Contents
PART I FUNDAMENTALS OF MASS TRANSFER MODELING
CHAPTER 1 INTRODUCTION TO MODELING OF MASS TRANSFER PROCESSES
1.1.1 What Is Interfacial Mass Transfer?
1.1.2 What Causes Mass Transfer?
1.2 Preliminaries: Continuum and Concentration
1.2.1 The Continuum Assumption
1.2.2 Concentration: Mole Units
1.2.3 Concentration: Mass Units
1.2.4 Concentration: Partial Pressure Units
1.3.1 Molar and Mass Flux: Definition
1.4 Concentration Jump at Interface
1.4.1 Gas–Liquid Interface: Henry’s Law
1.4.2 Vapor–Liquid Interface: Raoult’s Law
1.4.3 Liquid–Liquid Interface: Partition Constant
1.4.4 Fluid–Solid Interface: Adsorption Isotherm
1.4.5 Nonlinear Equilibrium Models
1.5.4 Semiconductor and Solar Devices
1.5.6 Application to Metallurgy and Metal Winning
1.5.7 Product Development and Product Engineering
1.5.8 Electrochemical Processes
1.5.9 Environmental Applications
1.6 Basic Methodology of Model Development
1.9.1 Stirred Tank Reactor: Mixing Model
1.9.2 Sublimation of a Solid Sphere: Mass Transfer Coefficient
1.10 Mesoscopic or Cross-Section Averaged Models
1.10.1 Solid Dissolution from a Wall
CHAPTER 2 EXAMPLES OF DIFFERENTIAL (1-D) BALANCES
2.1.1 Steady State Diffusion across a Slab
2.1.2 Steady State Diffusion with Reaction in a Slab
2.1.3 Transient Diffusion in a Slab
2.1.4 Diffusion with Convection
2.2.1 Steady State Radial Diffusion
2.2.2 Steady State Mass Transfer with Reaction
2.2.3 Transient Diffusion in a Cylinder
2.3.1 Steady State Diffusion across a Spherical Shell
2.3.3 Transient Diffusion in Spherical Coordinates
CHAPTER 3 EXAMPLES OF MACROSCOPIC MODELS
3.1.1 In and Out Terms from Flow
3.1.2 Wall or Interface Transfer Term
3.2.1 Differential Equations for the Reactor
3.3 Reactor–Separator Combination
3.4 Sublimation of a Spherical Particle
3.4.1 Correlation for Mass Transfer Coefficient
3.5 Dissolved Oxygen Concentration in a Stirred Tank
3.6 Continuous Stirred Tank Reactor
3.7 Tracer Experiments: Test for Backmixed Assumption
3.7.1 Interconnected Cells Model
3.7.2 Model Composed of Active and Dead Zone
3.8.2 Backmixed–Backmixed Model
CHAPTER 4 EXAMPLES OF MESOSCOPIC MODELS
4.1 Solid Dissolution from a Wall
4.1.2 Mass Transfer Correlations in Pipe Flow
4.3.3 NTU and HTU Representation
CHAPTER 5 EQUATIONS OF MASS TRANSFER
5.2.1 Mass Fraction Averaged Velocity
5.2.2 Mole Fraction Averaged Velocity
5.3 Properties of Diffusion Flux
5.5.2 Constant-Density Systems
5.5.3 Overall Continuity: Mass Basis
5.5.5 Overall Continuity: Mole Basis
5.6 Common Boundary Conditions
5.7 Macroscopic Models: Single-Phase Systems
5.8 Multiphase Systems: Local Volume Averaging
CHAPTER 6 DIFFUSION-DOMINATED PROCESSES AND THE FILM MODEL
6.1 Steady State Diffusion: No Reaction
6.1.2 Diffusion-Induced Convection
6.1.4 Low Flux Model: The Laplace Equation
6.2 Diffusion-Induced Convection
6.2.1 Conditions for the Validity of the Low Flux Model
6.2.3 Drift Flux Correction Factor
6.2.4 Mole Fraction Profiles in UMD
6.3 Film Concept in Mass Transfer Analysis
