Fluid-gas and fluid-structure interactions in complex fluids

点击翻译按钮获取中文摘要

Non-Newtonian fluids are ubiquitous in the pharmaceutical, polymer processing and food industries and in medicine. Examples are paints, molten plastics, detergents, ketchup, toothpaste, yoghurt, blood and synovial fluid. Many rich and fascinating flow phenomena may be observed in such fluids and the present Discovery Grant proposal is concerned with how flowing non-Newtonian fluids behave when they have an interface either with a gas or an immersed solid. Three problems, in particular, have been identified at the present time as having particular importance in medicine and industry. The first is the behaviour of bubbles rising in a non-Newtonian fluid. Bubbles are important in the water treatment process and design of reactors and in different fields such as polymer sciences, composites, boiling, plastic foam processing and bubble absorption. When a single bubble rises in a non-Newtonian fluid it has been observed that there may be, under certain circumstances, a sudden increase in the bubble's terminal rise velocity as a function of its volume. We wish to investigate this further with a carefully constructed mathematical model and numerical method. The second is the problem of determining the shape of a polymer jet as it is extruded from a die slit. Extrusion flows of thermoplastics are common in the manufacture of items such as wire coatings, plastic films and sheeting, and piping and tubing. When the polymer leaves the die there is usually a significant increase in the cross-sectional area of the fluid jet compared to that of the die exit. Beyond some critical value of the volume flow rate, in addition to swelling, surface disturbances may also appear on the extruded polymer, having a disastrous effect on the final product quality. We need to be able to calculate both the extrudate shape and the critical volume flow rate in order to be able to keep operating conditions in the stable zone. In this Discovery Grant application we propose a new application of a mesh-free numerical method to solve this problem. The third problem is to determine the conditions under which a blood clot (thrombus) can detach from the vessel wall of a small artery and be transported through the microvasculature even as far as the brain. According to Statistics Canada stroke has been the third leading cause of death in Canada in each of 2000, 2010 and 2011. Ischemic stroke, accounting for some 85% of all strokes, occurs when blood supply to the brain is cut off or, at least, reduced significantly. This may be caused by a clot breaking away from a vessel wall and becoming lodged in a smaller brain artery (embolic stroke). In our Discovery Grant proposal we model blood in the artery as a non-Newtonian fluid and describe a way of modelling the thrombus as a network of fibres. Using our model we will also determine the conditions under which the thrombus may detach from a vessel wall, an event that would lead to an increased risk of embolic stroke.