Cover image for Interfacial transport phenomena
Title:
Interfacial transport phenomena
Personal Author:
Edition:
2nd ed.
Publication Information:
New York, NY : Springer, 2007
Physical Description:
vi, 827 p. : ill. ; 23 cm.
ISBN:
9780387384382
General Note:
Available online version
Electronic Access:
FullText

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30000010101121 QC175.2 S52 2007 Open Access Book
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30000003489451 QC 175.2 S52 2007 Open Access Book
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Summary

Summary

This is an extensively revised second edition of "Interfacial Transport Phenomena", a unique presentation of transport phenomena or continuum mechanics focused on momentum, energy, and mass transfer at interfaces. It discusses transport phenomena at common lines or three-phase lines of contact. The emphasis is upon achieving an in-depth understanding based upon first principles. It includes exercises and answers, and can serve as a graduate level textbook.


Table of Contents

J. D. Chen
1 Kinematics and Conservation of Massp. 1
1.1 Motionp. 2
1.1.1 Bodyp. 2
1.1.2 Stretch and Rotation [19, p. 17]p. 6
1.2 Motion of Multiphase Bodiesp. 7
1.2.1 What are Phase Interfaces?p. 7
1.2.2 Three-Dimensional Interfacial Regionp. 7
1.2.3 Dividing surfacep. 8
1.2.4 Dividing Surface as a Model for a Three-Dimensional Interfacial Regionp. 9
1.2.5 Motion of Dividing Surfacep. 9
1.2.6 Stretch and Rotation within Dividing Surfacesp. 17
1.2.7 More about Surface Velocityp. 18
1.2.8 Rate of Deformationp. 21
1.2.9 Moving Common Lines: Qualitative Descriptionp. 25
1.2.10 Moving Common Lines: Emission of Material Surfaces [16]p. 37
1.2.11 Moving Common Lines: Velocity is Multivalued on a Rigid Solidp. 43
1.2.12 Moving Common Lines: Quantitative Descriptionp. 47
1.3 Massp. 52
1.3.1 Conservation of Massp. 52
1.3.2 Surface Mass Densityp. 55
1.3.3 Surface Transport Theoremp. 60
1.3.4 Transport Theorem for Body Containing Dividing Surfacep. 67
1.3.5 Jump Mass Balancep. 70
1.3.6 Location of Dividing Surfacep. 73
1.3.7 Transport Theorem for Body Containing Intersecting Dividing Surfacesp. 73
1.3.8 Mass Balance at a Common Linep. 79
1.3.9 Comment on Velocity Distribution in Neighborhood of Moving Common Line on Rigid Solidp. 85
1.3.10 More Comments on Velocity Distribution, in Neighborhood of Moving Common Line on Rigid Solidp. 90
1.4 Framep. 93
1.4.1 Changes of Framep. 93
1.4.2 Frame Indifferent Scalars, Vectors, and Tensorsp. 99
1.4.3 Equivalent Motionsp. 100
1.4.4 Principle of Frame Indifferencep. 105
2 Foundations for Momentum Transferp. 107
2.1 Forcep. 107
2.1.1 What are Forces?p. 107
2.1.2 Momentum and Moment of Momentum Balancesp. 111
2.1.3 Body Forces and Contact Forcesp. 113
2.1.4 Momentum Balance at Dividing Surfacesp. 115
2.1.5 Surface Stress Tensorp. 117
2.1.6 Jump Momentum Balancep. 119
2.1.7 T[superscript (sigma)] is Symmetric Tangential Tensorp. 121
2.1.8 Surface Velocity, Surface Stress, and Surface Body Forcep. 124
2.1.9 Momentum Balance at Common Linep. 125
2.1.10 Momentum Balance at Common Line on Relatively Rigid Solidp. 130
2.1.11 Factors Influencing Measured Contact Anglesp. 133
2.1.12 Relationships for Measured Contact Anglesp. 136
2.1.13 More Comments Concerning Moving Common Lines and Contact Angles on Rigid Solids and Their Relation to the Disjoining Pressurep. 137
2.2 Correcting Material Behavior for Intermolecular Forces from Adjacent Phases [20]p. 140
2.2.1 The Correctionp. 143
2.2.2 One Unbounded Dividing Surface: View (iv)p. 146
2.2.3 One Thin Lens or Fracture: View (iv)p. 150
2.2.4 One Thin Film: View (v)p. 152
2.2.5 A Discontinuous Thin Film: View (v)p. 156
2.2.6 One Unbounded Common Line: View (iv)p. 157