6.3.1 Boundary Layer Concept for Fluid–Solid Mass Transfer
6.3.2 Film Model Approximation
6.3.3 Film Model: Determinacy Correction Factor
6.4 Surface Reactions: Role of Mass Transfer
6.4.1 Low Flux Model: First-Order Reaction
6.4.2 Low Flux Model: Nonlinear Reactions
6.4.3 High Flux Model: Effect of Product Counter-Diffusion
6.5 Gas–Liquid Interface: Two-Film Model
6.5.1 Mass Transfer Coefficients
6.5.2 Overall Mass Transfer Coefficient
CHAPTER 7 PHENOMENA OF DIFFUSION
7.1 Diffusion Coefficients in Gases
7.1.1 Model Based on Kinetic Theory
7.1.2 Frictional Interpretation
7.1.3 Multicomponent Diffusion
7.2 Diffusion Coefficients in Liquids
7.3.1 Activity Correction Factor
7.3.2 Activity Coefficient Models
7.5 Diffusion of Fluids in Porous Solids
7.5.1 Single-Pore Gas Diffusion: Effect of Pore Size
7.5.2 Liquid-Filled Pores: Hindered Diffusion
7.5.3 Porous Catalysts: Effective Diffusivity
CHAPTER 8 TRANSIENT DIFFUSION PROCESSES
8.1 Transient Diffusion Problems in 1-D
8.2 Solution for Slab: Dirichlet Case
8.2.1 Dimensionless Representation
8.2.3 Evaluation of the Series Coefficient
8.3 Solutions for Slab: Robin Condition
8.4 Solution for Cylinders and Spheres
8.5 Transient Non-Homogeneous Problems
8.5.1 D-D Problem in Slab Geometry
8.5.2 Transient Diffusion with Reaction
8.6 2-D Problems: Product Solution Method
8.7 Semi-Infinite Slab Analysis
8.7.1 Constant Surface Concentration
8.8 Penetration Theory of Mass Transfer
8.9 Transient Diffusion with Variable Diffusivity
8.10 Eigenvalue Computations with CHEBFUN
8.11 Computations with PDEPE Solver
8.11.1 Sample Code for 1-D Transient Diffusion with Reaction
CHAPTER 9 BASICS OF CONVECTIVE MASS TRANSPORT
9.1 Definitions for External and Internal Flows
9.2 Relation to Differential Model
9.3.1 Other Derived Dimensionless Groups
9.4 Mass Transfer in Flows in Pipes and Channels
9.5 Mass Transfer in Flow over a Flat Plate
9.6 Mass Transfer for Film Flow
9.7 Mass Transfer from a Solid Sphere
9.8 Mass Transfer from a Gas Bubble
9.8.1 Bubble Swarms and Bubble Columns
9.9 Mass Transfer in Mechanically Agitated Tanks
9.10 Gas–Liquid Mass Transfer in a Packed Bed Absorber
9.10.1 Liquid Side Coefficient
CHAPTER 10 CONVECTIVE MASS TRANSFER: THEORY FOR INTERNAL LAMINAR FLOW
10.1 Mass Transfer in Laminar Flow in a Pipe
10.1.2 Constant Wall Concentration: The Dirichlet Problem
10.1.3 Concentration, Wall Mass Flux, and Sherwood Number
10.2 Wall Reaction: The Robin Problem
10.4 Channel Flows with Mass Transfer
10.5 Mass Transfer in Film Flow
10.5.1 Solid Dissolution at a Wall in Film Flow
10.5.2 Gas Absorption from Interface in Film Flow
10.6 Numerical Solution with PDEPE
CHAPTER 11 MASS TRANSFER IN LAMINAR BOUNDARY LAYERS
11.1 Flat Plate with Low Flux Mass Transfer
11.1.3 Scaling Results and the Analogies
11.1.4 Exact or Blasius Analysis
11.2 Integral Balance Approach
11.2.1 Integral Momentum Balance
11.2.2 Integral Species Mass Balance
11.2.3 Solution for No Reaction Case
11.2.4 Solution for Homogeneous Reaction
