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Mass Transfer Processes: Modeling, Computations, and Design, First Edition

Book Description

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

  1. Cover Page
  2. About This E-Book
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Preface
    1. Key Distinguishing Features
    2. Intended Audience
    3. Style of Presentation
    4. Topical Outline
      1. Part I
      2. Part II
      3. Part III
    5. For Instructors
    6. Acknowledgments
  7. About the Author
  8. Notation
    1. Greek Letters
    2. Common Subscripts
    3. Acronyms
  9. Part I: Fundamentals of Mass Transfer Modeling
    1. Chapter 1. Introduction to Modeling of Mass Transfer Processes
      1. 1.1 What Is Mass Transfer?
        1. 1.1.1 What Is Interfacial Mass Transfer?
        2. 1.1.2 What Causes Mass Transfer?
      2. 1.2 Preliminaries: Continuum and Concentration
        1. 1.2.1 The Continuum Assumption
        2. 1.2.2 Concentration: Mole Units
        3. 1.2.3 Concentration: Mass Units
        4. 1.2.4 Concentration: Partial Pressure Units
      3. 1.3 Flux Vector
        1. 1.3.1 Molar and Mass Flux: Definition
        2. 1.3.2 Convection Flux
        3. 1.3.3 Diffusion Flux
      4. 1.4 Concentration Jump at Interface
        1. 1.4.1 Gas–Liquid Interface: Henry’s Law
        2. 1.4.2 Vapor–Liquid Interface: Raoult’s Law
        3. 1.4.3 Liquid–Liquid Interface: Partition Constant
        4. 1.4.4 Fluid–Solid Interface: Adsorption Isotherm
        5. 1.4.5 Nonlinear Equilibrium Models
      5. 1.5 Application Examples
        1. 1.5.1 Reacting Systems
        2. 1.5.2 Unit Operations
        3. 1.5.3 Bioseparations
        4. 1.5.4 Semiconductor and Solar Devices
        5. 1.5.5 Biomedical Applications
        6. 1.5.6 Application to Metallurgy and Metal Winning
        7. 1.5.7 Product Development and Product Engineering
        8. 1.5.8 Electrochemical Processes
        9. 1.5.9 Environmental Applications
      6. 1.6 Basic Methodology of Model Development
      7. 1.7 Conservation Principle
      8. 1.8 Differential Models
      9. 1.9 Macroscopic Scale
        1. 1.9.1 Stirred Tank Reactor: Mixing Model
        2. 1.9.2 Sublimation of a Solid Sphere: Mass Transfer Coefficient
        3. 1.9.3 Model for Mixer-Settler
        4. 1.9.4 Equilibrium Stage Model
      10. 1.10 Mesoscopic or Cross-Section Averaged Models
        1. 1.10.1 Solid Dissolution from a Wall
        2. 1.10.2 Tubular Flow Reactor
      11. 1.11 Compartmental Models
      12. Summary
      13. Review Questions
      14. Problems
    2. Chapter 2. Examples of Differential (1-D) Balances
      1. 2.1 Cartesian Coordinates
        1. 2.1.1 Steady State Diffusion across a Slab
        2. 2.1.2 Steady State Diffusion with Reaction in a Slab
        3. 2.1.3 Transient Diffusion in a Slab
        4. 2.1.4 Diffusion with Convection
      2. 2.2 Cylindrical Coordinates
        1. 2.2.1 Steady State Radial Diffusion
        2. 2.2.2 Steady State Mass Transfer with Reaction
        3. 2.2.3 Transient Diffusion in a Cylinder
      3. 2.3 Spherical Coordinates
        1. 2.3.1 Steady State Diffusion across a Spherical Shell
        2. 2.3.2 Diffusion and Reaction
        3. 2.3.3 Transient Diffusion in Spherical Coordinates
      4. Summary
      5. Review Questions
      6. Problems
    3. Chapter 3. Examples of Macroscopic Models
      1. 3.1 Macroscopic Balance
        1. 3.1.1 In and Out Terms from Flow
        2. 3.1.2 Wall or Interface Transfer Term
        3. 3.1.3 Rate Term
        4. 3.1.4 Accumulation Term
      2. 3.2 The Batch Reactor
        1. 3.2.1 Differential Equations for the Reactor
        2. 3.2.2 ODE45 with CHEBFUN
