Affiliation: College of Arts and Sciences, Department of Mathematics
This dissertation presents results on the effects of sharp density variations in the dynamics of settling spheres in viscous-dominated regimes by a combination of experimental, analytical, and numerical tools. Particles settling through naturally-stratified fluids, such as the ocean and the atmosphere, affect many aspects of life, from air quality and pollution clearing times to the formation of thin aggregate layers in the upper ocean. In this thesis, we develop an understanding of the dynamics that affect these problems by studying the behavior of a sphere falling under gravity through a two-layer fluid. We have found that the sphere slows down dramatically as it passes through the density transition. In this system, we demonstrate the importance of the entrained fluid to the delayed settling of the particle due to its added buoyancy force. In particular, we compare long residence times at the interface rivaling the ones observed for porous spheres and marine snow - aggregates that occur naturally in the ocean- in similar configurations. We call these cases the entrainment dominated regimes, where diffusion of salt could play an active role and it is therefore needed in the modeling. The developed first principle model is a highly coupled system that captures the most significant aspects of settling in a sharp two-layer fluid. We discuss previously implemented approximations and new experimental regimes where the approximation is no longer valid. The asymptotic approaches and exact solutions for the sphere exterior problem of the Stokes equations will be compared in a parametric study of relevance for experiments. The region of validity for the approximations, the full theory agreement, and the possible need to include diffusion in the entrainment dominated regimes will be discussed and explained. The single particle theory further sheds light in the settling rates of marine aggregates falling through sharp density transitions, and how this ultimately affects marine carbon cycling. In addition to solid spheres, we have examined porous, and drilled spheres , obtaining range of parameters that enhance the residence time at the interface. We have also investigated this phenomenon extensively through experiments by observing clouds of solid particles as they settle through a sharply stratified water column.