Algorithms for Simulating Flows of Complex Fluids: Fluid-Solid Mixtures and Liquid Crystals

该项目考虑了微观结构特性影响宏观流动的模拟流体系统的算法的构建和分析。液晶是这类流体中的一个重要类别，在这种情况下，反映分子几何形状的微观结构特性通常被纳入连续介质模型。另一个例子是含有粘弹性颗粒的流。如果流体流过的通道与颗粒的尺寸相当，则有必要明确计算颗粒的运动，以确定它们所经受的应力。如果颗粒很小，许多连续介质模型必须考虑其弹性，这里提出的研究是由与工程师的合作推动的，他们希望确定机械心脏辅助装置内小间隙中受损红细胞的分布和损伤。 这个具体项目考虑开发和分析用于模拟流体系统的计算机算法，其中微观结构特性影响物理流动。微观结构特性可能是由于弹性颗粒（如红细胞）或分子结构（如长聚合物链）的存在。如果流体流过的通道与颗粒或分子的尺寸相当，则有必要明确计算它们的运动，以确定它们所经历的应力。 如果粒子很小，那么许多连续介质模型必须考虑它们的弹性。

This project considers the construction and analysis of algorithms for the simulating fluid systems where microstructural properties influence the macroscopic flow. Liquid crystals are an important class of such fluids, and in this instance the microstructural properties reflecting the geometry of the molecules are usually incorporated into a continuum model. Another example is flows containing visco-elastic particles. If the passages through which the fluid flows are of comparable dimension to the particles, it is necessary to explicitly compute the motion of the particles in order to determine the stresses they experience. If the particles are small and numerous continuum models must account for their elasticity.The research proposed here was motivated by collaborative work with engineers who wish to determine the distribution of and damage to damage red blood cells in the small clearances within mechanical heart assist devices. This specific project considers the development and analysis of computer algorithms for the simulating fluid systems where microstructural properties influence the physical flow. The microstructural properties may be due the presence of elastic particles, (such as red blood cells) or molecular structure (such as long polymer chains). If the passages through which the fluid flows are of comparable dimension to the particles or molecules, it is necessary to explicitly compute their motion in order to determine the stresses they experience. If the particles are small and numerous continuum models must account for their elasticity.