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

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

Table of Contents:
Preface xxix About the Author xxxvii Notation xxxix   Part I: Fundamentals of Mass Transfer Modeling 1   Chapter 1: Introduction to Modeling of Mass Transfer Processes 3 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   Part II: Reacting Systems 565   Chapter 17: Laminar Flow Reactor 567 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   Chapter 20: Gas–Liquid Reactions: Film Theory Models 661 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   Part III: Mass Transfer–Based Separations 809   Chapter 25: Humidification and Drying 811 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   Chapter 27: Gas Transport in Membranes 871 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   Chapter 28: Liquid Separation Membranes 897 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   References 965 Index 979

About the Author :
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.