Meyer Theory of Dispersed Multiphase Flow

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center The University of Wisconsin-Madison May 26-28, 1982
1. Auflage 2014
ISBN: 978-1-4832-6469-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 398 Seiten, Web PDF

Mathematics Research Center Symposium: Theory of Dispersed Multiphase Flow covers the proceedings of an advanced seminar conducted by the Mathematics Research Center of the University of Wisconsin-Madison on May 26-28, 1982. The book focuses on solutions of long chain polymers in liquids, magnetic control of particle suspensions in fluid streams, aerosols, dense granular flows, and ice crystals or vapor bubbles dispersed in river waters. The selection first elaborates on the effects of interactions between particles on the rheology of dispersions; rheology of concentrated macromolecular solutions; and a survey of results in the mathematical theory of fluidization. Discussions focus on Rayleigh-Taylor instabilities, linear instability theory, steady solutions, general theory for polymer solutions and suspensions, electrostatically concentrated suspensions, and pair interaction theories. The text then examines instability in settling of suspensions due to Brownian effects; enhanced sedimentation in vessels having inclined walls; and simple kinetic theory of Brownian diffusion in vapors and aerosols. The text takes a look at the simulation of aerosol dynamics, continuum modeling of two-phase flows, multiphase mixture theory for fluid-particle flows, and mixture theory for turbulent diffusion of heavy particles. Topics include plane gravity flow, decomposition and averaging, isothermal flows of dilute suspensions, kinematics and the equations of motion, diffusional regularization, kinematic waves, and aerosol formation and growth in uniform systems. The selection is a valuable source of data for researchers interested in the theory of dispersed multiphase flow.

Autoren/Hrsg.

Meyer, Richard E.

