Interfacial transport phenomena

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010101121	QC175.2 S52 2007	Open Access Book	Book	Searching... Unknown
Searching... SPACE KL Main Library	30000003489451	QC 175.2 S52 2007	Open Access Book	Book	Searching... Unknown

Transport phenomena is used here to describe momentuin, energy, mass, and entropy transfer [1, 2]. It includes thermodynamics, a special case of which is thermosiaiics. Interfacial transport phenomena refers to momentum, energy, mass, and entropy transfer within the immediate neighborhood of a phase interface, including the thermodynamics of the interface. In terms of qualitative physical observations, this is a very old field. Pliny the Elder (Gains Plinius Secundus, 23-79 A. D. ; Pliny [3]) described divers who released small quantities of oil from their mouths, in order to damp capillary ripples on the ocean surface and in this way provide more uniform lighting for their work. Similar stories were retold by Benjamin Franklin, who conducted experiments of his own in England [4]. In terms of analysis, this is a generally young field. Surface thermostat ics developed relatively early, starting with Gibbs [5] and continuing with important contributions by many others (see Chap. 4). Derjaguin and Lan dau [6] and Verwey and Overbeek [7] indicated how London-van der Waals and electrostatic double-layer forces were to be incorporated in continuum mechanics, now often referred to as DLVO theory. But prior to 1960, there were relatively few notable papers concerned with the analysis of dynamic systems. Two stand out in my mind. Boussinesq [8] recognized the surface stress tensor and proposed the constitutive equation that we now refer to as the Boussinesq surface fluid model (Sect. 4. 9. 5).