3 Applications of the Differential Balances to Momentum Transferp. 159
3.1 Philosophyp. 159
3.1.1 Structure of Problemp. 159
3.1.2 Approximationsp. 161
3.2 Only Interfacial Tensionp. 162
3.2.1 Classes of Problemsp. 162
3.2.2 Spinning Drop Interfacial Tensiometer [21]p. 164
3.2.3 Meniscal Breakoff Interfacial Tensiometerp. 171
3.2.4 Pendant Dropp. 182
3.2.5 Sessile Dropp. 188
3.3 Applications of Our Extension of Continuum Mechanics to the Nanoscalep. 194
3.3.1 Supercritical Adsorption [22]p. 195
3.3.2 Static Contact Angle [20]p. 202
3.3.3 A Review of Coalescencep. 208
3.3.4 Coalescence [23-25]p. 215
3.3.5 Moving Common Line and Receding Contact Anglep. 234
3.3.6 Nanoscale Fracture [26]p. 248
4 Foundations for Simultaneous Momentum, Energy, and Mass Transferp. 261
4.1 Viewpointp. 261
4.1.1 Viewpoint in Considering Multicomponent Materialsp. 261
4.1.2 Body, Motion, and Material Coordinates of Species Ap. 262
4.1.3 Motion of Multicomponent Dividing Surfacep. 264
4.1.4 More about Surface Velocity of Species Ap. 267
4.2 Mass Balancep. 269
4.2.1 Species Mass Balancep. 269
4.2.2 Concentrations, Velocities, and Mass Fluxesp. 275
4.2.3 Location of Multicomponent Dividing Surfacep. 277
4.3 Further Comments on Viewpointp. 279
4.3.1 Further Comments on Viewpoint of Multicomponent Materialsp. 279
4.4 Massp. 281
4.4.1 Conservation of Massp. 281
4.5 Forcep. 284
4.5.1 Momentum and Moment of Momentum Balancesp. 284
4.5.2 Jump Momentum Balancep. 284
4.5.3 T[superscript sigma] is Symmetric, Tangential Tensorp. 286
4.6 Energyp. 287
4.6.1 Rate of Energy Transmissionp. 287
4.6.2 Energy Balancep. 287
4.6.3 Radiant and Contact Energy Transmissionp. 288
4.6.4 Jump Energy Balancep. 290
4.7 Entropyp. 295
4.7.1 Entropy Inequalityp. 295
4.7.2 Radiant and Contact Entropy Transmissionp. 297
4.7.3 Jump Entropy Inequalityp. 299
4.8 Behavior as Restricted by Entropy Inequalityp. 304
4.8.1 Behavior of Multicomponent Materialsp. 304
4.8.2 Bulk Behavior: Implications of Entropy Inequalityp. 304
4.8.3 Surface Behavior: Implications of Jump Entropy Inequalityp. 316
4.8.4 Surface Behavior: Adsorption Isotherms and Equations of Statep. 332
4.8.5 Alternative Forms for the Energy Balances and the Entropy Inequalitiesp. 349
4.9 Behavior as Restricted by Frame Indifferencep. 352
4.9.1 Other Principles to be Consideredp. 352
4.9.2 Alternative Independent Variables in Constitutive Equationsp. 353
4.9.3 Bulk Behavior: Constitutive Equations for Stress Tensor, Energy Flux Vector and Mass Flux Vectorp. 355
4.9.4 Surface Behavior: Constitutive Equations for Surface Stress Tensorp. 358
4.9.5 Boussinesq Surface Fluidp. 358
4.9.6 Simple Surface Materialp. 361
4.9.7 Surface Isotropy Groupp. 366
4.9.8 Isotropic Simple Surface Materialsp. 369
4.9.9 Simple Surface Solidp. 371
4.9.10 Simple Surface Fluidp. 373
4.9.11 Fading Memory and Special Cases of Simple Surface Fluidp. 374
4.9.12 Simple Surface Fluid Crystalsp. 377
4.9.13 Surface Behavior: Constitutive Equations for Surface Energy Flux Vectorp. 377
4.9.14 Surface Behavior: Constitutive Equations for Surface Mass Flux Vectorp. 379
4.10 Intrinsically Stable Equilibrium [27]p. 382
4.10.1 Stable Equilibriump. 382
4.10.2 Constraints on Isolated Systemsp. 383
4.10.3 Implications of (4.10.2-24) for Intrinsically Stable Equilibriump. 390
4.10.4 Implications of (4.10.2-25) for Intrinsically Stable Equilibriump. 397
4.11 Thermodynamics of Single-Component, Elastic, Crystalline Surface Solids [28]p. 409
4.11.1 Thermodynamics of Surface Crystalsp. 409
4.11.2 Constraints on Isolated Systemsp. 413
4.11.3 Implications of Equilibriump. 416
4.11.4 Stress-Deformation Behavior of Single-Walled Carbon Nanotubesp. 423
5 Applications of the Differential Balances to Momentum, Energy and Mass Transferp. 429
