 | Vrentas J.S. Diffusion and mass transfer / J.S.Vrentas, C.M.Vrentas. - Boca Raton: CRC press/Taylor & Francis, 2013. - xxi, 622 p.: ill., tab. - Bibliogr.: 587-597. - Ind.: p.599-622. - ISBN 978-1-4665-1568-0
Шифр: (И/Ж-B87) 02
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List of Figures ................................................ xi
List of Tables ............................................... xvii
Preface ....................................................... xix
Authors ....................................................... xxi
1 Introduction ................................................. 1
1.1 Generalized Transport Phenomena Approach to Problem
Analysis ................................................ 1
1.2 General Content ......................................... 3
2 Conservation Laws and Field Equations ........................ 5
2.1 Concentrations, Velocities, and Fluxes .................. 5
2.2 Thermodynamics of Purely Viscous Fluid Mixtures ......... 9
2.3 Conservation of Mass for a One-Component System ........ 13
2.4 4 Conservation of Mass for a Mixture ................... 14
2.5 Modification of Field Equations for Mass Transfer ...... 16
2.6 Conservation of Linear Momentum for One-Component
Systems ................................................ 21
2.7 Conservation of Linear Momentum for a Mixture .......... 25
2.8 Conservation of Moment of Momentum for One-Component
Systems ................................................ 27
2.9 Conservation of Moment of Momentum for a Mixture ....... 29
2.10 Strategies for the Solution of Mass Transfer Problems .. 30
3 Boundary Conditions ......................................... 33
3.1 Definitions ............................................ 33
3.2 Jump Balances for Mass Conservation .................... 34
3.3 Jump Balances for Linear Momentum Conservation ......... 36
3.4 Postulated Boundary Conditions at Phase Interfaces ..... 37
3.5 Boundary Conditions in the Absence of Mass Transfer .... 38
3.6 Utilization of Jump Balances ........................... 41
3.7 Additional Comments on Boundary Conditions ............. 45
3.8 Boundary Conditions and Uniqueness of Solutions ........ 50
4 Constitutive Equations ...................................... 55
4.1 Constitutive Principles ................................ 55
4.1.1 Principle of Determinism ........................ 56
4.1.2 Principle of Equipresence ....................... 56
4.1.3 Principle of Local Action ....................... 56
4.1.4 Principle of Material Frame Indifference ........ 58
4.1.5 Principle of Material Invariance ................ 64
4.1.6 Principle of Dissipation (Entropy Inequality) ... 65
4.2 First-Order Theory for Binary Systems .................. 68
4.3 Combined Field and Constitutive Equations for First-
Order Binary Theory .................................... 73
4.4 First-Order Theory for Ternary Systems ................. 77
4.5 Special Second-Order Theory for Binary Systems ......... 80
4.6 Viscoelastic Effects in Flow and Diffusion ............. 85
4.6.1 Deborah Number .................................. 86
4.6.2 Constitutive Expression for the Extra Stress
for a First-Order Fluid ......................... 88
4.6.3 Viscoelastic Diffusion Flux ..................... 91
4.7 Validity of Constitutive Equations ................... 93
5 Parameters in Constitutive Equations ........................ 99
5.1 General Approach in Parameter Determination ............ 99
5.2 Diffusion in Polymer-Solvent Mixtures ................. 100
5.3 Diffusion in Infinitely Dilute Polymer Solutions ...... 104
5.4 Diffusion in Dilute Polymer Solutions ................. 107
5.5 Diffusion in Concentrated Polymer Solutions -
Free-Volume Theory for Self-Diffusion ................. 111
5.5.1 Volumetric Behavior for Rubbery Polymer-
Solvent Systems ................................ 112
5.5.2 Volumetric Behavior for Glassy Polymer-
Solvent Systems ................................ 116
5.5.3 Formulation of Equations for Self-Diffusion
Coefficients ................................... 119
5.5.4 Formulation of Predictive Method for Dj ........ 121
5.5.5 Predictions of Dx .............................. 123
