Browsing by Subject "Droplet"

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    Fluid Interfacial Dynamics: From Droplets to Thin Films
    (2024-05) Chen, Zih-Yin
    Many natural processes and industrial applications involve the understanding and modeling of interfacial fluid dynamics. Examples include the coating of a substrate with a liquid, the removal of liquid films from substrates, transport processes, droplets impact on substrates, etc. Given the ubiquity and significance of interfacial fluid flows, the overall goal of this thesis is to advance our fundamental understanding of interfacial fluid dynamics through theoretical modeling. To achieve this goal, we conduct three studies related to interfacial dynamics involving droplets and liquid films: (i) droplet impact dynamics with granular materials, (ii) droplet dynamics with an air jet, and (iii) dynamics of a liquid film with an undulating surface. Motivated by spray coating processes, we investigate how the presence of particles on a substrate changes the droplet impact dynamics. We analyze the spreading dynamics and splashing criterion of an impacting droplet on a layer of particles. A theoretical model is developed to consider the momentum of the spreading liquid and the time-dependent distribution of particles. Additionally, we establish a droplet splashing criterion based on the interaction between the impacting droplet and the particles. Our results provide insight into how the presence of particles lowers the critical impact velocity at which a droplet exhibits splashing, as the particle area fraction is systematically increased. We then focus on the dynamics of a partially-wetting droplet under an impinging air jet. We built a two-dimensional lubrication model of the droplet that incorporates the external pressure of the impinging turbulent jet, in addition to the capillary and hydrostatic pressures of the droplet. Also, the simulations of the contact-line motion by using precursor film and disjoining pressure allows us to capture the physics of different droplet behaviors, which had previously been observed experimentally. Our simulations exhibit a comparable time-scale of droplet deformations and similar outcomes as the experimental observations. We also obtain the analytical steady-state solutions of the droplet shapes and construct the minimum criteria for droplet splitting and depinning. Lastly, we investigate the interfacial dynamics of a thin liquid film over an undulating solid substrate. To explore the physical mechanisms of free surface flows driven by periodic undulations, we developed a two-dimensional thin-film mathematical model. The model combines the effects of inertia, viscosity, gravity, and surface tension in a tractable way. Our model reveals that in the regime where gravity dominates over surface tension (i.e., large Bond number, Bo), the effects of surface tension drop out of the analysis, allowing the flow rate to only depend on Re and Ca/Bo, where Ca is the capillary number. In this same regime, we learn that inertia (Re) tends to enhance the flow rate, while increasing Ca/Bo reduces the flow rate.
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    Heat transfer to droplets in developing boundary layers at low capillary numbers
    (2014-08) Wenzel, Everett
    This thesis describes the heating rate of a small liquid droplet in a developing boundary layer wherein the boundary layer thickness scales with the droplet radius. Surface tension modifies the nature of thermal and hydrodynamic boundary layer development, and consequently the droplet heating rate. A physical and mathematical description precedes a reduction of the complete problem to droplet heat transfer in an analogy to Stokes' first problem, which is numerically solved by means of the Lagrangian volume of fluid methodology.For Reynolds numbers of order one, the dispersed phase Prandtl number significantly influences the droplet heating rate only in the transient period when the thermal boundary layer first reaches the droplet surface. As the dispersed phase Prandtl number increases, so does the duration of the transient. At later times, when the the droplet becomes fully engulfed by the boundary layer, the heating rate becomes a function of only the constant heat flux boundary condition. This characteristic holds for all Peclet and Weber numbers, but the spatial behavior of the droplet differs for small and large Peclet and Weber numbers.Simulation results allow for the development of a predictive tool for the boiling entry length of dilute systems in channel flow. The tool relies on an assumption of temperature equivalency between the droplet and the thermal boundary layer evaluated in absence of the dispersed phase, which is supported by the computational results. Solutions for plug and fully developed flow do not differ appreciably, suggesting a precise description of the fluid mechanics is not necessary for an approximation of the boiling entry length. Future experimental work is required to validate the predictive models derived in this thesis.