Fluid-gas and fluid-structure interactions in complex fluids

非牛顿流体在制药、聚合物加工、食品工业和医学中无处不在。例如油漆、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，目前的发现基金提案涉及流动的非牛顿流体在与气体或浸没的固体有界面时的行为。在医药和工业领域，目前已经确定了三个特别重要的问题。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以及聚合物科学、复合材料、沸腾、塑料泡沫加工和气泡吸收等不同领域都很重要。当一个气泡在非牛顿流体中上升时，已经观察到，在某些情况下，气泡的最终上升速度可能会突然增加，这是气泡体积的函数。我们希望通过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的形状，因为它是从模具狭缝挤出。热塑性塑料的挤出流动在诸如电线涂层，塑料薄膜和薄板以及管道和管材等物品的制造中很常见。当聚合物离开模具时，流体射流的横截面积通常比模具出口的横截面积显著增加。超过体积流量的某个临界值，除了膨胀外，挤出的聚合物还可能出现表面扰动，对最终产品质量产生灾难性的影响。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域。在这个发现基金申请中，我们提出了一种新的无网格数值方法的应用来解决这个问题。***第三个问题是确定在什么条件下血凝块（血栓）可以从小动脉的血管壁上脱离，并通过微血管运输，甚至远至大脑。根据加拿大统计局的数据，在2000年、2010年和2011年，中风一直是加拿大第三大死亡原因。缺血性中风约占所有中风的85%，发生在大脑血液供应被切断或至少显著减少时。这可能是由于血栓从血管壁上脱落并滞留在较小的脑动脉（栓塞性中风）。在我们的发现基金提案中，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，这一事件将导致栓塞性中风的风险增加

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.**