      3. 3.3 Reactor–Separator Combination
      4. 3.4 Sublimation of a Spherical Particle
        1. 3.4.1 Correlation for Mass Transfer Coefficient
      5. 3.5 Dissolved Oxygen Concentration in a Stirred Tank
      6. 3.6 Continuous Stirred Tank Reactor
        1. 3.6.1 First-Order Reaction
        2. 3.6.2 Second-Order Reaction
      7. 3.7 Tracer Experiments: Test for Backmixed Assumption
        1. 3.7.1 Interconnected Cells Model
        2. 3.7.2 Model Composed of Active and Dead Zone
      8. 3.8 Liquid–Liquid Extraction
        1. 3.8.1 Mass Transfer Rate
        2. 3.8.2 Backmixed–Backmixed Model
        3. 3.8.3 Equilibrium Stage Model
        4. 3.8.4 Stage Efficiency
      9. Summary
      10. Review Questions
      11. Problems
    4. Chapter 4. Examples of Mesoscopic Models
      1. 4.1 Solid Dissolution from a Wall
        1. 4.1.1 Model Details
        2. 4.1.2 Mass Transfer Correlations in Pipe Flow
      2. 4.2 Tubular Flow Reactor
        1. 4.2.1 Plug Flow Closure
        2. 4.2.2 Dispersion Closure
      3. 4.3 Mass Exchangers
        1. 4.3.1 Single Stream
        2. 4.3.2 Two Streams
        3. 4.3.3 NTU and HTU Representation
      4. Summary
      5. Review Questions
      6. Problems
    5. Chapter 5. Equations of Mass Transfer
      1. 5.1 Flux Form
        1. 5.1.1 Mole Basis
        2. 5.1.2 Mass Basis
      2. 5.2 Frame of Reference
        1. 5.2.1 Mass Fraction Averaged Velocity
        2. 5.2.2 Mole Fraction Averaged Velocity
      3. 5.3 Properties of Diffusion Flux
      4. 5.4 Pseudo-Binary Diffusivity
      5. 5.5 Concentration Form
        1. 5.5.1 Mass Basis
        2. 5.5.2 Constant-Density Systems
        3. 5.5.3 Overall Continuity: Mass Basis
        4. 5.5.4 Mole Basis
        5. 5.5.5 Overall Continuity: Mole Basis
        6. 5.5.6 Common Simplifications
      6. 5.6 Common Boundary Conditions
      7. 5.7 Macroscopic Models: Single-Phase Systems
      8. 5.8 Multiphase Systems: Local Volume Averaging
      9. Summary
      10. Review Questions
      11. Problems
    6. Chapter 6. Diffusion-Dominated Processes and the Film Model
      1. 6.1 Steady State Diffusion: No Reaction
        1. 6.1.1 Combined Flux Equation
        2. 6.1.2 Diffusion-Induced Convection
        3. 6.1.3 Determinacy Condition
        4. 6.1.4 Low Flux Model: The Laplace Equation
      2. 6.2 Diffusion-Induced Convection
        1. 6.2.1 Conditions for the Validity of the Low Flux Model
        2. 6.2.2 Analysis for UMD
        3. 6.2.3 Drift Flux Correction Factor
        4. 6.2.4 Mole Fraction Profiles in UMD
      3. 6.3 Film Concept in Mass Transfer Analysis
        1. 6.3.1 Boundary Layer Concept for Fluid–Solid Mass Transfer
        2. 6.3.2 Film Model Approximation
        3. 6.3.3 Film Model: Determinacy Correction Factor
      4. 6.4 Surface Reactions: Role of Mass Transfer
        1. 6.4.1 Low Flux Model: First-Order Reaction
        2. 6.4.2 Low Flux Model: Nonlinear Reactions
        3. 6.4.3 High Flux Model: Effect of Product Counter-Diffusion
      5. 6.5 Gas–Liquid Interface: Two-Film Model
        1. 6.5.1 Mass Transfer Coefficients
        2. 6.5.2 Overall Mass Transfer Coefficient
      6. Summary
      7. Review Questions
      8. Problems
    7. Chapter 7. Phenomena of Diffusion
      1. 7.1 Diffusion Coefficients in Gases
        1. 7.1.1 Model Based on Kinetic Theory
        2. 7.1.2 Frictional Interpretation
        3. 7.1.3 Multicomponent Diffusion
      2. 7.2 Diffusion Coefficients in Liquids
        1. 7.2.1 Stokes-Einstein Model
        2. 7.2.2 Wilke-Chang Equation
      3. 7.3 Non-Ideal Liquids
        1. 7.3.1 Activity Correction Factor
        2. 7.3.2 Activity Coefficient Models
