ingest cdrApp 2018-08-23T17:59:39.404Z d39a25df-af15-48e9-aec2-c9af81a997a2 modifyDatastreamByValue RELS-EXT fedoraAdmin 2018-08-23T18:00:31.183Z Setting exclusive relation addDatastream MD_TECHNICAL fedoraAdmin 2018-08-23T18:00:42.525Z Adding technical metadata derived by FITS addDatastream MD_FULL_TEXT fedoraAdmin 2018-08-23T18:01:05.868Z Adding full text metadata extracted by Apache Tika modifyDatastreamByValue RELS-EXT fedoraAdmin 2018-08-23T18:01:28.543Z Setting exclusive relation modifyDatastreamByValue MD_DESCRIPTIVE cdrApp 2018-09-27T15:22:04.581Z modifyDatastreamByValue MD_DESCRIPTIVE cdrApp 2019-03-21T16:25:30.628Z Holly Arrowood Author Department of Mathematics College of Arts and Sciences Oil Droplets Rising through Density-Stratified Fluid at Low Reynolds Number Sharp density stratifications occur naturally in the ocean, and play a important role in the dynamics of settling marine snow particles and the dispersion of oil from seeps or spills. When passing through a sharp density transition between two miscible fluid layers, rising immiscible drops slow to well below terminal velocity due to the entrainment of bottom-layer fluid. This dissertation presents an experimentally-validated, numerically-assisted, first-principles model of an oil drop rising in a cylindrical tank of sharply-stratified fluid at low Reynolds number. The mathematical model presented in this dissertation model adapts previous work on a settling sphere in sharply-stratified fluid to the significantly more complex case of a rising fluid sphere. A Green's function formulation is used to model the density-driven flow, while the method of reflections and method of multipoles are adapted to correct for the increased drag on the drop due to the cylindrical boundary. The numerical implementation of this model is also based upon previous work for a solid sphere, but requires attention to a number of numerical considerations not present in the solid sphere case. Finally, an experimental study is used to validate the final model within its regime of validity. Additional experimental observations of surfactant effects are detailed as well. Summer 2018 2018 Fluid mechanics Droplets, Fluid Dynamics, Green's function, Sharp stratification, Stokes Flow, Stratified fluid eng Doctor of Philosophy Dissertation University of North Carolina at Chapel Hill Graduate School Degree granting institution Mathematics Roberto Camassa Thesis advisor Richard McLaughlin Thesis advisor Gregory Forest Thesis advisor Laura Miller Thesis advisor David Adalsteinsson Thesis advisor text Holly Arrowood Creator Department of Mathematics College of Arts and Sciences Oil Droplets Rising through Density-Stratified Fluid at Low Reynolds Number Sharp density stratifications occur naturally in the ocean, and play a important role in the dynamics of settling marine snow particles and the dispersion of oil from seeps or spills. When passing through a sharp density transition between two miscible fluid layers, rising immiscible drops slow to well below terminal velocity due to the entrainment of bottom-layer fluid. This dissertation presents an experimentally-validated, numerically-assisted, first-principles model of an oil drop rising in a cylindrical tank of sharply-stratified fluid at low Reynolds number. The mathematical model presented in this dissertation model adapts previous work on a settling sphere in sharply-stratified fluid to the significantly more complex case of a rising fluid sphere. A Green's function formulation is used to model the density-driven flow, while the method of reflections and method of multipoles are adapted to correct for the increased drag on the drop due to the cylindrical boundary. The numerical implementation of this model is also based upon previous work for a solid sphere, but requires attention to a number of numerical considerations not present in the solid sphere case. Finally, an experimental study is used to validate the final model within its regime of validity. Additional experimental observations of surfactant effects are detailed as well. Fluid mechanics Droplets; Fluid Dynamics; Green's function; Sharp stratification; Stokes Flow; Stratified fluid Doctor of Philosophy Dissertation University of North Carolina at Chapel Hill Graduate School Degree granting institution Mathematics Roberto Camassa Thesis advisor Richard McLaughlin Thesis advisor Gregory Forest Thesis advisor Laura Miller Thesis advisor David Adalsteinsson Thesis advisor 2018 2018-08 eng text Holly Arrowood Creator Department of Mathematics College of Arts and Sciences Sharp density stratifications occur naturally in the ocean, and play a important role in the dynamics of settling marine snow particles and the dispersion of oil from seeps or spills. When passing through a sharp density transition between two miscible fluid layers, rising immiscible drops slow to well below terminal velocity due to the entrainment of bottom-layer fluid. This dissertation presents an experimentally-validated, numerically-assisted, first-principles model of an oil drop rising in a cylindrical tank of sharply-stratified fluid at low Reynolds number. The mathematical model presented in this dissertation model adapts previous work on a settling sphere in sharply-stratified fluid to the significantly more complex case of a rising fluid sphere. A Green's function formulation is used to model the density-driven flow, while the method of reflections and method of multipoles are adapted to correct for the increased drag on the drop due to the cylindrical boundary. The numerical implementation of this model is also based upon previous work for a solid sphere, but requires attention to a number of numerical considerations not present in the solid sphere case. Finally, an experimental study is used to validate the final model within its regime of validity. Additional experimental observations of surfactant effects are detailed as well. Fluid mechanics Droplets; Fluid Dynamics; Green's function; Sharp stratification; Stokes Flow; Stratified fluid Doctor of Philosophy Dissertation University of North Carolina at Chapel Hill Graduate School Degree granting institution Roberto Camassa Thesis advisor Richard McLaughlin Thesis advisor Gregory Forest Thesis advisor Laura Miller Thesis advisor David Adalsteinsson Thesis advisor 2018 2018-08 eng text Arrowood_unc_0153D_18117.pdf uuid:7cdad50b-fa40-4a41-9be1-18deb5357986 2020-08-23T00:00:00 2018-07-23T13:35:36Z proquest application/pdf 5422409