Testing the Boundaries: Analysis, Experimentation, and Simulation of Boundary-Dominated Interactions on Fluid Phenomena

Throughout my time at the Joint Fluids Lab at UNC Chapel Hill, I have focused on the intricate interplay between fluids and the solid boundaries that either contain or are contained by the fluids. From an analytical and numerical perspective, these boundaries are often viewed as an inconvenient and overlooked aspect of reality within fluid modeling due to the increased complexity they introduce. For instance, boundary layers, sharp corners, contact points, and material lines necessitate a meticulous meshing near boundaries, as well as innovative modeling approaches to effectively capture their impacts. As I will demonstrate in this dissertation, an otherwise simple fluid behavior can be drastically changed if boundaries are involved. To begin, chapter 1 explores how in the shallow water regime a solid boundary intersecting an interfacial cavity can create a shock. I then present a derivation of the time at which the shock forms, followed by a technique for determining the moment when the interface separates from the bottom boundary. In chapter 2, I build on the work from the previous chapter and focus on the paraboloid cavity. For this special geometry, the boundary produces a seemingly non-physical, persistent connection to the interface. Additionally, the model establishes a scaling factor for the interfacial separation from the bottom boundary. I then verify the model predictions through a novel experiment of the two dimensional problem. In chapter 3, I explore through simulation how a no-slip boundary can produce a fluid shell around a sedimenting particle as it passes through a sharp stratification that delays settling. I then demonstrate that, without the assistance of diffusion, this shell can indefinitely impede the spheres descent. Lastly, in chapter 4, I show that by adding perturbations in channel and pipe boundaries I can significantly enhance or diminish the diffusion of passive tracers for both the lubrication and Stokes regime.