      4. 7.4 Solid–Solid Diffusion
        1. 7.4.1 Vacancy Diffusion
        2. 7.4.2 Interstitial Diffusion
      5. 7.5 Diffusion of Fluids in Porous Solids
        1. 7.5.1 Single-Pore Gas Diffusion: Effect of Pore Size
        2. 7.5.2 Liquid-Filled Pores: Hindered Diffusion
        3. 7.5.3 Porous Catalysts: Effective Diffusivity
      6. 7.6 Heterogeneous Media
      7. 7.7 Polymeric Membranes
      8. 7.8 Other Complex Effects
      9. Summary
      10. Review Questions
      11. Problems
    8. Chapter 8. Transient Diffusion Processes
      1. 8.1 Transient Diffusion Problems in 1-D
      2. 8.2 Solution for Slab: Dirichlet Case
        1. 8.2.1 Dimensionless Representation
        2. 8.2.2 Series Solution
        3. 8.2.3 Evaluation of the Series Coefficient
        4. 8.2.4 Illustrative Results
        5. 8.2.5 Average Concentration
      3. 8.3 Solutions for Slab: Robin Condition
      4. 8.4 Solution for Cylinders and Spheres
        1. 8.4.1 Long Cylinder
        2. 8.4.2 Sphere
        3. 8.4.3 One-Term Approximation
      5. 8.5 Transient Non-Homogeneous Problems
        1. 8.5.1 D-D Problem in Slab Geometry
        2. 8.5.2 Transient Diffusion with Reaction
      6. 8.6 2-D Problems: Product Solution Method
      7. 8.7 Semi-Infinite Slab Analysis
        1. 8.7.1 Constant Surface Concentration
        2. 8.7.2 Integral Method
        3. 8.7.3 Pulse Response
      8. 8.8 Penetration Theory of Mass Transfer
      9. 8.9 Transient Diffusion with Variable Diffusivity
      10. 8.10 Eigenvalue Computations with CHEBFUN
      11. 8.11 Computations with PDEPE Solver
        1. 8.11.1 Sample Code for 1-D Transient Diffusion with Reaction
      12. Summary
      13. Review Questions
      14. Problems
    9. Chapter 9. Basics of Convective Mass Transport
      1. 9.1 Definitions for External and Internal Flows
      2. 9.2 Relation to Differential Model
      3. 9.3 Key Dimensionless Groups
        1. 9.3.1 Other Derived Dimensionless Groups
      4. 9.4 Mass Transfer in Flows in Pipes and Channels
        1. 9.4.1 Laminar Flow
        2. 9.4.2 Turbulent Flow
        3. 9.4.3 Channel Flow
      5. 9.5 Mass Transfer in Flow over a Flat Plate
        1. 9.5.1 Laminar Flow
        2. 9.5.2 Turbulent Flow
        3. 9.5.3 The j-Factor
      6. 9.6 Mass Transfer for Film Flow
        1. 9.6.1 Solid to Liquid
        2. 9.6.2 Gas to Liquid
      7. 9.7 Mass Transfer from a Solid Sphere
      8. 9.8 Mass Transfer from a Gas Bubble
        1. 9.8.1 Bubble Swarms and Bubble Columns
      9. 9.9 Mass Transfer in Mechanically Agitated Tanks
      10. 9.10 Gas–Liquid Mass Transfer in a Packed Bed Absorber
        1. 9.10.1 Liquid Side Coefficient
        2. 9.10.2 Gas Side Coefficient
        3. 9.10.3 Transfer Area
      11. Summary
      12. Review Questions
      13. Problems
    10. Chapter 10. Convective Mass Transfer: Theory for Internal Laminar Flow
      1. 10.1 Mass Transfer in Laminar Flow in a Pipe
        1. 10.1.1 Dimensionless Form
        2. 10.1.2 Constant Wall Concentration: The Dirichlet Problem
        3. 10.1.3 Concentration, Wall Mass Flux, and Sherwood Number
      2. 10.2 Wall Reaction: The Robin Problem
        1. 10.2.1 Solution Using CHEBFUN
        2. 10.2.2 Illustrative Results
      3. 10.3 Entry Region Analysis
      4. 10.4 Channel Flows with Mass Transfer
      5. 10.5 Mass Transfer in Film Flow
        1. 10.5.1 Solid Dissolution at a Wall in Film Flow
        2. 10.5.2 Gas Absorption from Interface in Film Flow
      6. 10.6 Numerical Solution with PDEPE
      7. Summary
      8. Review Questions
      9. Problems
    11. Chapter 11. Mass Transfer in Laminar Boundary Layers
