Meyer Waves on Fluid Interfaces

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 18-20, 1982
1. Auflage 2014
ISBN: 978-1-4832-6514-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 370 Seiten, Web PDF

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.

Autoren/Hrsg.

Meyer, Richard E.

Inhaltsverzeichnis

1;Front Cover;1
2;Waves on Fluid Interfaces;4
3;Copyright Page;5
4;Table of Contents;6
5;SENIOR CONTRIBUTORS;8
6;PREFACE;10
7;CHAPTER 1. FINITE-AMPLITUDE INTERFACIAL WAVES;12
7.1;1. INTRODUCTION;12
7.2;2. WEAKLY NONLINEAR WAVES;15
7.3;3. NUMERICAL METHODS;17
7.4;4. A SPECIAL CLASS OF SOLUTIONS;19
7.5;5. RESULTS;20
7.6;REFERENCES;25
8;CHAPTER 2. INSTABILITY OF FINITE-AMPLITUDE INTERFACIAL WAVES;28
8.1;1. INTRODUCTION;28
8.2;2. GOVERNING EQUATIONS;29
8.3;3. THE WAVE OF ZERO HEIGHT;32
8.4;4. WATER WAVES: A SPECIAL CASE;33
8.5;5. RESULTS FOR INTERFACIAL WAVES WITH CURRENT JUMP;34
8.6;6. DISCUSSION;50
8.7;REFERENCES;51
9;CHAPTER 3. FINITE-AMPLITUDE WATER WAVES WITH SURFACE TENSION;52
9.1;1. INTRODUCTION;52
9.2;2. FORMULATION;52
9.3;3. PERTURBATION SOLUTIONS;53
9.4;4. REFORMULATION AS AN INTEGRO-DIFFERENTIAL EQUATION;55
9.5;5. NUMERICAL PROCEDURE;58
9.6;6. DISCUSSION OF THE RESULTS;60
9.7;REFERENCES;62
10;CHAPTER 4. GENERALIZED VORTEX METHODS FOR FREE-SURFACE FLOWS;64
10.1;1. INTRODUCTION;64
10.2;2. BOUNDARY INTEGRAL TECHNIQUES;66
10.3;3. GENERALISED VORTEX METHOD;72
10.4;4. ACCELERATING FLUID LAYERS;82
10.5;REFERENCES;91
11;CHAPTER 5. A REVIEW OF SOLUTION METHODS FOR VISCOUS FLOW IN THE PRESENCE OF DEFORMABLE BOUNDARIES;94
11.1;A. INTRODUCTION;94
11.2;B. THE BASIC PROBLEM;95
11.3;C. SOLUTION METHODS FOR VANISHINGLY SMALL REYNOLDS NUMBERS;98
11.4;D. SOLUTION METHODS FOR FINITE REYNOLDS NUMBER;108
11.5;REFERENCES;119
12;CHAPTER 6. ON EXISTENCE CRITERIA FOR FLUID INTERFACES IN THE ABSENCE OF GRAVITY;124
12.1;1. INTRODUCTION;124
12.2;2. SPECIAIJZED DOMAINS–NECESSARY CONDITIONS;126
12.3;3. SUFFICIENT CONDITIONS FOR EXISTENCE–MORE GENERAL DOMAINS;128
12.4;4. SUBSIDIARY VARIATIONAL PROBLEM;132
12.5;5. CONTINUOUS AND DISCONTINUOUS DISAPPEARANCE OF CAPILLARY SURFACES;132
12.6;REFERENCES;133
13;CHAPTER 7. CAPILLARY WAVES AND INTERFACIAL STRUCTURE;134
13.1;1. INTRODUCTION;134
13.2;2. GRADIENT THEORY OF INHOMOGENEOUS FLUID;135
13.3;3. EQUILIBRIUM DENSITY PROFILE AND TENSION OF A PLANAR INTERFACE;136
