On Elastic Complex Fluids with Complex Microstructure

本项目的目标是研究弹性复杂流体的流变学和流体动力学行为。 我们特别感兴趣的是那些由于流体微观结构的影响。 采用统一的能量变分法，考虑了动能和弹性内能的竞争，探讨了弹性变量的输运与诱导弹性应力之间的特殊耦合。 我们将重点讨论几个问题：1）不同材料混合物中的自由界面运动; 2）液晶流中的奇异运动和构型; 3）其他弹性复杂流体，包括聚合物材料、电动流体和粘弹性材料的多尺度模型。 这个项目将包括偏微分方程理论，变分法，渐近分析和数值技术。 它涵盖了静态和时间依赖的演变问题所产生的不同材料。 我们对这些材料的分子结构、流动模式、相变、缺陷动力学以及力学和流变性能感兴趣。复杂流体包括一大类软材料，如聚合物溶液、液晶溶液、肺表面活性剂溶液、电流变流体、磁流变流体和血液悬浮液。 物理性质由熵和结构分子间弹性力和界面相互作用的相互作用决定。 这些材料表现出许多复杂的流变学和流体动力学特性，这些特性对生物和工业过程非常重要。 应用包括通过表面活性剂注射治疗气道闭合疾病;用于喷墨打印机的聚合物添加剂;燃料注射;灭火器;结构振动的磁流变阻尼;医疗微流体诊断设备;以及血细胞的变形和运输。 在复杂流体的建模和分析中，存在着许多重要的数学问题。 系统的复杂性需要新的数学方法，在许多情况下，需要新的概念。 该项目的研究旨在加强和促进分析和理解具有挑战性的物理问题之间的这一重要联系。

The goal of this project is to study the rheological and hydrodynamic behavior of elastic complex fluids. We are particularly interested in those due to the effects of the fluid microstructures. A unified energetic variational approach, taking into account the competition of the kinetic and the internal elastic energies, is employed to explore the special coupling between the transport of the elastic variables and the induced elastic stresses. We will focus on several problems: 1) free interface motions in the mixtures of different materials; 2) singularity motions and configurations in liquid crystal flows; 3) other elastic complex fluids, including multiscale models of polymeric materials, electro-kinetic fluids and viscoelastic materials. This project will incorporate theories of partial differential equations, calculus of variations, asymptotic analysis, and numerical techniques. It covers both static and time dependent evolution problems arising from different materials. We are interested in molecule configurations; flow patterns; phase transitions; defect dynamics; and the mechanical and rheological properties of these materials.Complex fluids comprise a large class of soft materials, such as polymeric solutions, liquid crystal solutions, pulmonary surfactant solutions, electro-rheological fluids, magneto-rheological fluids and blood suspensions. The physical properties are determined by the interplay of entropic and structural intermolecular elastic forces and interfacial interactions. These materials exhibit many intricate rheological and hydrodynamic features that are very important to biological and industrial processes. Applications include the treatment of airway closure disease by surfactant injection; polymer additives for inkjet printers; fuel injection; fire extinguishers; magneto-rheological damping of structural vibrations; medical micro-fluidic diagnostic devices; and deformation and transport of blood cells. There are many important mathematical problems in the modeling and analysis of complex fluids. The complexity of the systems requires new mathematical methods and in many cases, new concepts. The research of this project is designed to enhance and contribute to this important link between analysis and the understanding of challenging physical problems.