This volume presents the findings of a workshop held at the Institute for Mathematics and its Applications. It brings together ideas of mathematicians and researchers in the physical sciences in the areas of particulate flow and rheology. Flow of particles in a fluid occurs in food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. In many of these processes, the rheology of such materials as they undergo transport and processing is important in design, operation, and efficiency. Consequently, using these materials represents a technological challenge. In spite of the phenomenal advances in computation and computers, simulation of the motion of more than a few particles in a fluid is impractical. Therefore, effective media models and two-fluid models are important in the description of particle-fluid flows. The volume offers chapters addressing issues of ensemble averaging, microstructure behavior, and the analysis of two-continuua models. The span of practical to theoretical approaches to particulate flow makes this volume appeal to researchers interested in deriving or applying particulate flow models. The IMA and the symposium organizers hope that this volume will contribute to increasing dialogue between mathematicians and physical scientists interested in particulate flow.