Collaborative Research: Smoluchowski Equations: Analysis of Dynamics, Singularities and Statistics in Complex Fluid-Particle Mixtures

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In this collaborative project, the investigators study theinteraction between fluids and particle distributions. Theyexamine the nonlinear Smoluchowski equations with both passive andactive interaction with an ambient fluid. The specific goals are:a study of the transition to nematic states in the highconcentration limit, effects of shear, complex dynamics and modesof coupling. Particular attention is given to the activeinteractions with fluids, singularity formation, the stabilizationof high concentration suspensions, and the dissipation effects dueto the insertions. Many biological and artificial materials are involved inprocesses in which melts or fluid flows carry inserted particles. The orientation of the particles and their overall distributioninfluence the physical and chemical properties of the mixture. The investigators carry out a mathematical study of models of suchmixtures. The goals are to describe qualitatively the patternsformed by the particles, which of these patterns are stable, whatare the conditions for the creation of discontinuities in thepatterns, and what are the energetics and bulk physical propertiesassociated with them. Better understanding of the effects ofsmall-scale nonequilibrium dynamics on large-scale transport incomplex particle-fuid systems, such as the viscous polymersuspensions considered here, is important in chemistry, biology,and engineering.