predict the onset, shape and scaling of the condensate on a square lattice. We indicate further extensions in the outlook.

Surface tension is an essential force for the functioning of the world and life. Centuries of study, and still, new applications and limits of surface tension are being explored. Water has always drawn attention for its high surface tension value, 72mN/m compared to ethanol's 20mN/m. The high surface tension allows for numerous applications, superhydrophobic surfaces being one that takes heavy advantage of that value. Superhydrophobicsurfaceshave a high surface energy cost with water, resulting in small contact areas with high advancing and receding contact angles and low contact angle hysteresis. This results in very low adhesion on the surfaces. Here we study the ability of superhydrophobic surfaces with their low adhesion to shed meltwater from frost, showing a decrease in frost thickness to below 3mm for the meltwater to shed. We then take another approach to removing water from a surface, rather than increasing the surface energy cost, we introduce a difference in surface energy cost. Introducing a porous surface across from a solid one, droplets transfer from the solid to the porous, removing over 90% of the volume of the droplet from the solid surface. We thoroughly examine and model the hydrodynamics of the transfer process, varying the solid surface, the donor surface, and the liquid. This bridging between surfaces is then applied to fog harps, examining the efficiencies of large-form fog harps. Fog harps have shown a 3 to 5 times increase in water collection compared to the industry-standard mesh collector. However, droplets from fog collected on the wires eventually grow large enough to touch neighboring wires. Tominimizetheirsurfaceenergy, they begin pulling wires together, "tangling" them. This can potentially reduce efficiency, but has not been applied to large-scale harps until here. Another application of surface tension is then examined, using lower surface tension oils, but trapping them in microstructures to make slippery liquid-infused porous surfaces (SLIPS). The oil coats the microstructure, due to its lower surface tension. This creates a lubricating layer on the surface, along with potential air pockets reducing friction further. These surfaces have been studied extensively with liquids being placed on them, but here we begin to examine them when solids are used instead, showing some interesting cases where increasing the viscosity of the oil actually decreases the friction force. / Doctor of Philosophy / Sponges are something everyone has used, and most people can tell you that they work using surface tension. And for most people, that's enough. It's actually more useful to know to squeeze your sponge dry when you're done to prevent mold than it is to know that it holds onto liquids because of surface tension. But the point here was to take the study of sponges and surface tension to the extreme. To the point that some knowledge is going to be gained solely for the sake of gaining knowledge. Not all knowledge will have immediate uses, but this doesn't take value away from the knowledge, or any eventual uses it might have. So we start this by looking at the building of scientific knowledge and noticing that a brick is missing. Superhydrophobic surfaces, surfaces that water doesn't want to touch, have been studied very extensively and their properties have been thoroughly explored. However, a direct comparison of the defrosting behaviors, the process of frost melting on a surface, between superhydrophobic and hydrophobic surfaces had not been done. Water does prefer to be on a hydrophobic surface compared to a superhydrophobic one, but it's still uncomfortable. A plate was treated so that half was hydrophobic and the other half was superhydrophobic. Frost was grown across the surface and then melted simultaneously, allowing us to characterize the differences in the behaviors, highlighting the ability of the superhydrophobic surface to shed water droplets at smaller sizes than other surfaces. Next is a pure fluid mechanics work supporting a heat transfer application. Evaporation, for enhanced heat transfer, and a hydrophilic wick, essentially a sponge, are paired to create a plate with one-way heat transfer. Heating side A can heat side B, but heating side B can't heat side A. Water in the wick gets heated, evaporates from side A and then condenses on side B, carrying heat with it. The condensation grows until it touches the wick, which then pulls it in, allowing it to be evaporated again and cycling more heat. When side B, the smooth surface, is heated, the water can evaporate off it and condense in the wick, but then it has no way to return, preventing further heat transfer. The process of droplets being pulled from side B to the wick in side A is key to the process. It's a sponge pulling water in using surface tension. However, all the smaller pieces have been taken for granted. The second piece is a systematic study of this capture mechanism, exploring the effects of changing liquids, donor surfaces, and receiving porous wicks. The third is a continuation of the lab's previous work on Fog Harps, arrays of vertical fibers held in place to let fog run into them. The droplets grow until they slide down and can be collected. The wires of the harp are close enough that the water can actually start to tangle them together. This tangling can increase the water needed for sliding and collection to begin. Tensioning the wires can help mitigate the tangling. Here we show harps on around 1,$text{m}^2$, using optimal wire size and spacing that is possible for mass manufacturing. The harps were tested in the lab using humidifiers to generate fog for the harps to collect. Finally, an initial study of solid objects being pulled across oil-infused microstructured surfaces. The microstructure helps keep the oil on the surface thanks to the surface energy of the oil. These oil-infused surfaces have been studied extensively when liquids are placed on them, but not with solid objects. Solid objects can exert significantly more pressure than liquids, which naturally want to spread when they reach a certain thickness. Experiments were performed with a variety of oil viscosities, microstructures, and oil excess thicknesses. This work is not entirely complete but a significant portion of it is presented here.

