Ebook: Particulate Flows: Processing and Rheology

This IMA Volume in Mathematics and its Applications PARTICULATE FLOWS: PROCESSING AND RHEOLOGY is based on the proceedings of a very successful one-week workshop with the same title, which was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Donald A. Drew, Daniel D. Joseph, and Stephen L. Passman for their excellent work as organizers of the meeting. We also take this opportunity to thank the National Science Foun­ dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Particulate Flows: Processing and Rheology was held January 8-12, 1996 at the Institute for Mathematics and its Applications on the University of Minnesota Twin Cities campus as part of the 1995- 96 Program on Mathematical Methods in Materials Science. There were about forty participants, and some lively discussions, in spite of the fact that bad weather on the east coast kept some participants from attending, and caused scheduling changes throughout the workshop. Heterogeneous materials can behave strangely, even in simple flow sit­ uations. For example, a mixture of solid particles in a liquid can exhibit behavior that seems solid-like or fluid-like, and attempting to measure the "viscosity" of such a mixture leads to contradictions and "unrepeatable" experiments. Even so, such materials are commonly used in manufacturing and processing.

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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.

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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.
Content:
Front Matter....Pages i-ix
Compressible Flow of Granular Materials....Pages 1-22
Effective Media Theory Using Nearest Neighbor Pair Distributions....Pages 23-53
Bifurcation with Symmetry in Multi-Phase Flows....Pages 55-66
Three Dimensional Viscoelasticity in Finite Strain: Formulation of a Rate-Type Constitutive Law Consistent with Dissipation....Pages 67-87
Drag in a Porous Medium: An Example of the Use of Ensemble Averaged Hydrodynamic Potentials....Pages 89-97
Ensemble Averaging Techniques for Disperse Flows....Pages 99-136
Bubbly Flows with Gravity and Viscosity....Pages 137-142
Back Matter....Pages 143-149

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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.
Content:
Front Matter....Pages i-ix
Compressible Flow of Granular Materials....Pages 1-22
Effective Media Theory Using Nearest Neighbor Pair Distributions....Pages 23-53
Bifurcation with Symmetry in Multi-Phase Flows....Pages 55-66
Three Dimensional Viscoelasticity in Finite Strain: Formulation of a Rate-Type Constitutive Law Consistent with Dissipation....Pages 67-87
Drag in a Porous Medium: An Example of the Use of Ensemble Averaged Hydrodynamic Potentials....Pages 89-97
Ensemble Averaging Techniques for Disperse Flows....Pages 99-136
Bubbly Flows with Gravity and Viscosity....Pages 137-142
Back Matter....Pages 143-149
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