      1. 11.1 Flat Plate with Low Flux Mass Transfer
        1. 11.1.1 Concentration Equation
        2. 11.1.2 Velocity Equations
        3. 11.1.3 Scaling Results and the Analogies
        4. 11.1.4 Exact or Blasius Analysis
      2. 11.2 Integral Balance Approach
        1. 11.2.1 Integral Momentum Balance
        2. 11.2.2 Integral Species Mass Balance
        3. 11.2.3 Solution for No Reaction Case
        4. 11.2.4 Solution for Homogeneous Reaction
      3. 11.3 High Flux Analysis
        1. 11.3.1 Film Model
        2. 11.3.2 Integral Balance Method
        3. 11.3.3 Blasius Approach
      4. 11.4 Mass Transfer for Flow over Inclined and Curved Surfaces
        1. 11.4.1 Pressure Variation Term
        2. 11.4.2 Integral Balance Method for Inclined and Curved Surfaces
        3. 11.4.3 Inclined Plates: Use of Similarity Variable
        4. 11.4.4 Wedge Flow: Falkner-Skan Equation
        5. 11.4.5 Stagnation Point (Hiemenz) Flow
        6. 11.4.6 Flow over a Rotating Disk
        7. 11.4.7 Flow past a Sphere
      5. 11.5 Bubbles and Drops
        1. 11.5.1 Rigid Bubbles
        2. 11.5.2 Spherical Cap Bubbles
      6. Summary
      7. Review Questions
      8. Problems
    12. Chapter 12. Convective Mass Transfer in Turbulent Flow
      1. 12.1 Properties of Turbulent Flow
        1. 12.1.1 Transition Criteria
        2. 12.1.2 Characteristics of Fully Turbulent Flow
        3. 12.1.3 Stochastic Nature
      2. 12.2 Properties of Time Averaging
      3. 12.3 Time-Averaged Equation of Mass Transfer
        1. 12.3.1 Turbulent Mass Flux
        2. 12.3.2 Reynolds Stresses
        3. 12.3.3 Reaction Contribution
      4. 12.4 Closure Models
        1. 12.4.1 Turbulent Schmidt Number
        2. 12.4.2 Prandtl’s Model for Eddy Viscosity
      5. 12.5 Velocity and Turbulent Diffusivity Profiles
        1. 12.5.1 Universal Velocity Profiles
        2. 12.5.2 Eddy Diffusivity Profiles
        3. 12.5.3 Wall Shear Stress Relations
      6. 12.6 Turbulent Mass Transfer in Channels and Pipes
        1. 12.6.1 Simplified Analysis: Constant Wall Flux
        2. 12.6.2 Stanton Number Calculation for Boundary Layers
        3. 12.6.3 Analogy with Momentum Transfer
        4. 12.6.4 Stanton Number for Pipe Flows
      7. 12.7 Van Driest Model for Large Sc
      8. 12.8 Turbulent Mass Transfer at Gas–Liquid Interface
        1. 12.8.1 Damping of Turbulence
        2. 12.8.2 Marangoni Effect
        3. 12.8.3 Interfacial Turbulence
      9. Summary
      10. Review Questions
      11. Problems
    13. Chapter 13. Macroscopic and Compartmental Models
      1. 13.1 Stirred Reactor: The Backmixing Assumption
      2. 13.2 Transient Balance: Tracer Studies
        1. 13.2.1 Step Input
        2. 13.2.2 Pulse or Bolus Input
        3. 13.2.3 Age Distribution Functions
        4. 13.2.4 Tracer Response for Tanks in Series Model
      3. 13.3 Moment Analysis of Tracer Data
        1. 13.3.1 Moments from Laplace Transform of Response
      4. 13.4 Tanks in Series Models: Reactor Performance
      5. 13.5 Macrofluid Models
        1. 13.5.1 Second-Order Reaction
        2. 13.5.2 Zero-Order Reaction
      6. 13.6 Variance-Based Models for Partial Micromixing
      7. 13.7 Compartmental Models
        1. 13.7.1 Matrix Representation
      8. 13.8 Compartmental Models for Environmental Transport
        1. 13.8.1 Fugacity of Pollutants in Each Compartment
        2. 13.8.2 Level I or Equilibrium Model
        3. 13.8.3 Level II Model: Advection Effects
        4. 13.8.4 Level III Model: Intermedia Transport Effects
        5. 13.8.5 Level IV Model: Transient Effects
      9. 13.9 Fluid–Fluid Systems
        1. 13.9.1 Backmixed–Backmixed Model