Wetting, which addresses either spontaneous or forced spreading of liquids on a solid surface, is a ubiquitous phenomenon in nature and can be observed by us on a daily basis, e.g., rain drops falling on a windshield and lubricants protecting our corneas. The study of wetting phenomena can be traced back to the observation of water rising in a capillary tube by Hauksbee in 1706 and still remains as a hot topic, since it lays the foundation for a wide spectrum of applications, such as fluid mechanics, surface chemistry, micro/nanofluidic devices, and phase change heat transfer enhancement. Generally, wetting is governed by the dynamic and static behaviors of the three-phase contact line. Therefore, a deep insight into the dynamics and statics of three-phase contact line at nanoscale is necessary for the technological advancement in nanotechnology and nanoscience. This dissertation aims to understand the dynamic wetting under a molecular kinetic framework and resolve the reconfiguration of liquid molecules at the molecular region of contact line. Water spreading on polytetrafluoroethylene surfaces is selected as a classical example to study the dynamic behaviors of three-phase contact line. To accommodate the moving contact line paradox, the excess free energy is considered to be dissipated in the form of molecular dissipation. As-formed contact line friction/dissipation coefficient is calculated for water interacting with PTFE surfaces with varying structures and is found to be on the same order of magnitude with dynamic viscosity. From an ab initio perspective, contact line friction is decomposed into contributions from solid-liquid retarding and viscous damping. A mathematical model is established to generalize the overall friction between a droplet and a solid surface, which is able to clarify the static-to-kinetic transition of solid-liquid friction without introducing contact angle hysteresis. Moreover, drag reduction on lotus-leaf-like surface is accounted for as well. For the first time, the concept of contact line friction is used in the rational design of a superhydrophobic condenser surface for continuous dropwise condensation. We focus on the transport and reconfiguration of liquid molecules confined by a solid wall to shed light on the morphology of the molecular region of a three-phase contact line. A governing equation, which originates from the free energy analysis of a nonuniform monocomponent system, is derived to describe the patterned oscillations of liquid density. By comparing to the Reynolds transport theorem, we find that the oscillatory profiles of interfacial liquids are indeed governed in a combined manner by self-diffusion, surface-induced convection and shifted glass transition. Particularly for interfacial water, the solid confining effects give rise to a bifurcating configuration of hydrogen bonds. Such unique configuration consists of repetitive layer-by-layer water sheets with intra-layer hydrogen bonds and inter-layer defects. Molecular dynamics simulations on the interfacial configuration of water on solid surfaces reveal a quadratic dependence of adhesion on solid-liquid affinity, which bridges the gap between macroscopic interfacial properties and microscopic parameters. / Doctor of Philosophy / The study of wetting phenomena can be traced back to the observation of water rising in a capillary tube by Hauksbee in 1706 and still remains as a hot topic, since it lays the foundation for a wide spectrum of applications, such as fluid mechanics, surface chemistry, micro/nanofluidic devices, and phase change heat transfer enhancement. The conventional hydrodynamic analysis with no slip boundary condition predicts a diverging shear stress at the contact line as well as an unbounded shear force exerted on the solid surface. To accommodate this paradox, different mechanism and models have been proposed to clarify the slip between a moving contact line and a solid surface. Although almost all models yield reasonable agreement with experimental observations or numerical simulations, it is still difficult to pick up a specific model using only macroscopic properties and experiment-accessible quantities, because the energy dissipation mechanism during dynamic wetting is not identified and the contact line deforms over different length scales. In this dissertation, we ascribe the energy dissipation in dynamic wetting to contact line friction/dissipation under the framework of molecular kinetic theory, as it is assumed that the contact line is constantly oscillating around its equilibrium position. By decomposing contact line friction into two contributions: solid-liquid retarding and viscous damping, we are able to derive a universal model for the contact line friction. This model predicts a decaying solid-liquid friction on superhydrophobic surfaces, corresponding to the lotus effect. In the meantime, this model is able to clarify the recently-discovered static-to-kinetic transition of frictional force between a sessile drop and a solid surface. Later, we used the concept of contact line friction in the droplet growth process in dropwise condensation so as to promote the rational design of superhydrophobic condenser surfaces for sustainable dropwise condensation. As the morphology of a contact line is dependent on the length scale of interest, we focus on the molecular region of contact line. We study the transport and structural change of liquid molecules that are several molecular layers away from the solid surface. It is found that liquid molecules in this region experience patterned density oscillations, which cannot be simply attributed to the random deviations from continuum limit. By combining free energy analysis and Reynolds transport theorem, it is demonstrated that the omnipresent density oscillations arise from the collective effects of self-diffusion, surface-induced convection and shifted glass transition. For liquid water, we propose a bifurcating hydrogen bonding network in contrast to its tetrahedron configuration in bulk water.

