In this collaborative project, the investigators study the interaction between fluids and particle distributions. They examine the nonlinear Smoluchowski equations with both passive and active interaction with an ambient fluid. The specific goals are: a study of the transition to nematic states in the high concentration limit, effects of shear, complex dynamics and modes of coupling. Particular attention is given to the active interactions with fluids, singularity formation, the stabilization of high concentration suspensions, and the dissipation effects due to the insertions.
Many biological and artificial materials are involved in processes in which melts or fluid flows carry inserted particles. The orientation of the particles and their overall distribution influence the physical and chemical properties of the mixture. The investigators carry out a mathematical study of models of such mixtures. The goals are to describe qualitatively the patterns formed by the particles, which of these patterns are stable, what are the conditions for the creation of discontinuities in the patterns, and what are the energetics and bulk physical properties associated with them. Better understanding of the effects of small-scale nonequilibrium dynamics on large-scale transport in complex particle-fuid systems, such as the viscous polymer suspensions considered here, is important in chemistry, biology, and engineering.
