In the present thesis, we investigate the interfacial dynamics of a three-dimensional droplet in a viscous fluid flowing through a square microfluidic channel with a rectangular cross-sectional constriction. The effects of various parameters of the two fluids and the sizes of the constriction geometry are considered. The numerical computation for the current problem requires a highly-accurate and efficient method owing to the very small/large deformation of the droplet shape at low/high flow rates, the small droplet-solid gap and the complicated three-dimensional geometries. An efficient fully-implicit three-dimensional Spectral Boundary Element method developed by Dimitrakopoulos is employed.

Our results show that the droplet dynamics is significantly influenced by the non-symmetric shape of the rectangular cross-sectional constriction, i.e. owing to the constriction shape the droplet deforms much less in the flow-direction by forming a flat disk shape. As the capillary number is decreased, the droplet deformation in the flow-direction decreases owing to the larger surface tension. The effects of the viscosity ratio are complicated with viscosity ratio near unity showing the largest deformation.