Mechanical deformations of nucleic acids (NA) play a very important role in many biological life processes. The bending persistence length of DNA is of specific interest, because so much eukaryotic DNA that stores genetic information is tightly packed inside cell nuclei, even though DNA is considered to be a relatively stiff biopolymer. However, recent experiments suggest that DNA may be more flexible than its persistence length (~ 150 bp or ~ 47 nm) suggests, especially for fragments shorter than 100 bp. It is important to reconcile these two seemingly competing pictures of DNA bending by providing a model that can explain the novel results without discrediting old experiments and the widely-accepted worm-like chain model. Another factor that influences both molecular geometry as well as mechanical properties is the ionic atmosphere surrounding the NA. It is known that multivalent ions with charge of +3e and higher can condense DNA into aggregates at high enough concentration. However, most conventional models cannot explain why RNA and DNA condense at different concentrations. Furthermore, our recent simulation results suggest that even though DNA persistence length decreases with multivalent ion concentration due to increasing electrostatic screening, RNA actually becomes stiffer due to a structural transition from the internal binding of the counterions. / Ph. D.

The subgroup decomposition method (SDM) has recently been developed as an improvement over the consistent generalized energy condensation theory for treatment of the energy variable in deterministic particle transport problems. By explicitly preserving reaction rates of the fine-group energy structure, the SDM directly couples a consistent coarse-group transport calculation with a set of fixed-source "decomposition sweeps" to provide a fine-group flux spectrum. This paper will outline the implementation of the SDM into the three-dimensional, discrete ordinates (SN) deterministic transport code TITAN. The new version of TITAN, TITAN-SDM, is tested using 1-D and 2-D benchmark problems based on the Japanese designed High Temperature Engineering Test Reactor (HTTR). In addition to accuracy, this study examines the efficiency of the SDM algorithm in a 3-D SN transport code. / Master of Science

A numerical analysis of laminar film condensation and the prediction of aerosol formation is presented for a gas-vapor mixture undergoing forced flow through a vertical tube. This analysis is useful for estimating the sizes and operating conditions of condensers used for removing vapors from gas-vapor mixtures. The ability to predict the possibility of aerosol formation without expensive experimental studies makes it practical to design condensers in which aerosol formation is impossible. Three different vapors (water, mercury, and benzene) mixed with air are considered in the analysis at three different inlet vapor mass fractions (50% of saturated, 75% of saturated, and saturated). The results indicate that condensers could effectively be used to remove vapors from gas/vapor mixtures and therefore, that design estimates could be determined from the model presented here. The results also show that inlet vapor mass fractions as low as 50% of saturation for water and benzene and 25% of saturation for mercury could cause aerosol formation in the bulk flow field. Aerosol formation degrades the performance of a condenser in removing vapor because the vapor condenses in the bulk flow where it is not easily removed without the use of a filtering medium. / Master of Science