5.5.6 Self-Diffusion for Ternary Systems ............. 127
5.6 4 Diffusion in Concentrated Polymer Solutions -
Mutual Diffusion Process .............................. 128
5.7 Diffusion in Crosslinked Polymers ..................... 137
5.8 Additional Properties of Diffusion Coefficients ....... 140
6 Special Behaviors of Polymer-Penetrant Systems ............. 149
6.1 Volumetric Behavior of Polymer-Penetrant Systems ...... 149
6.2 Sorption Behavior of Polymer-Penetrant Systems ........ 154
6.3 Antiplasticization .................................... 166
6.4 Nonequilibrium at Polymer-Penetrant Interfaces ........ 169
7 Mathematical Apparatus ..................................... 175
7.1 Basic Definitions ..................................... 175
7.2 Classification of Second-Order Partial Differential
Equations ............................................. 179
7.3 Specification of Boundary Conditions .................. 182
7.4 Sturm-Liouville Theory ................................ 184
7.5 Series and Integral Representations of Functions ...... 189
7.6 Solution Methods for Partial Differential Equations ... 193
7.7 Separation of Variables Method ........................ 194
7.8 Separation of Variables Solutions ..................... 196
7.9 Integral Transforms ................................... 204
7.10 Similarity Transformations ............................ 212
7.11 Green's Functions for Ordinary Differential
Equations ............................................. 214
7.12 Green's Functions for Elliptic Equations .............. 222
7.13 Green's Functions for Parabolic Equations ............. 229
7.14 Perturbation Solutions ................................ 235
7.15 Weighted Residual Method .............................. 237
8 Solution Strategy for Mass Transfer Problems ............... 241
8.1 Proposed Solution Methods ............................. 241
8.2 Induced Convection .................................... 244
9 Solutions of a General Set of Mass Transfer Problems ....... 249
9.1 Mixing of Two Ideal Gases ............................. 249
9.2 Steady Evaporation of a Liquid in a Tube .............. 255
9.3 Unsteady-State Evaporation ............................ 258
9.4 Analysis of Free Diffusion Experiments ................ 262
9.5 Dissolution of a Rubbery Polymer ...................... 265
9.6 Bubble Growth from Zero Initial Size .................. 273
9.7 Stability Behavior and Negative Concentrations in
Ternary Systems ....................................... 277
9.8 Analysis of Impurity Migration in Plastic Containers .. 282
9.9 Efficiency of Green's Function Solution Method ........ 286
9.10 Mass Transfer in Tube Flow ............................ 288
9.11 Time-Dependent Interfacial Resistance ................. 294
9.12 Laminar Liquid Jet Diffusion Analysis ................. 299
9.13 Analysis of the Diaphragm Cell ........................ 300
9.14 Dissolved Organic Carbon Removal from Marine
Aquariums ............................................. 304
9.15 Unsteady Diffusion in a Block Copolymer ............... 308
9.16 Drying of Solvent-Coated Polymer Films ................ 314
9.17 Flow and Diffusion Past a Flat Plate with Solid
Dissolution ........................................... 318
9.18 4 Gas Absorption in Vertical Laminar Liquid Jets ...... 324
9.19 Utilization of Polymers in Drug Delivery .............. 329
9.20 Gas Absorption and Diffusion into a Falling Liquid
Film .................................................. 336
10 Perturbation Solutions of Mass Transfer Moving Boundary
Problems ................................................... 339
10.1 Dissolution of a Plane Surface of a Pure Gas Phase .... 340
10.2 Bubble Dissolution .................................... 347
10.3 Singular Perturbations in Moving Boundary Problems .... 350
10.4 Dropping Mercury Electrode ............................ 359
10.5 Sorption in Thin Films ................................ 364
10.6 Numerical Analysis of Mass Transfer Moving Boundary
Problems .............................................. 370
11 Diffusion and Reaction ..................................... 373
11.1 Design of a Tubular Polymerization Reactor ............ 373
