Mass Transfer Processes
Modeling, Computations, and Design
International Series in the Physical and Chemical Engineering Sciences Series

The All-in-One Guide to Mass Transport Phenomena: From Theory to Examples and Computation

Mass transfer processes exist in practically all engineering fields and many biological systems; understanding them is essential for all chemical engineering students, and for practitioners in a broad range of practices, such as biomedical engineering, environmental engineering, material engineering, and the like. Mass Transfer Processes combines a modern, accessible introduction to modeling and computing these processes with demonstrations of their application in designing reactors and separation systems.

P. A. Ramachandran?s integrated approach balances all the knowledge readers need to be effective, rather than merely paying lip service to some crucial topics. He covers both analytical and numerical solutions to mass transfer problems, demonstrating numerical problem-solving with widely used software packages, including MATLAB and CHEBFUN. Throughout, he links theory to realistic examples, both traditional and contemporary.

• Theory, examples, and in-depth coverage of differential, macroscopic, and mesoscopic modeling
• Physical chemistry aspects of diffusion phenomena
• Film models for calculating local mass transfer rates and diffusional interaction in gas?solid and gas?liquid reaction systems
• Application of mass transfer models in rate-based separation processes, and systems with simultaneous heat and mass transfer
• Convective mass transfer: empirical correlation, internal and external laminar flows, and turbulent flows
• Heterogeneous systems, from laminar flow reactors, diffusion-reaction models, reactive membranes, and electrochemical reactors
• Computations of mass transfer effects in multicomponent systems
• Solid?gas noncatalytic reactions for chemical, metallurgical, environmental, and electronic processes
• Applications in electrochemical and biomedical systems
• Design calculations for humidification, drying, and condensation systems and membrane-based separations
• Analysis of adsorption, chromatography, electrodialysis, and electrophoresis

