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### Available:*

Library | Item Barcode | Call Number | Material Type | Status |
---|---|---|---|---|

Searching... | 30000010101121 | QC175.2 S52 2007 | Open Access Book | Searching... |

Searching... | 30000003489451 | QC 175.2 S52 2007 | Open Access Book | Searching... |

### On Order

### 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 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 |