Author | Finn, Robert. author |
---|---|
Title | Equilibrium Capillary Surfaces [electronic resource] / by Robert Finn |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8584-4 |
Descript | XVI, 246 p. online resource |
1 Introduction -- 1.1. Mean Curvature -- 1.2. Laplaceโs Equation -- 1.3. Angle of Contact -- 1.4. The Method of Gauss; Characterization of the Energies -- 1.5. Variational Considerations -- 1.6. The Equation and the Boundary Condition -- 1.7. Divergence Structure -- 1.8. The Problem as a Geometrical One -- 1.9. The Capillary Tube -- 1.10. Dimensional Considerations -- Notes to Chapter 1 -- 2 The Symmetric Capillary Tube -- 2.1. Historical and General -- 2.2. The Narrow Tube; Center Height -- 2.3. The Narrow Tube; Outer Height -- 2.4. The Narrow Tube; Estimates Throughout the Trajectory -- 2.5. Height Estimates for Tubes of General Size -- 2.6. Meniscus Height; Narrow Tubes -- 2.7. Meniscus Height; General Case -- 2.8. Comparisons with Earlier Theories -- Notes to Chapter 2 -- 3 The Symmetric Sessile Drop -- 3.1. The Correspondence Principle -- 3.2. Continuation Properties -- 3.3. Uniqueness and Existence -- 3.4. The Envelope -- 3.5. Comparison Theorems -- 3.6. Geometry of the Sessile Drop; Small Drops -- 3.7. Geometry of the Sessile Drop; Larger Drops -- Notes to Chapter 3 -- 4 The Pendent Liquid Drop -- 4.1. Mise en Scรจne -- 4.2. Local Existence -- 4.3. Uniqueness -- 4.4. Global Behavior; General Remarks -- 4.5. Small 0| -- 4.6. Appearance of Vertical Points -- 4.7. Behavior for Large 0| -- 4.8. Global Behavior -- 4.9. Maximum Vertical Diameter -- 4.10. Maximum Diameter -- 4.11. Maximum Volume -- 4.12. Asymptotic Properties -- 4.13. The Singular Solution -- 4.14. Isolated Character of Global Solutions -- 4.15. Stability -- Notes to Chapter 4 -- 5 Asymmetric Case; Comparison Principles and Applications -- 5.1. The General Comparison Principle -- 5.2. Applications -- 5.3. Domain Dependence -- 5.4. A Counterexample -- 5.5. Convexity -- Notes to Chapter 5 -- 6 Capillary Surfaces Without Gravity -- 6.1. General Remarks -- 6.2. A Necessary Condition -- 6.3. Sufficiency Conditions -- 6.4. Sufficiency Conditions II -- 6.5. A Subsidiary Extremal Problem -- 6.6. Minimizing Sequences -- 6.7. The Limit Configuration -- 6.8. The First Variation -- 6.9. The Second Variation -- 6.10. Solution of the Jacobi Equation -- 6.11. Convex Domains -- 6.12. Continuous and Discontinuous Disappearance -- 6.13. An Example -- 6.14. Another Example -- 6.15. Remarks on the Extremals -- 6.16. Example 1 -- 6.17. Example 2 -- 6.18. Example 3 -- 6.19. The Trapezoid -- 6.20. Tail Domains; A Counterexample -- 6.21. Convexity -- 6.22. A Counterexample -- 6.23. Transition to Zero Gravity -- Notes to Chapter 6 -- 7 Existence Theorems -- 7.1. Choice of Venue -- 7.2. Variational Solutions -- 7.3. Generalized Solutions -- 7.4. Construction of a Generalized Solution -- 7.5. Proof of Boundedness -- 7.6. Uniqueness -- 7.7. The Variational Condition; Limiting Case -- 7.8. A Necessary and Sufficient Condition -- 7.9. A Limiting Configuration -- 7.10. The Case ยต>ยต0>1 -- 7.11. Application: A General Gradient Bound -- Notes to Chapter 7 -- 8 The Capillary Contact Angle -- 8.1. Everyday Experience -- 8.2. The Hypothesis -- 8.3. The Horizontal Plane; Preliminary Remarks -- 8.4. Necessity for ? -- 8.5. Proof that ? is Monotone -- 8.6. Geometrically Imposed Stability Bounds -- 8.7. A Further Kind of Instability -- 8.8. The Inclined Plane; Preliminary Remarks -- 8.9. Integral Relations, and Impossibility of Constant Contact Angle -- 8.10. The Zero-Gravity Solution -- 8.11. Postulated Form for ? -- 8.12. Formal Analytical Solution -- 8.13. The Expansion; Leading Terms -- 8.14. Computer Calculations -- 8.15. Discussion -- 8.16. Further Discussion -- Notes to Chapter 8 -- 9 Identities and Isoperimetric Relations