Oil Droplets Rising through Density-Stratified Fluid at Low Reynolds Number

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  • March 21, 2019
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  • Arrowood, Holly
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • 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.
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  • In Copyright
Advisor
  • McLaughlin, Richard
  • Adalsteinsson, David
  • Forest, Gregory
  • Miller, Laura
  • Camassa, Roberto
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2018
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