Thin film flows in curved tubes - Chutsagulprom, N (2010)
The main motivation of this thesis comes from a desire to understand the behaviours of blood flow in the vicinity of atheroma. The initiation and development of atherosclerosis in arteries are normally observed in the areas of low or oscillating wall shear stress, such as on the outer wall of a bifurcation and the inside of the bends. We start by building on the background to the areas related to our models. We focus on the models of fluid flow travelling through a curved tube of uniform curvature because most arteries are tapered and curved. The flow of an incompressible Newtonian fluid in a curved tube is modelled. The derivation of the corresponding equations of the motion is presented. The equations are then solved for a steady and oscillatory driving axial pressure gradient. In each case, the flow is governed by different dimensionless parameters. The problem is solved for a variety of parameter regimes by using asymptotic technique as well as numerical method. Some aspects of thin-film flows are studied. The well-known thin film equation is derived using lubrication theory. The stability of a thin film in a straight tube and the effects of a surfactant droplet on a liquid film are presented. The moving contact line problem, one of the controversial topics in fluid dynamics, is also discussed. The leading-order equations governing thin-film flow over a stationary curved substrate is derived. Various approaches and the application of flow on particular substrates are shown. Finally, we model two-layer viscous fluids using lubrication approximation. By assuming the thickness of a lower liquid layer is much thinner than that of the upper liquid layer, the equation governing the liquid-liquid interface is derived. The steady-state and trasient solutions of the evolution equation is computed both analytically and computationally.