Fluid-gas and fluid-structure interactions in complex fluids

非牛顿流体普遍存在于制药、聚合物加工和食品工业以及医学中。例如涂料、熔融塑料、洗涤剂、番茄酱、牙膏、酸奶、血液和滑液。在这种流体中可以观察到许多丰富而迷人的流动现象，目前的发现补助金提案关注的是流动的非牛顿流体在与气体或浸没固体有界面时的行为。目前，有三个问题被认为在医学和工业中特别重要。 第一个是气泡在非牛顿流体中上升的行为。气泡在水处理过程和反应器设计中以及在不同领域如聚合物科学、复合材料、沸腾、塑料泡沫加工和气泡吸收中是重要的。当单个气泡在非牛顿流体中上升时，已经观察到，在某些情况下，气泡的终端上升速度作为其体积的函数可能突然增加。我们希望通过一个精心构建的数学模型和数值方法来进一步研究这一点。 第二个问题是确定聚合物射流从模口狭缝挤出时的形状的问题。热塑性塑料的挤出流动在诸如电线涂层、塑料薄膜和片材以及管道和管材等物品的制造中是常见的。当聚合物离开模头时，与模头出口的横截面积相比，流体射流的横截面积通常显著增加。超过体积流率的某个临界值，除了溶胀之外，挤出的聚合物上还可能出现表面扰动，对最终产品质量具有灾难性影响。我们需要能够计算挤出物形状和临界体积流量，以便能够将操作条件保持在稳定区。在这个发现补助金申请，我们提出了一个新的应用程序的无网格数值方法来解决这个问题。 第三个问题是确定血凝块（血栓）可以从小动脉的血管壁分离并通过微血管系统甚至远至大脑运输的条件。根据加拿大统计局的数据，中风在2000年、2010年和2011年都是加拿大第三大死亡原因。缺血性中风约占所有中风的85%，当大脑的血液供应被切断或至少显着减少时发生。这可能是由于凝块从血管壁脱落并卡在较小的脑动脉中（栓塞性中风）。在我们的发现资助提案中，我们将动脉中的血液建模为非牛顿流体，并描述了一种将血栓建模为纤维网络的方法。使用我们的模型，我们还将确定血栓可能从血管壁分离的条件，这是一种会导致栓塞性中风风险增加的事件。

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.