J. D. Chen

1 Kinematics and Conservation of Mass	p. 1
1.1 Motion	p. 2
1.1.1 Body	p. 2
1.1.2 Stretch and Rotation [19, p. 17]	p. 6
1.2 Motion of Multiphase Bodies	p. 7
1.2.1 What are Phase Interfaces?	p. 7
1.2.2 Three-Dimensional Interfacial Region	p. 7
1.2.3 Dividing surface	p. 8
1.2.4 Dividing Surface as a Model for a Three-Dimensional Interfacial Region	p. 9
1.2.5 Motion of Dividing Surface	p. 9
1.2.6 Stretch and Rotation within Dividing Surfaces	p. 17
1.2.7 More about Surface Velocity	p. 18
1.2.8 Rate of Deformation	p. 21
1.2.9 Moving Common Lines: Qualitative Description	p. 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 Solid	p. 43
1.2.12 Moving Common Lines: Quantitative Description	p. 47
1.3 Mass	p. 52
1.3.1 Conservation of Mass	p. 52
1.3.2 Surface Mass Density	p. 55
1.3.3 Surface Transport Theorem	p. 60
1.3.4 Transport Theorem for Body Containing Dividing Surface	p. 67
1.3.5 Jump Mass Balance	p. 70
1.3.6 Location of Dividing Surface	p. 73
1.3.7 Transport Theorem for Body Containing Intersecting Dividing Surfaces	p. 73
1.3.8 Mass Balance at a Common Line	p. 79
1.3.9 Comment on Velocity Distribution in Neighborhood of Moving Common Line on Rigid Solid	p. 85
1.3.10 More Comments on Velocity Distribution, in Neighborhood of Moving Common Line on Rigid Solid	p. 90
1.4 Frame	p. 93
1.4.1 Changes of Frame	p. 93
1.4.2 Frame Indifferent Scalars, Vectors, and Tensors	p. 99
1.4.3 Equivalent Motions	p. 100
1.4.4 Principle of Frame Indifference	p. 105
2 Foundations for Momentum Transfer	p. 107
2.1 Force	p. 107
2.1.1 What are Forces?	p. 107
2.1.2 Momentum and Moment of Momentum Balances	p. 111
2.1.3 Body Forces and Contact Forces	p. 113
2.1.4 Momentum Balance at Dividing Surfaces	p. 115
2.1.5 Surface Stress Tensor	p. 117
2.1.6 Jump Momentum Balance	p. 119
2.1.7 T[superscript (sigma)] is Symmetric Tangential Tensor	p. 121
2.1.8 Surface Velocity, Surface Stress, and Surface Body Force	p. 124
2.1.9 Momentum Balance at Common Line	p. 125
2.1.10 Momentum Balance at Common Line on Relatively Rigid Solid	p. 130
2.1.11 Factors Influencing Measured Contact Angles	p. 133
2.1.12 Relationships for Measured Contact Angles	p. 136
2.1.13 More Comments Concerning Moving Common Lines and Contact Angles on Rigid Solids and Their Relation to the Disjoining Pressure	p. 137
2.2 Correcting Material Behavior for Intermolecular Forces from Adjacent Phases [20]	p. 140
2.2.1 The Correction	p. 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 Transfer	p. 159
3.1 Philosophy	p. 159
3.1.1 Structure of Problem	p. 159
3.1.2 Approximations	p. 161
3.2 Only Interfacial Tension	p. 162
3.2.1 Classes of Problems	p. 162
3.2.2 Spinning Drop Interfacial Tensiometer [21]	p. 164
3.2.3 Meniscal Breakoff Interfacial Tensiometer	p. 171
3.2.4 Pendant Drop	p. 182
3.2.5 Sessile Drop	p. 188
3.3 Applications of Our Extension of Continuum Mechanics to the Nanoscale	p. 194
3.3.1 Supercritical Adsorption [22]	p. 195
3.3.2 Static Contact Angle [20]	p. 202
3.3.3 A Review of Coalescence	p. 208
3.3.4 Coalescence [23-25]	p. 215
3.3.5 Moving Common Line and Receding Contact Angle	p. 234
3.3.6 Nanoscale Fracture [26]	p. 248
4 Foundations for Simultaneous Momentum, Energy, and Mass Transfer	p. 261
4.1 Viewpoint	p. 261
4.1.1 Viewpoint in Considering Multicomponent Materials	p. 261
4.1.2 Body, Motion, and Material Coordinates of Species A	p. 262
4.1.3 Motion of Multicomponent Dividing Surface	p. 264
4.1.4 More about Surface Velocity of Species A	p. 267
4.2 Mass Balance	p. 269
4.2.1 Species Mass Balance	p. 269
4.2.2 Concentrations, Velocities, and Mass Fluxes	p. 275
4.2.3 Location of Multicomponent Dividing Surface	p. 277
4.3 Further Comments on Viewpoint	p. 279
4.3.1 Further Comments on Viewpoint of Multicomponent Materials	p. 279
4.4 Mass	p. 281
4.4.1 Conservation of Mass	p. 281
4.5 Force	p. 284
4.5.1 Momentum and Moment of Momentum Balances	p. 284
4.5.2 Jump Momentum Balance	p. 284
4.5.3 T[superscript sigma] is Symmetric, Tangential Tensor	p. 286
4.6 Energy	p. 287
4.6.1 Rate of Energy Transmission	p. 287
4.6.2 Energy Balance	p. 287
4.6.3 Radiant and Contact Energy Transmission	p. 288
4.6.4 Jump Energy Balance	p. 290
4.7 Entropy	p. 295
4.7.1 Entropy Inequality	p. 295
4.7.2 Radiant and Contact Entropy Transmission	p. 297
4.7.3 Jump Entropy Inequality	p. 299
4.8 Behavior as Restricted by Entropy Inequality	p. 304
4.8.1 Behavior of Multicomponent Materials	p. 304
4.8.2 Bulk Behavior: Implications of Entropy Inequality	p. 304
4.8.3 Surface Behavior: Implications of Jump Entropy Inequality	p. 316
4.8.4 Surface Behavior: Adsorption Isotherms and Equations of State	p. 332