Inhaltsverzeichnis

1;Front Cover;1
2;Theory of Dispersed Multiphase Flow;4
3;Copyright Page;5
4;Table of Contents;6
5;Senior Contributors;8
6;Preface;10
7;Chapter 1. Effects of Interactions between Particles on the Rheology of Dispersions;12
7.1;1. INTRODUCTION;12
7.2;2. QUALITATIVE INTERPRETATIONS;13
7.3;3. PAIR INTERACTION THEORIES;19
7.4;4. THE TRANSITION FROM DILUTE TO CONCENTRATED;32
7.5;5. ELECTRQSTATICALLY CONCENTRATED SUSPENSIONS;36
7.6;REFERENCES;41
7.7;ACKNOWLEDGEMENTS;43
7.8;NOMENCLATURE;43
8;Chapter 2. Rheology of Concentrated Macromolecular Solutions;46
8.1;1. INTRODUCTION;46
8.2;2. GENERAL THEORY FOR POLYMER SOLUTIONS AND SUSPENSIONS;47
8.3;3. RODLIKE POLYMERS IN DILUTE SOLUTIONS;55
8.4;4. RODLIKE POLYMERS IN CONCENTRATED SOLUTION;58
8.5;REFERENCES;65
9;Chapter 3. A Survey of Some Results in the Mathematical Theory of Fluidization;68
9.1;INTRODUCTION;68
9.2;BASIC EQUATIONS;69
9.3;STEADY SOLUTIONS;71
9.4;SCALING;72
9.5;LINEAR INSTABILITY THEORY;72
9.6;WEAK NON-LINEAR WAVES;76
9.7;VORTEX INSTABILITIES;76
9.8;STEADY TRAVELLING WAVE SOLUTIONS;79
9.9;RAYLEIGH-TAYLOR INSTABILITIES;80
9.10;CONCLUSIONS;81
9.11;REFERENCES;81
10;Chapter 4. Instability in Settling of Suspensions Due to Brownian Effects;84
10.1;REFERENCES;90
11;Chapter 5. Enhanced Sedimentation in Vessels Having Inclined Walls. The Boycott Effect;92
11.1;1. INTRODUCTION.;92
11.2;2. THEORY AND EXPERIMENTS FOR LAMINAR FLOW.;95
11.3;3. THEORY AND EXPERIMENTS FOR UNSTABLE FLOW;99
11.4;4. SUMMARY;103
11.5;REFERENCES;105
12;Chapter 5. Simple Kinetic Theory of Brownian Diffusion in Vapors and Aerosols;108
12.1;1. INTRODUCTION.;108
12.2;2. DROPLET/PARTICLE GROWTH BY CONDENSATION/EVAPORATION.;110
12.3;3. SIMPLE KINETIC THEORY OF VAPOR DIFFUSION.;112
12.4;4. THE KINETIC BOUNDARY CONDITION FOR VAPOR CONDENSATION.;114
12.5;5. APPLICATION: DIFFUSIONAL TRANSPORT TO A SPHERE.;115
12.6;6. BROWNIAN DIFFUSION OF FLUID-BORNE PARTICLES.;117
12.7;7. THE KINETIC BOUNDARY CONDITION FOR PARTICLE DEPOSITION.;122
12.8;8. COAGULATION.;125
12.9;9. AEROSOL DEPOSITION IN A FINE CAPILLARY.;130
12.10;REFERENCES;143
13;Chapter 6. Simulation of Aerosol Dynamics;146
13.1;1. Introduction.;146
13.2;2. Aerosol Formation and Growth in Uniform Systems.;148
13.3;3. Aerosol Formation and Growth in Non-Uniform Systems.;169
13.4;4. Summary;179
13.5;REFERENCES;180
14;Chapter 7. Continuum Modeling of Two-Phase Flows;184
14.1;Introduction;184
14.2;Averaging;186
14.3;Averaged Equations;189
14.4;Kinematic Waves;195
14.5;Diffusional Regularization;197
14.6;Conclusion;200
14.7;REFERENCES;201
15;Chapter 8. A Multiphase Mixture Theory for Fluid-Particle Flows;202
15.1;1. INTRODUCTION;202
15.2;2. KINEMATICS AND THE EQUATIONS OF MOTION;205
15.3;3. THE ENTROPY INEQUALITY;208
15.4;4. CONSTITUTIVE EQUATIONS FOR FLUID-PARTICLE FLOWS;212
15.5;5. ISOTHERMAL FLOWS OF DILUTE SUSPENSIONS;216
15.6;6. APPLICATION TO TRANSLATIONAL BROWNIAN MOTION;219
15.7;7 . POISEUILLE FLOW OF DILUTE SUSPENSIONS;221
15.8;8. RHEOLOGICAL PROPERTIES OF DILUTE SUSPENSIONS;229
15.9;9. CONCLUSION;232
15.10;REFERENCES;234
15.11;Acknowledgement;237
16;Chapter 9. Mixture Theory for Turbulent Diffusion of Heavy Particles;238
16.1;Theory;240
16.2;Decomposition and averaging;242
16.3;Plane gravity flow;243
16.4;Modeling the correlation CU;249
16.5;Comparison to experiment;251
16.6;Summary;259
16.7;REFERENCES;260
17;Chapter 10. Waves in Gas-Liquid Flows;262
17.1;§1. Introduction;262
17.2;§2. Pressure waves in two-phase flow;263
17.3;3. Separated flows with relative velocity;270
17.4;§4. Fluctuations;274
17.5;REFERENCES;278
18;Chapter 11. Frazil Ice;282
18.1;BACKGROUND AND INTRODUCTION;282
18.2;GENERAL DESCRIPTION;283
18.3;FRAZIL ICE AS A TWO-PHASE FLOW;284
18.4;SUPERCOOLING;285
18.5;INITIAL NUCLEATION;287
18.6;FRAZIL CRYSTALS;288
18.7;PARTICLE MECHANICS;289
18.8;CLUSTERING AND FLOCCULATION;290
18.9;ACTIVE AND PASSIVE FRAZIL;291
18.10;ENTRAINMENT OF FRAZIL AT A SURFACE BARRIER;293
18.11;DEPOSITION AND EROSION OF FRAZIL;295
18.12;INSTRUMENTATION;297
18.13;SUMMARY;298
18.14;REFERENCES;298
18.15;ACKNOWLEDGMENT;300
19;Chapter 12. Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials;302
19.1;INTRODUCTORY IDEAS;302
19.2;CONSTITUTIVE RELATIONS;309
19.3;EQUATIONS OF MOTION AND THE CRITICAL STATE APPROXIMATION;320
19.4;PHYSICAL FEATURES AND MATHEMATICAL FORMULATION OF THE WEDGE-SHAPED HOPPER PROBLEM;325
19.5;STRUCTURE OF THE SOLUTION OF THE HOPPER PROBLEM;328
19.6;SOLUTION OF THE EQUATIONS FOR HOPPER FLOW;331
19.7;A RE-EXAMINATION OF THE EXIT BOUNDARY CONDITION;340
19.8;CONCLUSION;344
19.9;REFERENCES;345
20;Chapter 13. Granular Flows at High Shear Rates;350
20.1;1. INTRODUCTION;350
20.2;2. EXPERIMENTAL MEASUREMENTS OF STRESSES;351
20.3;3. DENSE GAS TYPE THEORY FOR INELASTIC GRANULES;357
20.4;4. APPLICATION OF THE THEORY TO SOME SIMPLE FLOWS;361
20.5;5. CONCLUSION;367
20.6;REFERENCES;368
21;Chapter 14. Theory and Experiments in the Mechanics of Magnetically Stabilized Fluidized Solids;370
21.1;1. INTRODUCTION;370
21.2;2. EQUATIONS OF MOTION;372
21.3;2. STABILITY OF THE UNBOUNDED BED;373
21.4;3. THE SEMI-INFINITE BED;377
21.5;4. PARADOXICAL RESULTS OF FINITE LENGTH BEDS;380
21.6;5. THE STRESS BOUNDARY CONDITION;383
21.7;6. NON-UNIFORM VOIDAGE DISTRIBUTION IN FINITE LENGTH BEDS;385
21.8;7. YIELD STRESS DISTRIBUTION: ANOTHER PARADOX RESOLVED;390
21.9;8. CONCLUSION;393
21.10;REFERENCES;393
22;Index;396