Waves on Fluid Interfaces (eBook)

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 18-20, 1982

Richard E. Meyer (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
370 Seiten
Elsevier Science (Verlag)
978-1-4832-6514-8 (ISBN)

Infos

Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.

Inhalt

Front Cover 1
Waves on Fluid Interfaces 4
Copyright Page 5
Table of Contents 6
SENIOR CONTRIBUTORS 8
PREFACE 10
CHAPTER 1. FINITE-AMPLITUDE INTERFACIAL WAVES 12
1. INTRODUCTION 12
2. WEAKLY NONLINEAR WAVES 15
3. NUMERICAL METHODS 17
4. A SPECIAL CLASS OF SOLUTIONS 19
5. RESULTS 20
REFERENCES 25
CHAPTER 2. INSTABILITY OF FINITE-AMPLITUDE INTERFACIAL WAVES 28
1. INTRODUCTION 28
2. GOVERNING EQUATIONS 29
3. THE WAVE OF ZERO HEIGHT 32
4. WATER WAVES: A SPECIAL CASE 33
5. RESULTS FOR INTERFACIAL WAVES WITH CURRENT JUMP 34
6. DISCUSSION 50
REFERENCES 51
CHAPTER 3. FINITE-AMPLITUDE WATER WAVES WITH SURFACE TENSION 52
1. INTRODUCTION 52
2. FORMULATION 52
3. PERTURBATION SOLUTIONS 53
4. REFORMULATION AS AN INTEGRO-DIFFERENTIAL EQUATION 55
5. NUMERICAL PROCEDURE 58
6. DISCUSSION OF THE RESULTS 60
REFERENCES 62
CHAPTER 4. GENERALIZED VORTEX METHODS FOR FREE-SURFACE FLOWS 64
1. INTRODUCTION 64
2. BOUNDARY INTEGRAL TECHNIQUES 66
3. GENERALISED VORTEX METHOD 72
4. ACCELERATING FLUID LAYERS 82
REFERENCES 91
CHAPTER 5. A REVIEW OF SOLUTION METHODS FOR VISCOUS FLOW IN THE PRESENCE OF DEFORMABLE BOUNDARIES 94
A. INTRODUCTION 94
B. THE BASIC PROBLEM 95
C. SOLUTION METHODS FOR VANISHINGLY SMALL REYNOLDS NUMBERS 98
D. SOLUTION METHODS FOR FINITE REYNOLDS NUMBER 108
REFERENCES 119
CHAPTER 6. ON EXISTENCE CRITERIA FOR FLUID INTERFACES IN THE ABSENCE OF GRAVITY 124
1. INTRODUCTION 124
2. SPECIAIJZED DOMAINS–NECESSARY CONDITIONS 126
3. SUFFICIENT CONDITIONS FOR EXISTENCE–MORE GENERAL DOMAINS 128
4. SUBSIDIARY VARIATIONAL PROBLEM 132
5. CONTINUOUS AND DISCONTINUOUS DISAPPEARANCE OF CAPILLARY SURFACES 132
REFERENCES 133
CHAPTER 7. CAPILLARY WAVES AND INTERFACIAL STRUCTURE 134
1. INTRODUCTION 134
2. GRADIENT THEORY OF INHOMOGENEOUS FLUID 135
3. EQUILIBRIUM DENSITY PROFILE AND TENSION OF A PLANAR INTERFACE 136
4. STABILITY OF FLUID AT EQUILIBRIUM 140
5. THERMAL FLUCTUATIONS IN HOMOGENEOUS FLUID 141
6. FLUCTUATIONS OF A PLANAR INTERFACE: CAPILLARY WAVES 145
7. RIGOROUS DENSITY FUNCTIONAL FREE ENERGY THEORY 153
REFERENCES 159
CHAPTER 8. INTERFACIAL AND CRITICAL PHENOMENA IN MICROEMULSIONS 162
ABSTRACT 162
1. Introduction 163
2. Theory 164
3. Experiment 167
4. Results 171
5. Conclusion 173
References 176
CHAPTER 9. ELECTROHYDRODYNAMIC SURFACE WAVES 178
1. BACKGROUND 178
2. Qualitative View of Field-Coupled Surface Waves With No Electric Shear Stress 184
3. DYNAMICS OF FREE-SURFACE MONOLAYERS 186
4. TRAVELING-WAVE INDUCED INTERFACIAL PUMPING 199
5. INTERNAL ELECTROHYDRODYNAMICS OF INTERFACES 205
6. SUMMARY REMARKS 209
REFERENCES 209
CHAPTER 10. SOLITARY WAVES ON DENSITY INTERFACES 212
1. INTRODUCTION 212
2. TIDAL GENERATION OF INTERNAL SOLITARY WAVES 214
3. THE PROPOGATION OF INTERNAL, SOLITARY WAVES 220
REFERENCES 229
CHAPTER 11. INTERFACIAL INSTABILITIES CAUSED BY AIR FLOWOVER A THIN LIQUID LAYER 232
1. INTRODUCTION 232
2. OBSERVED INSTABILITIES 235
3. PREDICTION OF TS and PS 237
4. STABILITY ANALYSIS OF THE LIQUID FILM 244
5. INTERPRETATION OF FILM INSTABILITIES 252
6. NOTATION 266
7. REFERENCES 269
CHAPTER 12. FILM WAVES 272
1. INTRODUCTION 272
2. BASIC EQUATIONS 273
3. SIMPLE FILM 274
4. MULTI-LAYERED FILM 290
5. CONCLUSION 294
REFERENCES 295
CHAPTER 13. RUPTURE OF THIN LIQUID FILMS 302
1. INTRODUCTION 302
2. FORMULATION 303
3. LONG-WAVE THEORY 305
4. LINEAR STABILITY THEORY 308
5. RESULTS 309
6. DISCUSSION 310
REFERENCES 313
CHAPTER 14. THE MOVING CONTACT LINE 314
1. INTRODUCTION 314
2. MECHANISM 315
3. INADEQUACY OF THE USUAL HYDRODYNAMIC MODEL 317
4. WELL-POSED BOUNDARY-VALUE PROBLEM 324
REFERENCES 333
CHAPTER 15. THE ENDOTHELIAL INTERFACE BETWEEN TISSUE AND BLOOD 336
1. INTRODUCTION 336
2. VESICULAR TRANSPORT 340
3. MARCOMOLECULE TRANSPORT ACROSS THE ARTERY WALL 345
4. FILTRATION ACROSS THE ARTERY WALL 353
5. TRANSPORT THROUGH THE INTERCELLULAR SPACE (OSMOSIS) 357
REFERENCES 363
INDEX 366

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
• Themenwelt: Technik
• ISBN-10: 1-4832-6514-5 / 1483265145
• ISBN-13: 978-1-4832-6514-8 / 9781483265148