Diffusion and mass transfer / James S. Vrentas, Christine M. Vrentas.

Format:

Book

Author/Creator:

Vrentas, James S.

Contributor:

Vrentas, Christine Mary Jarzebski, 1953-

Anne and Joseph Trachtman Memorial Book Fund.

Language:

English

Subjects (All):

Diffusion.

Mass transfer.

Physical Description:

xxi, 622 pages : illustrations ; 26 cm

Place of Publication:

Boca Raton : CRC Press, Taylor & Francis Group, c2013.

Summary:

A proper understanding of diffusion and mass transfer theory is critical for obtaining correct solutions to many transport problems. Diffusion and Mass Transfer presents a comprehensive summary of the theoretical aspects of diffusion and mass transfer and applies that theory to obtain detailed solutions for a large number of important problems. Particular attention is paid to various aspects of polymer behavior, including polymer diffusion, sorption in polymers, and volumetric behavior of polymer-solvent systems.

The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green's function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer-solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedimentation, drying of polymer films, and chromatography.

Presenting diffusion and mass transfer from both engineering and fundamental science perspectives, this book can be used as a text for a graduate-level course as well as a reference text for research in diffusion and mass transfer. The book includes mass transfer effects in polymers, which are very important in many industrial processes. The attention given to the proper setup of numerous problems along with the explanations and use of mathematical solution methods will help readers in properly analyzing mass transfer problems. Book jacket.

Contents:

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 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 D₁ 121

5.5.5 Predictions of D₁ 123

5.5.6 Self-Diffusion for Ternary Systems 127

5.6 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 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

15.1 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.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

1466515686

9781466515680

OCLC:

772111278

Publisher Number:

99953678567