Abstract
The motivation for this research into flow in pipes with non-uniform geometry comes from physiological flows. It is now widely believed that haemodynamics plays an important role in the initiation and development of atherosclerosis. Experiments have shown that the preferred sites for atherogenesis are regions of low wall shear stress. The build-up of atherosclerotic plaques in the coronary arteries can lead to arterial blockage and coronary failure. Previous studies have examined uniformly curved pipes and, more recently, uniformly curved and twisted pipes. However, it is well known that the arterial system displays non-uniform, time-dependent geometry. The main objective of this thesis is to describe flow in various pipes with weakly non-uniform curvature and torsion, with a view to understanding the resulting wall shear stress distribution and velocity profiles. The work herein models the flow of an incompressible Newtonian fluid through a pipe whose curvature and torsion vary along the pipe. The governing equations are first derived, then solved for both steady and oscillatory pressure gradients. The solution of these equations involves asymptotic and numerical techniques. The effects due to the non-uniform geometry and possible applications to physiology are discussed. Finally, the effects of torsion upon fluid motion are studied from the Lagrangian viewpoint, using numerical particle tracking.