Numerical approaches have been conducted to investigate the effect of droplet deformation and internal circulation on droplet dynamics. Although droplet drag is a classical area of study, there are still theoretical gaps in understanding the motion of large droplets. In applications such as spray combustion, droplets of various sizes are generated and move with the flow. Large droplets tend to deform in the flow, and they have complex interactions with the flow because of this deformation. To better model spray, the physical understanding of droplets needs to be improved. Under spray conditions, droplets are subjected to a high-temperature-and-pressure environment, and the coupling between liquid and gas is enhanced. Therefore the deformation and internal circulation will affect the droplet drag coefficient more significantly than they would under atmospheric conditions. To study the mechanism of how droplet shape and internal circulation influence droplet dynamics, we have used direct numerical simulation (DNS) to simulate a droplet falling at its terminal velocity in high-pressure air. An in-house code developed for interface-capturing DNS of multiphase flows is employed for the simulation. The drag coefficient is calculated, and the results are consistent with the existing literature for slightly deformed droplets. The results show that the drag coefficient is directly related to the droplet deformation and droplet internal circulation. This paper also develops an analytical theory to account for the effect of the Weber number and fluid properties on droplet deformation. / Master of Science / This study investigates how larger droplets interact with airflow in spray conditions. Classical droplet drag models are not accurate under extreme conditions due to the neglect the droplet deformation and droplet internal circulation. To better understand droplet dynamics and to improve the accuracy of droplet models, direct numerical simulations were conducted. In our simulations, a non-evaporating falling droplet in high-pressure air was modeled. Results show a direct link between drag coefficient and droplet shape and internal flow. We also derived an analytical scaling law to explore the parameters related to droplet deformation. This research enhances our understanding of droplet dynamics in spray conditions.

An analytical model is developed to quantify the heat transfer to droplets impinging on heated superhydrophobic (SH) surfaces. Integral analysis is used to incorporate an apparent temperature jump at the superhydrophobic surface as a boundary condition. This Thesis considers the scenario of both isotropic and anisotropic slip, as would be realized on post-cavity style and rib-cavity style SH surfaces. This thermal model is combined with a hydrodynamic model which incorporates velocity slip at the surface. Use of the two models allows determination of the overall cooling effectiveness, a metric outlined in contemporary work. The effect of varying velocity slip and temperature jump is determined for impact Weber numbers ranging from 20 to 150 and surface temperatures ranging from 60 to 100°C. The model results are compared to experiments and good agreement is shown. Heat transfer to a drop impacting superhydrophobic surfaces is decreased when compared to conventional surfaces. A correlation function for the total heat transfer (cooling effectiveness) as a function of relevant parameters is found for isotropic surfaces with a good fit. Anisotropic rib-cavity surfaces are compared to isotropic surfaces to explore the impact of anisotropic slip on the cooling effectiveness, with similar trends seen to that for isotropic surfaces. It's determined that anisotropic surfaces can be modeled with minimal error as an isotropic surface with a temperature jump length equal to the anisotropic surface's average temperature jump length.

<p> The major part of the present work dealt with adapting the droplet technique to the study of nucleation from solution of some analytically important metal chelates. Precipitation from homogenous solution was introduced as the means of gradually increasing the supersaturation in the droplets. This new method of producing supersaturation enabled the extention of the droplet technique to nucleation studies of sparingly soluble substances. </p> <p> In addition, a second novel way of achieving supersaturation in the droplets was devised. In contrast to the first method, which increased the amount of solute at constant droplet volume, the second method maintained the amount of solute constant, while gradually reducing the volume of the droplet. This permitted studies on nucleation from solution of soluble substances to be carried out isothermally. </p> <p> The two techniques mentioned above were applied successfully to the study of nucleation from solution of four analytically important metal chelates and to several inorganic salts, respectively. </p> / Thesis / Doctor of Philosophy (PhD)

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Most aircraft accidents are caused by technical problems or weather-related issues. One cause of weather-related incidents is inlight icing, which can induce negative performance characteristics and endanger the operation of an airplane. Various researchers investigating the problem of inlight icing have proposed ice-phobic coatings as one viable solution. For this purpose, it is critical to study the behavior of a droplet impact on different types of surfaces. As an alternative to physical testing, three-dimensional numerical simulation using computational fluid dynamics offers a promising strategy for evaluating the effects of surface characteristics. Using the volume of fluid method, three simulations of high-speed droplet impact on superhydrophobic surfaces with and without micro-scale roughness elements, were generated. The simulations showed that, for the roughness configurations considered, the superhydrophobic surfaces with micro-scale roughness elements were significantly less effective at repelling the droplet than the smooth superhydrophobic surfaces.

