Theory of Dispersed Multiphase Flow (eBook)

Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center The University of Wisconsin-Madison May 26-28, 1982

Richard E. Meyer (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
398 Seiten
Elsevier Science (Verlag)
978-1-4832-6469-1 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Theory of Dispersed Multiphase Flow 4
Copyright Page 5
Table of Contents 6
Senior Contributors 8
Preface 10
Chapter 1. Effects of Interactions between Particles on the Rheology of Dispersions 12
1. INTRODUCTION 12
2. QUALITATIVE INTERPRETATIONS 13
3. PAIR INTERACTION THEORIES 19
4. THE TRANSITION FROM DILUTE TO CONCENTRATED 32
5. ELECTRQSTATICALLY CONCENTRATED SUSPENSIONS 36
REFERENCES 41
ACKNOWLEDGEMENTS 43
NOMENCLATURE 43
Chapter 2. Rheology of Concentrated Macromolecular Solutions 46
1. INTRODUCTION 46
2. GENERAL THEORY FOR POLYMER SOLUTIONS AND SUSPENSIONS 47
3. RODLIKE POLYMERS IN DILUTE SOLUTIONS 55
4. RODLIKE POLYMERS IN CONCENTRATED SOLUTION 58
REFERENCES 65
Chapter 3. A Survey of Some Results in the Mathematical Theory of Fluidization 68
INTRODUCTION 68
BASIC EQUATIONS 69
STEADY SOLUTIONS 71
SCALING 72
LINEAR INSTABILITY THEORY 72
WEAK NON-LINEAR WAVES 76
VORTEX INSTABILITIES 76
STEADY TRAVELLING WAVE SOLUTIONS 79
RAYLEIGH-TAYLOR INSTABILITIES 80
CONCLUSIONS 81
REFERENCES 81
Chapter 4. Instability in Settling of Suspensions Due to Brownian Effects 84
REFERENCES 90
Chapter 5. Enhanced Sedimentation in Vessels Having Inclined Walls. The Boycott Effect 92
1. INTRODUCTION. 92
2. THEORY AND EXPERIMENTS FOR LAMINAR FLOW. 95
3. THEORY AND EXPERIMENTS FOR UNSTABLE FLOW 99
4. SUMMARY 103
REFERENCES 105
Chapter 5. Simple Kinetic Theory of Brownian Diffusion in Vapors and Aerosols 108
1. INTRODUCTION. 108
2. DROPLET/PARTICLE GROWTH BY CONDENSATION/EVAPORATION. 110
3. SIMPLE KINETIC THEORY OF VAPOR DIFFUSION. 112
4. THE KINETIC BOUNDARY CONDITION FOR VAPOR CONDENSATION. 114
5. APPLICATION: DIFFUSIONAL TRANSPORT TO A SPHERE. 115
6. BROWNIAN DIFFUSION OF FLUID-BORNE PARTICLES. 117
7. THE KINETIC BOUNDARY CONDITION FOR PARTICLE DEPOSITION. 122
8. COAGULATION. 125
9. AEROSOL DEPOSITION IN A FINE CAPILLARY. 130
REFERENCES 143
Chapter 6. Simulation of Aerosol Dynamics 146
1. Introduction. 146
2. Aerosol Formation and Growth in Uniform Systems. 148
3. Aerosol Formation and Growth in Non-Uniform Systems. 169
4. Summary 179
REFERENCES 180
Chapter 7. Continuum Modeling of Two-Phase Flows 184
Introduction 184
Averaging 186
Averaged Equations 189
Kinematic Waves 195
Diffusional Regularization 197
Conclusion 200
REFERENCES 201
Chapter 8. A Multiphase Mixture Theory for Fluid-Particle Flows 202
1. INTRODUCTION 202
2. KINEMATICS AND THE EQUATIONS OF MOTION 205
3. THE ENTROPY INEQUALITY 208
4. CONSTITUTIVE EQUATIONS FOR FLUID-PARTICLE FLOWS 212
5. ISOTHERMAL FLOWS OF DILUTE SUSPENSIONS 216
6. APPLICATION TO TRANSLATIONAL BROWNIAN MOTION 219
7 . POISEUILLE FLOW OF DILUTE SUSPENSIONS 221
8. RHEOLOGICAL PROPERTIES OF DILUTE SUSPENSIONS 229
9. CONCLUSION 232
REFERENCES 234
Acknowledgement 237
Chapter 9. Mixture Theory for Turbulent Diffusion of Heavy Particles 238
Theory 240
Decomposition and averaging 242
Plane gravity flow 243
Modeling the correlation CU 249
Comparison to experiment 251
Summary 259
REFERENCES 260
Chapter 10. Waves in Gas-Liquid Flows 262
§1. Introduction 262
§2. Pressure waves in two-phase flow 263
3. Separated flows with relative velocity 270
§4. Fluctuations 274
REFERENCES 278
Chapter 11. Frazil Ice 282
BACKGROUND AND INTRODUCTION 282
GENERAL DESCRIPTION 283
FRAZIL ICE AS A TWO-PHASE FLOW 284
SUPERCOOLING 285
INITIAL NUCLEATION 287
FRAZIL CRYSTALS 288
PARTICLE MECHANICS 289
CLUSTERING AND FLOCCULATION 290
ACTIVE AND PASSIVE FRAZIL 291
ENTRAINMENT OF FRAZIL AT A SURFACE BARRIER 293
DEPOSITION AND EROSION OF FRAZIL 295
INSTRUMENTATION 297
SUMMARY 298
REFERENCES 298
ACKNOWLEDGMENT 300
Chapter 12. Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials 302
INTRODUCTORY IDEAS 302
CONSTITUTIVE RELATIONS 309
EQUATIONS OF MOTION AND THE CRITICAL STATE APPROXIMATION 320
PHYSICAL FEATURES AND MATHEMATICAL FORMULATION OF THE WEDGE-SHAPED HOPPER PROBLEM 325
STRUCTURE OF THE SOLUTION OF THE HOPPER PROBLEM 328
SOLUTION OF THE EQUATIONS FOR HOPPER FLOW 331
A RE-EXAMINATION OF THE EXIT BOUNDARY CONDITION 340
CONCLUSION 344
REFERENCES 345
Chapter 13. Granular Flows at High Shear Rates 350
1. INTRODUCTION 350
2. EXPERIMENTAL MEASUREMENTS OF STRESSES 351
3. DENSE GAS TYPE THEORY FOR INELASTIC GRANULES 357
4. APPLICATION OF THE THEORY TO SOME SIMPLE FLOWS 361
5. CONCLUSION 367
REFERENCES 368
Chapter 14. Theory and Experiments in the Mechanics of Magnetically Stabilized Fluidized Solids 370
1. INTRODUCTION 370
2. EQUATIONS OF MOTION 372
2. STABILITY OF THE UNBOUNDED BED 373
3. THE SEMI-INFINITE BED 377
4. PARADOXICAL RESULTS OF FINITE LENGTH BEDS 380
5. THE STRESS BOUNDARY CONDITION 383
6. NON-UNIFORM VOIDAGE DISTRIBUTION IN FINITE LENGTH BEDS 385
7. YIELD STRESS DISTRIBUTION: ANOTHER PARADOX RESOLVED 390
8. CONCLUSION 393
REFERENCES 393
Index 396

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik ► Bauwesen
• ISBN-10: 1-4832-6469-6 / 1483264696
• ISBN-13: 978-1-4832-6469-1 / 9781483264691