Modeling Axisymmetric Flows (eBook)

Cover 1
Contents 6
Preface 12
Acknowledgments 14
Chapter 1. Laminar Axisymmetric Flows 16
1-1 Basic Dynamic and Kinematic Equations 17
1-2 Steady Fully Developed (Poiseuille) Flow 22
1-3 Flow through a Tube with a Variable Radiusu„The Lubrication Approximation 24
1-4 An Integral Technique for Solution of the Lubrication Equations 31
1-5 Axisymmetric Flow through a Leaky Tube 48
Problems 53
References 56
Chapter 2. Laminar Flow through a Tube with a Thin Annular Adherent Liquid Film 58
2-1 Axisymmetric Flow through a Lubricated Tube 59
2-2 Removal of an Annular Liquid Layer by Shearingm„A Quasi-steady Model 62
2-3 The Instability of a Static Annular Film of Liquid 63
2-4 The Deposition of a Thin Annular Film of Liquid inside Capillary 72
2-5 A More Careful Discussion of the Geometry and Dynamics of a Free Boundary Problem 77
2-6 Depletion of an Annular Liquid Film 85
Problems 89
References 91
Chapter 3. Steady Laminar Axisymmetric Flow from a Tube: Exit Effects 92
3-1 The Horizontal Jet 93
3-2 Draw-Down of a Vertical Jet 101
3-3 A Note on Dimensionless Groups 104
Problems 105
References 106
Chapter 4. The Transitions from Drops to a Coherent Jet and Back to Drops 108
4-1 Dripping from a Vertical Tube 109
4-2 Drops on Demand 112
4-3 Stability of the Horizontal Jet 117
Problems 137
References 138
Chapter 5. Impingement of a Coherent Jet Normal to a Rigid Surface 140
5-1 Introduction 140
5-2 A Boundary Layer Model (Watson, 1964) 144
5-3 The Hydraulic Jump 149
5-4 Displacement of a Thin Viscous Film by an Impinging Turbulent Jet 155
5-5 Two-Fluid Homann Flow 159
5-6 Laminar Flow over a Disk 166
Problems 170
References 173
Chapter 6. The Transfer of a Drop from a Capillary to an Impermeable Surface 176
6-1 Introduction 176
6-2 Shape of a Static Drop 177
6-3 Breakaway of a Pendent Drop 184
6-4 Stability of an Axisymmetric Bridge 188
6-5 Impact of a Drop with a Solid Surface 199
Problems 205
References 208
Chapter 7. The Isolated Drop on an Impermeable Surface 210
7-1 Spreading of an Isolated Drop with No Surface Tension 210
7-2 Spreading of a Drop with Surface Tension 214
Problems 221
References 223
Chapter 8. Capillary Penetration Dynamics 226
8-1 Introduction 226
8-2 Capillary Wicking 227
8-3 Radial Penetration through a Narrow Planar Space 235
8-4 Penetration Fed by a Drop of Finite Volume 240
8-5 Wicking of a Drop into a Porous Surface 245
Problems 251
References 254
Chapter 9. Ultrathin Films: Disjoining Pressure 256
9-1 Introduction 256
9-2 Effect of the Disjoining Pressure on Equilibrium Films 258
9-3 Dewetting 265
Problems 268
References 270
Chapter 10. The Interaction of a Deformable Drop with a Surface 272
10-1 The Approach of a Solid Sphere to a Rigid Plane 273
10-2 Slow Approach of a Viscous Drop to a Solid Surface 275
10-3 The Dimpled Drop 279
10-4 Film Evolution Equation for the Dimpled Drop 285
10-5 Drops and Bubbles Crossing Liquid Interfaces 292
10-6 Coalescence of Drops and Bubbles 298
Problems 304
References 306
Afterword 310
Index 312
Color Plate Section 316