        2. 13.9.2 Equilibrium Model
        3. 13.9.3 Mixing Cell Model
      10. 13.10 Models for Multistage Cascades
        1. 13.10.1 Equilibrium Model
      11. Summary
      12. Review Questions
      13. Problems
    14. Chapter 14. Mesoscopic Models and the Concept of Dispersion
      1. 14.1 Plug Flow Idealization
      2. 14.2 Dispersion Model
        1. 14.2.1 Boundary Conditions
        2. 14.2.2 Solution for a First-Order Reaction
        3. 14.2.3 Nonlinear Reactions
        4. 14.2.4 Dispersion Model: Numerical Code Using CHEBFUN
        5. 14.2.5 Criteria for Negligible Dispersion
      3. 14.3 Dispersion Coefficient: Tracer Response Method
        1. 14.3.1 Laplace Domain Solution
        2. 14.3.2 Moments of the Response Curve
        3. 14.3.3 Time Domain Solution
      4. 14.4 Taylor Model for Dispersion in Laminar Flow
      5. 14.5 Segregated Flow Model
      6. 14.6 Dispersion Coefficient Values for Some Common Cases
      7. 14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns
        1. 14.7.1 Plug-Backmixed Model
        2. 14.7.2 Non-Idealities in Two-Phase Flow
      8. 14.8 Tracer Response in Two-Phase Systems
        1. 14.8.1 Single Flowing Phase
        2. 14.8.2 Two Flowing Phases
      9. Summary
      10. Review Questions
      11. Problems
    15. Chapter 15. Mass Transfer: Multicomponent Systems
      1. 15.1 Constitutive Model for Multicomponent Transport
        1. 15.1.1 Binary Revisited
        2. 15.1.2 Generalization: The Stefan-Maxwell Model
      2. 15.2 Computations for a Reacting System
      3. 15.3 Heterogeneous Reactions
      4. 15.4 Non-Reacting Systems
        1. 15.4.1 Evaporation of a Liquid in a Ternary Mixture
        2. 15.4.2 Evaporation of a Binary Liquid Mixture
        3. 15.4.3 Equimolar Counter-Diffusion
      5. 15.5 Multicomponent Diffusivity Matrix
        1. 15.5.1 D Matrix Relation to Binary Pair Diffusivity
    16. Chapter 16. Mass Transport in Electrolytic Systems
      1. 16.1 Transport of Charged Species: Preliminaries
        1. 16.1.1 Mobility and Diffusivity
        2. 16.1.2 Nernst-Planck Equation
      2. 16.2 Charge Neutrality
      3. 16.3 General Expression for the Electric Field
        1. 16.3.1 Laplace Equation for the Potential
        2. 16.3.2 Transference Number
        3. 16.3.3 Mass Balance for Reacting Systems
      4. 16.4 Electrolyte Transport across Uncharged Membrane
      5. 16.5 Transport across a Charged Membrane
        1. 16.5.1 Interfacial Jump: Donnan Equation
        2. 16.5.2 Transport Rate
      6. 16.6 Transfer Rate in Diffusion Film near an Electrode
      7. Summary
      8. Review Questions
      9. Problems
  10. Part II: Reacting Systems
    1. Chapter 17. Laminar Flow Reactor
      1. 17.1 Model Equations and Key Dimensionless Groups
        1. 17.1.1 Dimensionless Model Equations
        2. 17.1.2 Boundary Conditions
      2. 17.2 Two Limiting Cases
        1. 17.2.1 Small B: Pure Convection Model
        2. 17.2.2 Large B: Plug Flow Model
      3. 17.3 Mesoscopic Dispersion Model
      4. 17.4 Other Examples of Flow Reactors
        1. 17.4.1 Channel Flow
        2. 17.4.2 Non-Newtonian Fluids
        3. 17.4.3 Heat Transfer Effects
        4. 17.4.4 Turbulent Flow Reactor: 2-D Model
        5. 17.4.5 Axial Dispersion Model for the Turbulent Case
      5. Summary
      6. Review Questions
      7. Problems
    2. Chapter 18. Mass Transfer with Reaction: Porous Catalysts
      1. 18.1 Catalyst Properties and Applications
        1. 18.1.1 Catalyst Properties
      2. 18.2 Diffusion-Reaction Model
        1. 18.2.1 First-Order Reaction
        2. 18.2.2 Zero-Order Reaction
        3. 18.2.3 nth-Order Reaction