5.1 Philosophyp. 429
5.1.1 Structure of Problems Involving Momentum Transferp. 429
5.1.2 Structure of Problems Involving Energy Transferp. 429
5.1.3 Structure of Problems Involving Mass Transferp. 431
5.2 Problems Involving Momentum Transferp. 432
5.2.1 Boussinesq Surface Fluid in a Knife-edge Surface Viscometerp. 432
5.2.2 Generalized Boussinesq Surface Fluid in a Deep Channel Surface Viscometerp. 449
5.2.3 Simple Surface Fluid in Curvilineal Surface Flows [29]p. 455
5.2.4 Simple Surface Fluid in a Deep Channel Surface Viscometer [29]p. 460
5.2.5 Simple Surface Fluid in an Oscillating Deep Channel Surface Viscometer [29]p. 463
5.2.6 Limiting Cases when Effects of Interfacial Viscosities Dominatep. 470
5.2.7 Displacement in a Capillary [30]p. 473
5.2.8 Several Interfacial Viscometers Suitable for Measuring Generalized Boussinesq Surface Fluid Behavior [31]p. 480
5.2.9 Stochastic Interfacial Disturbances Created by Thermal Noise and the Importance of the Interfacial Viscosities [32]p. 491
5.2.10 Capillary Rise [30, 33]p. 524
5.2.11 Common Line Motion in Systems with Simple Surface Fluid Material Behavior: Implications of the Entropy Inequality [34, 35]p. 534
5.2.12 More on Common Line Motion in Systems with Simple Surface Fluid Material Behavior: Implications in Polymer Extrusion [36]p. 563
5.3 Limiting Cases of Energy Transferp. 575
5.3.1 Motion of a Drop or Bubble [37; with D. Li]p. 575
5.4 Limiting Cases of Mass Transferp. 580
5.4.1 Motion of a Drop or Bubble [38; with D. Li]p. 580
5.4.2 Longitudinal and Transverse Waves [32]p. 587
A Differential Geometryp. 611
A.1 Physical Spacep. 611
A.1.1 Euclidean Spacep. 611
A.1.2 Notation in (E[superscript 2], V[superscript 3])p. 613
A.1.3 Surface in (E[superscript 3], V[superscript 3])p. 617
A.2 Vector Fieldsp. 617
A.2.1 Natural Basisp. 617
A.2.2 Surface Gradient of Scalar Fieldp. 624
A.2.3 Dual Basisp. 625
A.2.4 Covariant and Contravariant Componentsp. 625
A.2.5 Physical Componentsp. 626
A.2.6 Tangential and Normal Componentsp. 627
A.3 Second-Order Tensor Fieldsp. 629
A.3.1 Tangential Transformations and Surface Tensorsp. 629
A.3.2 Projection Tensorp. 631
A.3.3 Tangential Cross Tensorp. 633
A.3.4 Transposep. 636
A.3.5 Inversep. 637
A.3.6 Orthogonal Tangential Transformationp. 639
A.3.7 Surface Determinant of Tangential Transformationp. 641
A.3.8 Polar Decompositionp. 643
A.4 Third-Order Tensor Fieldsp. 646
A.4.1 Surface Tensorsp. 646
A.5 Surface Gradientp. 647
A.5.1 Spatial Vector Fieldp. 647
A.5.2 Vector Field is Explicit Function of Position in Spacep. 648
A.5.3 Vector Field is Explicit Function of Position on Surfacep. 649
A.5.4 Second-Order Tensor Fieldp. 660
A.5.5 Tensor Field is Explicit Function of Position in Spacep. 661
A.5.6 Tensor Field is Explicit Function of Position on Surfacep. 662
A.6 Integrationp. 666
A.6.1 Line Integrationp. 666
A.6.2 Surface Integrationp. 668
A.6.3 Surface Divergence Theoremp. 669
B Summary of Useful Equationsp. 673
B.1 Useful Equations for Single Component Systemsp. 673
B.1.1 Bulk Phasesp. 673
B.1.2 Dividing Surfacesp. 675
B.1.3 Common Linesp. 693
B.2 Useful Equations for Multicomponent Systems with Simultaneous Momentum, Energy, and Mass Transferp. 694
B.2.1 Concentrations, Velocities, and Fluxesp. 694
B.2.2 Jump Mass, Jump Energy, and Jump Entropy Balancep. 700
B.2.3 Specific Formsp. 704
C Applications of integral averaging to momentum, energy, and mass transferp. 735
C.1 Integral balancesp. 735
C.1.1 Integral overall mass balancep. 736
C.1.2 The Integral Mass Balance for Species Ap. 738
C.1.3 Integral momentum balancep. 739
C.1.4 Integral mechanical energy balancep. 742
C.1.5 The Integral Energy Balancep. 749
C.1.6 The Integral Entropy Inequalityp. 753
Notationp. 757
Referencesp. 773
Author Indexp. 809
Indexp. 821