Droplet evaporation and condensation are two important topics of interest, since these two phase-change phenomena not only occur in the cycle of global water, e.g., the formation of rain, fog, dew, and snow in nature, but also play a critical role in a variety of applications including phase-change heat transfer enhancement, surface chemistry and energy system optimization. Especially, in the past two decades, the rapid development of the nature-inspired non-wetting surfaces has promoted the applications of droplet-based phase change phenomena in various scenarios. However, most previous studies focused on the sessile droplets on one flat surface in the open space, and the effects of surface topography, i.e., surface curvature or configurations, on droplet evaporation and dropwise condensation are still elusive. This dissertation aims to explore droplet-based evaporation and condensation in more complex spaces and to elucidate how the surface topography affects the evaporating or coalescing droplet dynamics during these phase-change processes. The coalescence-induced jumping of nanodroplet on curved superhydrophobic surface is modeled via molecular dynamic simulations. As the surface curvature increases from 0 to 2, the corresponding energy conversion efficiency of jumping droplet during the coalescence process could be significantly improved about 20 times. To explain this curvature-enhanced jumping effect, the contact line dissipation, i.e., an important source of energy dissipation in nanoscale, is considered in our scaling energy analysis. And this energy-effective jumping of coalesced droplet could be mainly attributed to the reduction of contact line dissipation due to the decrease of contact line length and contact time on curved surface. As the droplets are confined between two parallel or non-parallel low-energy surfaces, i.e., hydrophobic or superhydrophobic surfaces, with a narrow gap, the total evaporation time of the squeezed droplets would be dramatically prolonged about two times. An ellipsoidal segment diffusion-driven model is established to successfully predict the evolution of contact radius and volume of the squeezed droplets during the evaporation process and to clarify it is the vapor enrichment inside the confined space giving rise to the mitigated evaporation. If two hydrophobic surfaces are configured as non-parallel, the confined droplet inside the V-shaped grooves would be self-transported towards the cusp/corner during the evaporation. Based on our energy and force analyses, the asymmetrically confined droplet would move towards an equilibrium location le, where the Laplace pressure induced force is balanced with normal adhesion force, to minimize its Gibbs surface energy. As le decreases during the evaporation, this equilibrium location would directionally shift towards the cusp, which could be regarded as the origin of this evaporation-triggered unidirectional motion. For the first time, the solvent transport and colloidal extraction could be accurately controlled in a combined manner. / Doctor of Philosophy / Droplet evaporation and condensation are two important topics of interest, since these two phase-change phenomena not only occur in the global cycle of water including the formation of rain, fog, dew, and snow in nature, but also play a critical role in a variety of applications including heat transfer enhancement, surface chemistry, and the energy system optimization. Generally, the droplets in these scenarios are deposited on one flat surface opened to the atmosphere. and the effects of surface topography on droplet evaporation and dropwise condensation are still elusive. This dissertation aims to explore droplet-based evaporation and condensation in more complex spaces and to clarify how the surface curvature or configurations affects evaporating or condensing droplet dynamics accompanying these phase change processes. As the coalesced droplet jumps off the curved superhydrophobic surfaces during dropwise condensation, the corresponding energy conversion efficiency would be significantly improved about 20 times due to the increases of curvature. It is demonstrated that the decrease of contact line length and contact time would give rise to the reduction of contact line dissipation, which should be the main factor driving this energy-effective jumping of the coalesced droplets. As the droplets are confined between two parallel or non-parallel low-energy surfaces, i.e., hydrophobic or superhydrophobic surfaces, with a narrow gap, the total evaporation time of the squeezed droplets would be dramatically prolonged about two times in the small space. An ellipsoidal segment diffusion-driven model is established to successfully predict the evolution of contact radius and volume of the squeezed droplets during the evaporation and to clarify it is the vapor enrichment in the confined space giving rise to the mitigated evaporation. If two hydrophobic surfaces are configured as non-parallel, the confined droplet inside the V-shaped grooves would be self-transported towards the cusp/corner of the structure during evaporation. Based on our energy and force analyses, the asymmetrically confined droplet would move towards an equilibrium location le, where the Laplace pressure induced force is balanced with normal adhesion force, to minimize its Gibbs surface energy. As le decreases in the scale of during the evaporation, this equilibrium location would directionally shift towards the cusp, which could be regarded as the origin of this evaporation-triggered unidirectional motion.