      3. 18.3 Multiple Species
      4. 18.4 Three-Phase Catalytic Reactions
        1. 18.4.1 Application Examples
        2. 18.4.2 Mass Transfer Effects
      5. 18.5 Temperature Effects in a Porous Catalyst
        1. 18.5.1 Equations for Heat and Mass Transport
        2. 18.5.2 Dimensionless Representation
        3. 18.5.3 Dimensionless Boundary Conditions
        4. 18.5.4 Estimate of the Temperature Gradients
      6. 18.6 Orthogonal Collocation Method
        1. 18.6.1 Basis of the Method
        2. 18.6.2 Two-Point Collocation
      7. 18.7 Finite Difference Methods
        1. 18.7.1 Central Difference Equations
        2. 18.7.2 Zero-Order Reaction
        3. 18.7.3 Nonlinear Kinetics
        4. 18.7.4 Neumann and Robin Conditions
      8. 18.8 Linking with Reactor Models
        1. 18.8.1 First-Order Reaction
        2. 18.8.2 Second-Order Reaction
        3. 18.8.3 Zero-Order Reaction
      9. Summary
      10. Review Questions
      11. Problems
    3. Chapter 19. Reacting Solids
      1. 19.1 Shrinking Core Model
        1. 19.1.1 No Solid Product
        2. 19.1.2 Solid Product: Ash Layer Effects
      2. 19.2 Volume Reaction Model
        1. 19.2.1 Kinetic Model
        2. 19.2.2 Concentration Profile for Gas and Solid
        3. 19.2.3 First-Order Reaction in B
        4. 19.2.4 Zero-Order Reaction
      3. 19.3 Other Models for Gas–Solid Reactions
        1. 19.3.1 Effect of Structural Changes
      4. 19.4 Solid–Solid Reactions
        1. 19.4.1 Classical Models
        2. 19.4.2 Dalvi-Suresh Contact Point Model
      5. Summary
      6. Review Questions
      7. Problems
    4. Chapter 20. Gas–Liquid Reactions: Film Theory Models
      1. 20.1 First-Order Reaction of Dissolved Gas
        1. 20.1.1 Boundary Conditions
        2. 20.1.2 Dimensionless Version
        3. 20.1.3 Flux Values at the Interface and into the Bulk
        4. 20.1.4 Enhancement Factor
      2. 20.2 Bulk Concentration and Bulk Reactions
        1. 20.2.1 Bulk Concentration
        2. 20.2.2 Absorption Rate Calculation for Ha < 0.2
      3. 20.3 Bimolecular Reactions
        1. 20.3.1 Dimensionless Representation
        2. 20.3.2 Invariance Property of the System
        3. 20.3.3 Analysis for Pseudo-First-Order Case
        4. 20.3.4 Analysis for Instantaneous Asymptote
        5. 20.3.5 Second-Order Case: An Approximate Solution
        6. 20.3.6 Instantaneous Case: Effect of Gas Film Resistance
        7. 20.3.7 Choice of Contactor Based on the Regimes of Absorption
      4. 20.4 Simultaneous Absorption of Two Gases
        1. 20.4.1 Model Equations
        2. 20.4.2 Dimensionless Representation
        3. 20.4.3 CHEBFUN Solution
      5. 20.5 Coupling with Reactor Models
        1. 20.5.1 Semibatch Reactor
        2. 20.5.2 Packed Column Absorber
      6. 20.6 Absorption in Slurries
        1. 20.6.1 Particle Size Effect
        2. 20.6.2 Instantaneous Reaction Case
      7. 20.7 Liquid–Liquid Reactions
      8. Summary
      9. Review Questions
      10. Problems
    5. Chapter 21. Gas–Liquid Reactions: Penetration Theory Approach
      1. 21.1 Concepts of Penetration Theory
        1. 21.1.1 First-Order or Pseudo-First-Order Reaction
        2. 21.1.2 Laplace Transform Method
        3. 21.1.3 Flux and the Average Rate of Mass Transfer
        4. 21.1.4 Relation between Film Theory and Penetration Theory
      2. 21.2 Bimolecular Reaction
        1. 21.2.1 Dimensionless Form of the Model
        2. 21.2.2 Illustrative Results
      3. 21.3 Instantaneous Reaction Case
      4. 21.4 Ideal Contactors
        1. 21.4.1 Laminar Jet Apparatus
        2. 21.4.2 Wetted Wall Column
        3. 21.4.3 Wetted Sphere
        4. 21.4.4 Stirred Cells
