Fluid Interfacial Dynamics: From Droplets to Thin Films

Abstract

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.