Wang, YechunThe current thesis includes two distinct projects. The first study involves the development of a novel three-dimensional Spectral Boundary Element algorithm for interfacial dynamics in Stokes flow. Our algorithm is the only available high-order/high-accuracy methodology for the problem of droplet deformation in viscous flows. By applying this algorithm to several interfacial problems, we find that our results are in excellent agreement with experimental findings, analytical predictions and previous numerical computations. The second project studies viscous flows over a protuberance on the inner wall of a solid microtube, a problem relevant to both physiological systems and microfluidic devices. The shear stress, drag and torque on the protuberance are determined as functions of the spreading angle and the relative size of the protuberance which may represent leukocytes, blood clots or endothelial cells on the microvessel wall. This study facilitates the understanding of mechano-transduction phenomena as well as cell adhesion in blood flow.en-USThesisEngineering, ChemicalEngineering, Mechanicalspectral boundary element methodinterfacial dynamicsfluid forceprotuberance