      5. Summary
      6. Review Questions
      7. Problems
    6. Chapter 22. Reactive Membranes and Facilitated Transport
      1. 22.1 Single Solute Diffusion
        1. 22.1.1 Model Equations
        2. 22.1.2 Dimensionless Representation
        3. 22.1.3 Invariant of the System
        4. 22.1.4 Instantaneous Reaction Asymptote
        5. 22.1.5 Pseudo-First-Order Reaction Asymptote
      2. 22.2 Co- and Counter-Transport
        1. 22.2.1 Model for Counter-Transport
        2. 22.2.2 Model for Co-Transport
      3. 22.3 Equilibrium Model: A Computational Scheme
        1. 22.3.1 Illustrative Results
      4. 22.4 Reactive Membranes in Practice
        1. 22.4.1 Emulsion Liquid Membranes (ELM)
        2. 22.4.2 Immobilized Liquid Membranes (ILM)
        3. 22.4.3 Fixed-Site Carrier Membranes
      5. Summary
      6. Review Questions
      7. Problems
    7. Chapter 23. Biomedical Applications
      1. 23.1 Oxygen Uptake in Lungs
        1. 23.1.1 Oxygen-Hemoglobin Equilibrium
        2. 23.1.2 Transport Steps for Oxygen Uptake
        3. 23.1.3 Meso-Model for the Capillary
      2. 23.2 Transport in Tissues: Krogh Model
        1. 23.2.1 Oxygen Variation in the Capillary
      3. 23.3 Compartmental Models for Pharmacokinetics
        1. 23.3.1 Basic Framework
        2. 23.3.2 Physiologically Based Compartments
      4. 23.4 Model for a Hemodialyzer
        1. 23.4.1 Model Formulation
        2. 23.4.2 Model for Patient-Dialyzer System
      5. Summary
      6. Review Questions
      7. Problems
    8. Chapter 24. Electrochemical Reaction Engineering
      1. 24.1 Basic Definitions
        1. 24.1.1 Anodic and Cathodic Reactions
        2. 24.1.2 Half Reactions and Overall Reaction
        3. 24.1.3 Classification of Electrode Reactions
        4. 24.1.4 Primary Variables
      2. 24.2 Thermodynamic Considerations: Nernst Equation
        1. 24.2.1 Equilibrium Cell Potential
      3. 24.3 Kinetic Model for Electrochemical Reactions
        1. 24.3.1 Butler-Volmer Equation
        2. 24.3.2 Tafel Equation
      4. 24.4 Mass Transfer Effects
        1. 24.4.1 Concentration Overpotential
      5. 24.5 Voltage Balance
      6. 24.6 Copper Electrowinning
        1. 24.6.1 Operating Current Density
        2. 24.6.2 Voltage Balance
        3. 24.6.3 Meso-Model for the Electrolyzer
      7. 24.7 Hydrogen Fuel Cell
      8. 24.8 Li-Ion Battery Modeling
        1. 24.8.1 Charging
        2. 24.8.2 Discharging
      9. Summary
      10. Review Questions
      11. Problems
  11. Part III: Mass Transfer–Based Separations
    1. Chapter 25. Humidification and Drying
      1. 25.1 Wet and Dry Bulb Temperature
        1. 25.1.1 The Lewis Relation
      2. 25.2 Humidification: Cooling Towers
        1. 25.2.1 Classification
        2. 25.2.2 General Design Considerations
      3. 25.3 Model for Counterflow
        1. 25.3.1 Mass Balance Equations
        2. 25.3.2 Enthalpy Balance Equations
        3. 25.3.3 Merkel Equation
      4. 25.4 Cross-Flow Cooling Towers
      5. 25.5 Drying
        1. 25.5.1 Types of Dryers
        2. 25.5.2 Types of Solids
        3. 25.5.3 Constant and Falling Rates
      6. 25.6 Constant Rate Period
      7. 25.7 Falling Rate Period
        1. 25.7.1 Empirical Models
        2. 25.7.2 Diffusion Type of Models
        3. 25.7.3 Capillary Flow Models
        4. 25.7.4 Choosing a Model
      8. Summary
      9. Review Questions
      10. Problems
    2. Chapter 26. Condensation
      1. 26.1 Condensation of Pure Vapor
        1. 26.1.1 Laminar Regime: Nusselt Model
        2. 26.1.2 Wavy and Turbulent Regime
      2. 26.2 Condensation of a Vapor with a Non-Condensible Gas
        1. 26.2.1 Mass Transfer Rate
