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

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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.