Capsule flow dynamics in microchannels plays a significant role in complex biological phenomena, such as the microcirculation, and in engineering applications, such as in microfluidic devices for drug delivery and cell sorting. In this thesis, we investigate the motion of elastic capsules in wall-bounded flows by extending the Membrane Spectral Boundary Element method developed by Dodson and Dimitrakopoulos for free-suspended flows.

First, a validation study of the method is performed for the axisymmetric capsule motion in a cylindrical channel. For a capsule moving along the centerline of a cylindrical channel, our computational model successfully reproduced the parachute shape observed in earlier experimental and computational studies. Next, we investigate the flow dynamics of a strain-hardening Skalak capsule moving along the centerline in a square and a rectangular channel. We examine how the capillary number and capsule size influence the deformation and physical properties of the capsule. For large capsules in a square channel, our investigation reveals that the steady-state capsule shape is non-axisymmetric. The capsule assumes a shape similar to the channel's cross-section i.e. a square shape with rounded edges. Buckling of the capsule's upstream end resulting in a negative edge curvature is observed at higher capillary numbers and for large capsule sizes. For the largest capsules studied, we also observe the development of dimples at the capsule's lateral surface. A comparative study of capsule motion and deformation in cylindrical and square channels shows that the capsule deformation in a cylindrical channel is similar to that in a square channel at a larger capillary number. In a rectangular channel, we observe a three-dimensional (i.e. non-axisymmetric) deformation of the capsule at high capillary numbers resulting in dimpling of the capsule's upstream end at steady state. We also consider the transient motion of a capsule in a converging square microchannel and investigate the influence of viscosity ratio, capillary number and capsule size on the evolution of capsule properties. As the capsule moves through the converging region a fluctuation in the geometric and physical properties of the capsule is observed.