1.1 What Is Mass Transfer? 5

1.2 Preliminaries: Continuum and Concentration 7

1.3 Flux Vector 10

1.4 Concentration Jump at Interface 15

1.5 Application Examples 20

1.6 Basic Methodology of Model Development 28

1.7 Conservation Principle 29

1.8 Differential Models 30

1.9 Macroscopic Scale 32

1.10 Mesoscopic or Cross-Section Averaged Models 37

1.11 Compartmental Models 43

Chapter 2: Examples of Differential (1-D) Balances 51

2.1 Cartesian Coordinates 52

2.2 Cylindrical Coordinates 67

2.3 Spherical Coordinates 73

Chapter 3: Examples of Macroscopic Models 85

3.1 Macroscopic Balance 87

3.2 The Batch Reactor 90

3.3 Reactor–Separator Combination 96

3.4 Sublimation of a Spherical Particle 101

3.5 Dissolved Oxygen Concentration in a Stirred Tank 104

3.6 Continuous Stirred Tank Reactor 106

3.7 Tracer Experiments: Test for Backmixed Assumption 110

3.8 Liquid–Liquid Extraction 112

Chapter 4: Examples of Mesoscopic Models 123

4.1 Solid Dissolution from a Wall 124

4.2 Tubular Flow Reactor 129

4.3 Mass Exchangers 134

Chapter 5: Equations of Mass Transfer 151

5.1 Flux Form 153

5.2 Frame of Reference 156

5.3 Properties of Diffusion Flux 163

5.4 Pseudo-Binary Diffusivity 165

5.5 Concentration Form 166

5.6 Common Boundary Conditions 171

5.7 Macroscopic Models: Single-Phase Systems 172

5.8 Multiphase Systems: Local Volume Averaging 175

Chapter 6: Diffusion-Dominated Processes and the Film Model 185

6.1 Steady State Diffusion: No Reaction 186

6.2 Diffusion-Induced Convection 193

6.3 Film Concept in Mass Transfer Analysis 198

6.4 Surface Reactions: Role of Mass Transfer 206

6.5 Gas–Liquid Interface: Two-Film Model 212

Chapter 7: Phenomena of Diffusion 223

7.1 Diffusion Coeffcients in Gases 224

7.2 Diffusion Coeffcients in Liquids 237

7.3 Non-Ideal Liquids 243

7.4 Solid–Solid Diffusion 246

7.5 Diffusion of Fluids in Porous Solids 248

7.6 Heterogeneous Media 254

7.7 Polymeric Membranes 256

7.8 Other Complex Effects 257

Chapter 8: Transient Diffusion Processes 265

8.1 Transient Diffusion Problems in 1-D 266

8.2 Solution for Slab: Dirichlet Case 267

8.3 Solutions for Slab: Robin Condition 276

8.4 Solution for Cylinders and Spheres 278

8.5 Transient Non-Homogeneous Problems 283

8.6 2-D Problems: Product Solution Method 285

8.7 Semi-Infinite Slab Analysis 287

8.8 Penetration Theory of Mass Transfer 294

8.9 Transient Diffusion with Variable Diffusivity 295

8.10 Eigenvalue Computations with CHEBFUN 297

8.11 Computations with PDEPE Solver 299

Chapter 9: Basics of Convective Mass Transport 309

9.1 Definitions for External and Internal Flows 310

9.2 Relation to Differential Model 311

9.3 Key Dimensionless Groups 313

9.4 Mass Transfer in Flows in Pipes and Channels 315

9.5 Mass Transfer in Flow over a Flat Plate 316

9.6 Mass Transfer for Film Flow 318

9.7 Mass Transfer from a Solid Sphere 320

9.8 Mass Transfer from a Gas Bubble 321

9.9 Mass Transfer in Mechanically Agitated Tanks 325

9.10 Gas–Liquid Mass Transfer in a Packed Bed Absorber 327

Chapter 10: Convective Mass Transfer: Theory for Internal Laminar Flow 335

10.1 Mass Transfer in Laminar Flow in a Pipe 336

10.2 Wall Reaction: The Robin Problem 344

10.3 Entry Region Analysis 348

10.4 Channel Flows with Mass Transfer 350

10.5 Mass Transfer in Film Flow 353

10.6 Numerical Solution with PDEPE 358

Chapter 11: Mass Transfer in Laminar Boundary Layers 365

11.1 Flat Plate with Low Flux Mass Transfer 366

11.2 Integral Balance Approach 376

11.3 High Flux Analysis 383

11.4 Mass Transfer for Flow over Inclined and Curved Surfaces 388

11.5 Bubbles and Drops 396

Chapter 12: Convective Mass Transfer in Turbulent Flow 403

12.1 Properties of Turbulent Flow 404

12.2 Properties of Time Averaging 406

12.3 Time-Averaged Equation of Mass Transfer 408

12.4 Closure Models 411

12.5 Velocity and Turbulent Diffusivity Profiles 413

12.6 Turbulent Mass Transfer in Channels and Pipes 417

12.7 Van Driest Model for Large Sc 425

12.8 Turbulent Mass Transfer at Gas–Liquid Interface 427

Chapter 13: Macroscopic and Compartmental Models 435

13.1 Stirred Reactor: The Backmixing Assumption 436

13.2 Transient Balance: Tracer Studies 438

13.3 Moment Analysis of Tracer Data 444

13.4 Tanks in Series Models: Reactor Performance 449

13.5 Macrofluid Models 450

13.6 Variance-Based Models for Partial Micromixing 453

13.7 Compartmental Models 454

13.8 Compartmental Models for Environmental Transport 459

13.9 Fluid–Fluid Systems 462

13.10 Models for Multistage Cascades 465

Chapter 14: Mesoscopic Models and the Concept of Dispersion 475

14.1 Plug Flow Idealization 476

14.2 Dispersion Model 478

14.3 Dispersion Coeffcient: Tracer Response Method 484

14.4 Taylor Model for Dispersion in Laminar Flow 488

14.5 Segregated Flow Model 491

14.6 Dispersion Coe[1]cient Values for Some Common Cases 493

14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns 495

14.8 Tracer Response in Two-Phase Systems 503

