This dissertation investigates the hemodynamic forces on biological cells adherent on vascular vessels as well as the interfacial dynamics of droplet motion in microfluidic channels. In addition, we develop a novel three-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow.

In physiological systems, the hemodynamic forces exerted on endothelial cells in vascular vessels affect the behavior of the cells via mechano-transduction. The hemodynamic forces also play a pivotal role in the adhesion of leukocytes onto the surface of blood vessels. This study investigates the relative importance and the nature of the two components of the hemodynamic force, i.e., the shear and normal force, on the cell and its vicinity. Based on computational investigation and scaling analysis, the study demonstrates that the normal force contributes significantly to the total hemodynamic force on the cell. This study points out the importance of the normal force exerted on biological cells attached to blood vessels which has been overlooked. This research may motivate experiments to identify the effects of the normal force on the functions of biological cells adhered in blood vessels. The results of the study are also applicable to the fluid forces over protuberances in microfluidic devices and porous media.

For the efficient study of droplet dynamics, we have developed a novel three-dimensional high-order/high-accuracy spectral boundary element algorithm for interfacial dynamics in Stokes flow. This methodology has been employed to several interfacial problems and the results are in excellent agreement with experimental findings, analytical predictions and previous numerical computations. We also investigate the droplet motion in confined geometries which is primarily motivated by the recent development of microfluidic devices and has applications in the enhanced oil recovery, lubrication and coating processes. We consider the buoyancy-driven droplet motion along a solid wall and the pressure-driven droplet motion in a micro-channel. The influence of capillary number, Bond number and viscosity ratio on the droplet motion and deformation is investigated.