        2. 26.2.2 Heat Transfer Rate and Ackermann Correction Factor
        3. 26.2.3 Interface Temperature Calculations
        4. 26.2.4 Condenser Model
      3. 26.3 Fog Formation
      4. 26.4 Condensation of Binary Gas Mixture
        1. 26.4.1 Condensation Rates: Unmixed Model
        2. 26.4.2 Calculation of the Interface Temperature
      5. 26.5 Condenser Model
        1. 26.5.1 Liquid and Vapor Phase Balances
      6. 26.6 Ternary Systems
        1. 26.6.1 Stefan-Maxwell Model
        2. 26.6.2 Condensation with Reaction
      7. Summary
      8. Review Questions
      9. Problems
    3. Chapter 27. Gas Transport in Membranes
      1. 27.1 Gas Separation Membranes
        1. 27.1.1 Membrane Classification
        2. 27.1.2 Transport Rate: Permeability
        3. 27.1.3 Transport Rate: Permeance
        4. 27.1.4 Selectivity
        5. 27.1.5 Sievert’s Law: Dissociative Diffusion
        6. 27.1.6 Nonlinear Effects in Membrane Transport
      2. 27.2 Gas Translation Model
      3. 27.3 Gas Permeator Models
        1. 27.3.1 Flux Relations
        2. 27.3.2 Local Concentration
        3. 27.3.3 Backmixed-Backmixed Model
        4. 27.3.4 Countercurrent Flow
        5. 27.3.5 Cross-Flow Pattern
      4. 27.4 Reactor Coupled with a Membrane Separator
      5. Summary
      6. Review Questions
      7. Problems
    4. Chapter 28. Liquid Separation Membranes
      1. 28.1 Classification Based on Pore Size
      2. 28.2 Transport in Semi-Permeable Membranes
        1. 28.2.1 Osmotic Pressure
        2. 28.2.2 Reverse Osmosis
        3. 28.2.3 Concentration Polarization Effects
        4. 28.2.4 Kedem-Katchalski Model
        5. 28.2.5 Equipment-Level Model
      3. 28.3 Forward Osmosis
      4. 28.4 Pervaporation
        1. 28.4.1 Illustrative Applications
        2. 28.4.2 Model for Permeate Flux
        3. 28.4.3 Local Permeate Composition
      5. Summary
      6. Review Questions
      7. Problems
    5. Chapter 29. Adsorption and Chromatography
      1. 29.1 Applications and Adsorbent Properties
      2. 29.2 Isotherms
        1. 29.2.1 Langmuir Model
        2. 29.2.2 Competitive Adsorption Isotherm
        3. 29.2.3 Freundlich Isotherms
        4. 29.2.4 BET Isotherm
      3. 29.3 Model for Batch Slurry Adsorber
        1. 29.3.1 Model Equations
        2. 29.3.2 Particle-Level Model
        3. 29.3.3 Linear Driving Force Model
        4. 29.3.4 Calculation of the Slurry Transients
        5. 29.3.5 Simulation Using the Collocation Method
        6. 29.3.6 Additional Complexities
      4. 29.4 Fixed Bed Adsorption
        1. 29.4.1 Equilibrium Model
        2. 29.4.2 Axial Dispersion Effects
        3. 29.4.3 Heterogeneous Model
        4. 29.4.4 Klinkenberg Equation
        5. 29.4.5 Scale-Up Aspects
      5. 29.5 Chromatography
      6. Summary
      7. Review Questions
      8. Problems
    6. Chapter 30. Electrodialysis and Electrophoresis
      1. 30.1 Technological Aspects
        1. 30.1.1 When to Use Electrodialysis
        2. 30.1.2 Membranes
        3. 30.1.3 Electrodialysis Reversal Process
        4. 30.1.4 Electrodialysis with Bipolar Membranes
      2. 30.2 Preliminary Design of an Electrodialyzer
        1. 30.2.1 Current and Voltage
        2. 30.2.2 Limiting Current
        3. 30.2.3 Detailed Models
      3. 30.3 Principle of Electrophoresis
        1. 30.3.1 Solutes with Fixed Type of Charge
        2. 30.3.2 Solutes with Charge Dependent on pH
      4. 30.4 Electrophoretic Separation Devices
        1. 30.4.1 Philpot Design
        2. 30.4.2 Hannig Design
        3. 30.4.3 Rotating Annular Bed
      5. Summary
      6. Review Questions
      7. Problems
  12. References
  13. Index
  14. Code Snippets