Chapter 15: Mass Transfer: Multicomponent Systems 517

15.1 Constitutive Model for Multicomponent Transport 518

15.2 Computations for a Reacting System 520

15.3 Heterogeneous Reactions 525

15.4 Non-Reacting Systems 528

15.5 Multicomponent Diffusivity Matrix 535

Chapter 16: Mass Transport in Electrolytic Systems 543

16.1 Transport of Charged Species: Preliminaries 544

16.2 Charge Neutrality 547

16.3 General Expression for the Electric Field 548

16.4 Electrolyte Transport across Uncharged Membrane 551

16.5 Transport across a Charged Membrane 553

16.6 Transfer Rate in Diffusion Film near an Electrode 556

17.1 Model Equations and Key Dimensionless Groups 568

17.2 Two Limiting Cases 572

17.3 Mesoscopic Dispersion Model 575

17.4 Other Examples of Flow Reactors 577

Chapter 18: Mass Transfer with Reaction: Porous Catalysts 585

18.1 Catalyst Properties and Applications 586

18.2 Diffusion-Reaction Model 588

18.3 Multiple Species 605

18.4 Three-Phase Catalytic Reactions 607

18.5 Temperature Effects in a Porous Catalyst 610

18.6 Orthogonal Collocation Method 615

18.7 Finite Difference Methods 617

18.8 Linking with Reactor Models 622

Chapter 19: Reacting Solids 635

19.1 Shrinking Core Model 636

19.2 Volume Reaction Model 644

19.3 Other Models for Gas–Solid Reactions 651

19.4 Solid–Solid Reactions 654

20.1 First-Order Reaction of Dissolved Gas 662

20.2 Bulk Concentration and Bulk Reactions 668

20.3 Bimolecular Reactions 672

20.4 Simultaneous Absorption of Two Gases 684

20.5 Coupling with Reactor Models 688

20.6 Absorption in Slurries 692

20.7 Liquid–Liquid Reactions 697

Chapter 21: Gas–Liquid Reactions: Penetration Theory Approach 705

21.1 Concepts of Penetration Theory 706

21.2 Bimolecular Reaction 712

21.3 Instantaneous Reaction Case 714

21.4 Ideal Contactors 717

Chapter 22: Reactive Membranes and Facilitated Transport 727

22.1 Single Solute Diffusion 729

22.2 Co- and Counter-Transport 736

22.3 Equilibrium Model: A Computational Scheme 739

22.4 Reactive Membranes in Practice 742

Chapter 23: Biomedical Applications 749

23.1 Oxygen Uptake in Lungs 751

23.2 Transport in Tissues: Krogh Model 757

23.3 Compartmental Models for Pharmacokinetics 760

23.4 Model for a Hemodialyzer 763

Chapter 24 Electrochemical Reaction Engineering 775

24.1 Basic Definitions 776

24.2 Thermodynamic Considerations: Nernst Equation 781

24.3 Kinetic Model for Electrochemical Reactions 786

24.4 Mass Transfer Eects 791

24.5 Voltage Balance 793

24.6 Copper Electrowinning 795

24.7 Hydrogen Fuel Cell 798

24.8 Li-Ion Battery Modeling 800

25.1 Wet and Dry Bulb Temperature 812

25.2 Humidification: Cooling Towers 815

25.3 Model for Counterflow 817

25.4 Cross-Flow Cooling Towers 825

25.5 Drying 827

25.6 Constant Rate Period 830

25.7 Falling Rate Period 833

Chapter 26: Condensation 845

26.1 Condensation of Pure Vapor 846

26.2 Condensation of a Vapor with a Non-Condensible Gas 850

26.3 Fog Formation 855

26.4 Condensation of Binary Gas Mixture 857

26.5 Condenser Model 861

26.6 Ternary Systems 864

27.1 Gas Separation Membranes 872

27.2 Gas Translation Model 879

27.3 Gas Permeator Models 881

27.4 Reactor Coupled with a Membrane Separator 890

28.1 Classification Based on Pore Size 898

28.2 Transport in Semi-Permeable Membranes 900

28.3 Forward Osmosis 907

28.4 Pervaporation 908

Chapter 29: Adsorption and Chromatography 919

29.1 Applications and Adsorbent Properties 920

29.2 Isotherms 921

29.3 Model for Batch Slurry Adsorber 924

29.4 Fixed Bed Adsorption 931

29.5 Chromatography 938

Chapter 30: Electrodialysis and Electrophoresis 945

30.1 Technological Aspects 946

30.2 Preliminary Design of an Electrodialyzer 951

30.3 Principle of Electrophoresis 955

30.4 Electrophoretic Separation Devices 957

P. A. Ramachandran is a professor at Washington University at St. Louis in the energy, environmental, and chemical engineering department. He holds bachelors and doctoral degrees in chemical engineering from the Bombay University Department of Chemical Technology. He has extensive teaching experience in transport phenomena, reaction engineering, and applied mathematics. His research interest is mainly in the application of transport phenomena principles to chemically reacting systems and development of continuum based models for multiphase reactor design. He is the author of Boundary Element Methods in Transport Phenomena and Advanced Transport Phenomena, and coauthor of Three-Phase Catalytic Reactors.

• Balances theory, computation, and examples spanning a wide spectrum of mass transfer fundamentals, applications, and phenomena
• Covers both analytical and package-based numerical solutions to mass transfer problems
• Includes sample applications and code snippets throughout, to complement explanations and reinforce key points
• Provides clear, complete coverage of reactive systems, including basic theory of rate processes, and practical modeling