Electric charges are often found in naturally or artificially formed droplets, such as raindrops and those generated by Kelvin's water dropper. In contrast to the impact of neutral droplets on a flat solid surface upon which a thin convex lens shape layer of the gas film is typically formed, I show that the delicate gas thin film can be fundamentally altered for even weakly charged droplets both experimentally and numerically. As the charge level is raised above a critical level of about 1% of the Rayleigh limit for representative impact conditions, the Maxwell stress overcomes the gas pressure buildup to deform the droplet bottom surface. A conical liquid tip forms and pierces Through the gas film, leading to a circular contact line moving outwards that does not trap any gas. The critical charge level only depends on the capillary number based on the gas viscosity. The deformation applies to common liquids and molten alloy droplets. Even dielectric surfaces can also induce conical deformation. The charged droplets can also deform upon hydrophobic surfaces, and increase the contact time on hydrophobic surfaces or even avoid bouncing. / Doctor of Philosophy / Electric charges are often found in naturally or artificially formed droplets, such as raindrops, waterfall, and inkjet printer. Neutral droplets impact on flat surfaces will usually trap a bubble inside because of the viscosity of air. The air bubble entrapped can be ignored if the droplet is water because the air bubble will eventually pinch-off. However, if the droplet is metal or some other viscous liquid, the air bubble will stay inside the liquid. This entrapped air bubble is undesired under some circumstances. For example, the existence of air bubble during metal 3D printing can influence the physical property. I show that the delicate gas thin film can be fundamentally altered for even weakly charged droplets both experimentally and numerically. As the charge level is raised above a critical level of about 1% of the maximum charges a droplet can carry for representative impact conditions, the electric stress will dominate the deformation of droplet. A conical liquid tip forms at the droplet bottom, avoiding the entrapment of air bubble. The critical charge level is experimentally proved to be only dependent on the gas viscosity and impact velocity. The deformation applies to common liquids and molten alloy droplets. Even dielectric surfaces can also induce conical deformation. The charged droplets can also deform upon hydrophobic surfaces, and increase the contact time on hydrophobic surfaces or even avoid bouncing.

Capillarity and dynamic wetting of non-Newtonian fluids are important in many natural and industrial processes, examples cover from a daily phenomenon as splashing of a cup of yogurt to advanced technologies such as additive manufacturing. The applicable non-Newtonian fluids are usually viscoelastic compounds of polymers and solvents. Previous experiments observed diverse interesting behaviors of a polymeric droplet on a wetted substrate or in a microfluidic device. However, our understanding of how viscoelasticity affects droplet dynamics remains very limited. This work intends to shed light on viscoelastic effect on two small scale processes, i.e., the motion of a wetting contact line and droplet splitting at a bifurcation tip.   Numerical simulation is employed to reveal detailed information such as elastic stresses and interfacial flow field. A numerical model is built, combining the phase field method, computational rheology techniques and computational fluid dynamics. The system is capable for calculation of realistic circumstances such as a droplet made of aqueous solution of polymers with moderate relaxation time, impacting a partially wetting surface in ambient air.   The work is divided into three flow cases. For the flow case of bifurcation tube, the evolution of the interface and droplet dynamics are compared between viscoelastic fluids and Newtonian fluids. The splitting or non-splitting behavior influenced by elastic stresses is analyzed. For the flow case of dynamic wetting, the flow field and rheological details such as effective viscosity and normal stress difference near a moving contact line are presented. The effects of shear-thinning and elasticity on droplet spreading and receding are analyzed, under inertial and inertialess circumstances. In the last part, droplet impact of both Newtonian and viscoelastic fluids are demonstrated. For Newtonian droplets, a phase diagram is drawn to visualize different impact regions for spreading, splashing and gas entrapment. For viscoelastic droplets, the viscoelastic effects on droplet deformation, spreading radius and contact line motion are revealed and discussed. / <p>QC 20160329</p>