11.2 Transport Effects in Low-Pressure CVD Reactors ........ 381
11.3 Solution of Reaction Problems with First-Order
Reactions ............................................. 385
11.4 Plug Flow Reactors with Variable Mass Density ......... 393
11.5 Bubble Dissolution and Chemical Reaction .............. 395
11.6 Danckwerts Boundary Conditions for Chemical Reactors .. 398
12 Transport in Nonporous Membranes ........................... 407
12.1 Assumptions Used in the Theory for Membrane
Transport ............................................. 407
12.2 Steady Mass Transport in Binary Membranes ............. 412
12.3 Steady Mass Transport in Ternary Membranes ............ 414
12.3.1 Gas Separations ................................ 416
12.3.2 Solvent Drag ................................... 418
12.3.3 Osmotic Effects ................................ 419
12.4 Unsteady Mass Transport in Binary Membranes ........... 422
12.5 Phase Inversion Process for Forming Asymmetric
Membranes ............................................. 427
12.6 Pressure Effects in Membranes ......................... 431
13 Analysis of Sorption and Desorption ........................ 433
13.1 Derivation of a Short-Time Solution Form for
Sorption in Thin Films ................................ 435
13.2 Sorption to a Film from a Pure Fluid of Finite
Volume ................................................ 437
13.3 A General Analysis of Sorption in Thin Films .......... 442
13.4 Analysis of Step-Change Sorption Experiments .......... 448
13.5 Integral Sorption in Glassy Polymers .................. 450
13.6 Integral Sorption in Rubbery Polymers ................. 461
13.7 Oscillatory Diffusion and Diffusion Waves ............. 466
14 Dispersion and Chromatography .............................. 473
14.1 Formulation of Taylor Dispersion Problem .............. 473
14.2 Dispersion in Laminar Tube Flow for Low Peclet
Numbers ............................................... 478
14.3 Dispersion in Laminar Tube Flow for Long Times ........ 483
14.4 Dispersion in Laminar Tube Flow for Short Times 486
14.5 Analysis of an Inverse Gas Chromatography
Experiment ............................................ 490
15 Effects of Pressure Gradients on Diffusion: Wave Behavior
and Sedimentation .......................................... 499
15.L Wave Propagation in Binary Fluid Mixtures ............. 499
15.2 Hyperbolic Waves ...................................... 503
15.3 Dispersive Waves ...................................... 505
15.4 Time Effects for Parabolic and Hyperbolic Equations ... 507
15.5 Sedimentation Equilibrium ............................. 511
16 Viscoelastic Diffusion ..................................... 515
16.1 Experimental Results for Sorption Experiments ......... 515
16.2 Viscoelastic Effects in Step-Change Sorption
Experiments ........................................... 524
16.3 Slow Bubble Dissolution in a Viscoelastic Fluid ....... 530
17 Transport with Moving Reference Frames ..................... 545
17.1 Relationships between Fixed and Moving Reference
Frames ................................................ 545
17.2 Field Equations in Moving Reference Frames ............ 548
17.3 Steady Diffusion in an Ultracentrifuge ................ 552
17.4 Material Time Derivative Operators .................... 554
17.5 Frame Indifference of Material Time Derivatives ....... 557
17.6 Frame Indifference of Velocity Gradient Tensor ........ 560
17.7 Rheological Implications .............................. 562
Appendix: Vector and Tensor Notation .......................... 565
A.l General Notation Conventions .......................... 565
A.2 Vectors ............................................... 566
A.3 Tensors ............................................... 569
A.4 Results for Curvilinear Coordinates ................... 576
A.5 Material and Spatial Representations .................. 578
A.6 Reynolds' Transport Theorem ........................... 583
References ................................................. 587
Index ......................................................... 599
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