4.8.5 Alternative Forms for the Energy Balances and the Entropy Inequalities	p. 349
4.9 Behavior as Restricted by Frame Indifference	p. 352
4.9.1 Other Principles to be Considered	p. 352
4.9.2 Alternative Independent Variables in Constitutive Equations	p. 353
4.9.3 Bulk Behavior: Constitutive Equations for Stress Tensor, Energy Flux Vector and Mass Flux Vector	p. 355
4.9.4 Surface Behavior: Constitutive Equations for Surface Stress Tensor	p. 358
4.9.5 Boussinesq Surface Fluid	p. 358
4.9.6 Simple Surface Material	p. 361
4.9.7 Surface Isotropy Group	p. 366
4.9.8 Isotropic Simple Surface Materials	p. 369
4.9.9 Simple Surface Solid	p. 371
4.9.10 Simple Surface Fluid	p. 373
4.9.11 Fading Memory and Special Cases of Simple Surface Fluid	p. 374
4.9.12 Simple Surface Fluid Crystals	p. 377
4.9.13 Surface Behavior: Constitutive Equations for Surface Energy Flux Vector	p. 377
4.9.14 Surface Behavior: Constitutive Equations for Surface Mass Flux Vector	p. 379
4.10 Intrinsically Stable Equilibrium [27]	p. 382
4.10.1 Stable Equilibrium	p. 382
4.10.2 Constraints on Isolated Systems	p. 383
4.10.3 Implications of (4.10.2-24) for Intrinsically Stable Equilibrium	p. 390
4.10.4 Implications of (4.10.2-25) for Intrinsically Stable Equilibrium	p. 397
4.11 Thermodynamics of Single-Component, Elastic, Crystalline Surface Solids [28]	p. 409
4.11.1 Thermodynamics of Surface Crystals	p. 409
4.11.2 Constraints on Isolated Systems	p. 413
4.11.3 Implications of Equilibrium	p. 416
4.11.4 Stress-Deformation Behavior of Single-Walled Carbon Nanotubes	p. 423
5 Applications of the Differential Balances to Momentum, Energy and Mass Transfer	p. 429
5.1 Philosophy	p. 429
5.1.1 Structure of Problems Involving Momentum Transfer	p. 429
5.1.2 Structure of Problems Involving Energy Transfer	p. 429
5.1.3 Structure of Problems Involving Mass Transfer	p. 431
5.2 Problems Involving Momentum Transfer	p. 432
5.2.1 Boussinesq Surface Fluid in a Knife-edge Surface Viscometer	p. 432
5.2.2 Generalized Boussinesq Surface Fluid in a Deep Channel Surface Viscometer	p. 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 Dominate	p. 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 Transfer	p. 575
5.3.1 Motion of a Drop or Bubble [37; with D. Li]	p. 575
5.4 Limiting Cases of Mass Transfer	p. 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 Geometry	p. 611
A.1 Physical Space	p. 611
A.1.1 Euclidean Space	p. 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 Fields	p. 617
A.2.1 Natural Basis	p. 617
A.2.2 Surface Gradient of Scalar Field	p. 624
A.2.3 Dual Basis	p. 625
A.2.4 Covariant and Contravariant Components	p. 625
A.2.5 Physical Components	p. 626
A.2.6 Tangential and Normal Components	p. 627
A.3 Second-Order Tensor Fields	p. 629
A.3.1 Tangential Transformations and Surface Tensors	p. 629
A.3.2 Projection Tensor	p. 631
A.3.3 Tangential Cross Tensor	p. 633
A.3.4 Transpose	p. 636
A.3.5 Inverse	p. 637
A.3.6 Orthogonal Tangential Transformation	p. 639
A.3.7 Surface Determinant of Tangential Transformation	p. 641
A.3.8 Polar Decomposition	p. 643
A.4 Third-Order Tensor Fields	p. 646
A.4.1 Surface Tensors	p. 646
A.5 Surface Gradient	p. 647
A.5.1 Spatial Vector Field	p. 647
A.5.2 Vector Field is Explicit Function of Position in Space	p. 648
A.5.3 Vector Field is Explicit Function of Position on Surface	p. 649
A.5.4 Second-Order Tensor Field	p. 660
A.5.5 Tensor Field is Explicit Function of Position in Space	p. 661
A.5.6 Tensor Field is Explicit Function of Position on Surface	p. 662
A.6 Integration	p. 666
A.6.1 Line Integration	p. 666
A.6.2 Surface Integration	p. 668
A.6.3 Surface Divergence Theorem	p. 669
B Summary of Useful Equations	p. 673
B.1 Useful Equations for Single Component Systems	p. 673
B.1.1 Bulk Phases	p. 673
B.1.2 Dividing Surfaces	p. 675
B.1.3 Common Lines	p. 693
B.2 Useful Equations for Multicomponent Systems with Simultaneous Momentum, Energy, and Mass Transfer	p. 694
B.2.1 Concentrations, Velocities, and Fluxes	p. 694
B.2.2 Jump Mass, Jump Energy, and Jump Entropy Balance	p. 700
B.2.3 Specific Forms	p. 704
C Applications of integral averaging to momentum, energy, and mass transfer	p. 735
C.1 Integral balances	p. 735
C.1.1 Integral overall mass balance	p. 736
C.1.2 The Integral Mass Balance for Species A	p. 738
C.1.3 Integral momentum balance	p. 739
C.1.4 Integral mechanical energy balance	p. 742
C.1.5 The Integral Energy Balance	p. 749
C.1.6 The Integral Entropy Inequality	p. 753
Notation	p. 757
References	p. 773
Author Index	p. 809
Index	p. 821

Available:*

On Order

Summary

Summary

Table of Contents