13.4;4. STABILITY OF FLUID AT EQUILIBRIUM;140
13.5;5. THERMAL FLUCTUATIONS IN HOMOGENEOUS FLUID;141
13.6;6. FLUCTUATIONS OF A PLANAR INTERFACE: CAPILLARY WAVES;145
13.7;7. RIGOROUS DENSITY FUNCTIONAL FREE ENERGY THEORY;153
13.8;REFERENCES;159
14;CHAPTER 8. INTERFACIAL AND CRITICAL PHENOMENA IN MICROEMULSIONS;162
14.1;ABSTRACT;162
14.2;1. Introduction;163
14.3;2. Theory;164
14.4;3. Experiment;167
14.5;4. Results;171
14.6;5. Conclusion;173
14.7;References;176
15;CHAPTER 9. ELECTROHYDRODYNAMIC SURFACE WAVES;178
15.1;1. BACKGROUND;178
15.2;2. Qualitative View of Field-Coupled Surface Waves With No Electric Shear Stress;184
15.3;3. DYNAMICS OF FREE-SURFACE MONOLAYERS;186
15.4;4. TRAVELING-WAVE INDUCED INTERFACIAL PUMPING;199
15.5;5. INTERNAL ELECTROHYDRODYNAMICS OF INTERFACES;205
15.6;6. SUMMARY REMARKS;209
15.7;REFERENCES;209
16;CHAPTER 10. SOLITARY WAVES ON DENSITY INTERFACES;212
16.1;1. INTRODUCTION;212
16.2;2. TIDAL GENERATION OF INTERNAL SOLITARY WAVES;214
16.3;3. THE PROPOGATION OF INTERNAL, SOLITARY WAVES;220
16.4;REFERENCES;229
17;CHAPTER 11. INTERFACIAL INSTABILITIES CAUSED BY AIR FLOWOVER A THIN LIQUID LAYER;232
17.1;1. INTRODUCTION;232
17.2;2. OBSERVED INSTABILITIES;235
17.3;3. PREDICTION OF TS and PS;237
17.4;4. STABILITY ANALYSIS OF THE LIQUID FILM;244
17.5;5. INTERPRETATION OF FILM INSTABILITIES;252
17.6;6. NOTATION;266
17.7;7. REFERENCES;269
18;CHAPTER 12. FILM WAVES;272
18.1;1. INTRODUCTION;272
18.2;2. BASIC EQUATIONS;273
18.3;3. SIMPLE FILM;274
18.4;4. MULTI-LAYERED FILM;290
18.5;5. CONCLUSION;294
18.6;REFERENCES;295
19;CHAPTER 13. RUPTURE OF THIN LIQUID FILMS;302
19.1;1. INTRODUCTION;302
19.2;2. FORMULATION;303
19.3;3. LONG-WAVE THEORY;305
19.4;4. LINEAR STABILITY THEORY;308
19.5;5. RESULTS;309
19.6;6. DISCUSSION;310
19.7;REFERENCES;313
20;CHAPTER 14. THE MOVING CONTACT LINE;314
20.1;1. INTRODUCTION;314
20.2;2. MECHANISM;315
20.3;3. INADEQUACY OF THE USUAL HYDRODYNAMIC MODEL;317
20.4;4. WELL-POSED BOUNDARY-VALUE PROBLEM;324
20.5;REFERENCES;333
21;CHAPTER 15. THE ENDOTHELIAL INTERFACE BETWEEN TISSUE AND BLOOD;336
21.1;1. INTRODUCTION;336
21.2;2. VESICULAR TRANSPORT;340
21.3;3. MARCOMOLECULE TRANSPORT ACROSS THE ARTERY WALL;345
21.4;4. FILTRATION ACROSS THE ARTERY WALL;353
21.5;5. TRANSPORT THROUGH THE INTERCELLULAR SPACE (OSMOSIS);357
21.6;REFERENCES;363
22;INDEX;366