11.3.2 Integral Balance Method
11.4 Mass Transfer for Flow over Inclined and Curved Surfaces
11.4.1 Pressure Variation Term
11.4.2 Integral Balance Method for Inclined and Curved Surfaces
11.4.3 Inclined Plates: Use of Similarity Variable
11.4.4 Wedge Flow: Falkner-Skan Equation
11.4.5 Stagnation Point (Hiemenz) Flow
11.4.6 Flow over a Rotating Disk
CHAPTER 12 CONVECTIVE MASS TRANSFER IN TURBULENT FLOW
12.1 Properties of Turbulent Flow
12.1.2 Characteristics of Fully Turbulent Flow
12.2 Properties of Time Averaging
12.3 Time-Averaged Equation of Mass Transfer
12.4.1 Turbulent Schmidt Number
12.4.2 Prandtl’s Model for Eddy Viscosity
12.5 Velocity and Turbulent Diffusivity Profiles
12.5.1 Universal Velocity Profiles
12.5.2 Eddy Diffusivity Profiles
12.5.3 Wall Shear Stress Relations
12.6 Turbulent Mass Transfer in Channels and Pipes
12.6.1 Simplified Analysis: Constant Wall Flux
12.6.2 Stanton Number Calculation for Boundary Layers
12.6.3 Analogy with Momentum Transfer
12.6.4 Stanton Number for Pipe Flows
12.7 Van Driest Model for Large Sc
12.8 Turbulent Mass Transfer at Gas–Liquid Interface
CHAPTER 13 MACROSCOPIC AND COMPARTMENTAL MODELS
13.1 Stirred Reactor: The Backmixing Assumption
13.2 Transient Balance: Tracer Studies
13.2.3 Age Distribution Functions
13.2.4 Tracer Response for Tanks in Series Model
13.3 Moment Analysis of Tracer Data
13.3.1 Moments from Laplace Transform of Response
13.4 Tanks in Series Models: Reactor Performance
13.6 Variance-Based Models for Partial Micromixing
13.8 Compartmental Models for Environmental Transport
13.8.1 Fugacity of Pollutants in Each Compartment
13.8.2 Level I or Equilibrium Model
13.8.3 Level II Model: Advection Effects
13.8.4 Level III Model: Intermedia Transport Effects
13.8.5 Level IV Model: Transient Effects
13.9.1 Backmixed–Backmixed Model
13.10 Models for Multistage Cascades
CHAPTER 14 MESOSCOPIC MODELS AND THE CONCEPT OF DISPERSION
14.2.2 Solution for a First-Order Reaction
14.2.4 Dispersion Model: Numerical Code Using CHEBFUN
14.2.5 Criteria for Negligible Dispersion
14.3 Dispersion Coefficient: Tracer Response Method
14.3.1 Laplace Domain Solution
14.3.2 Moments of the Response Curve
14.4 Taylor Model for Dispersion in Laminar Flow
14.6 Dispersion Coefficient Values for Some Common Cases
14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns
14.7.2 Non-Idealities in Two-Phase Flow
14.8 Tracer Response in Two-Phase Systems
CHAPTER 15 MASS TRANSFER: MULTICOMPONENT SYSTEMS
15.1 Constitutive Model for Multicomponent Transport
15.1.2 Generalization: The Stefan-Maxwell Model
15.2 Computations for a Reacting System
15.4.1 Evaporation of a Liquid in a Ternary Mixture
15.4.2 Evaporation of a Binary Liquid Mixture
15.4.3 Equimolar Counter-Diffusion
15.5 Multicomponent Diffusivity Matrix
15.5.1 Matrix Relation to Binary Pair Diffusivity
CHAPTER 16 MASS TRANSPORT IN ELECTROLYTIC SYSTEMS
16.1 Transport of Charged Species: Preliminaries
16.1.1 Mobility and Diffusivity
16.3 General Expression for the Electric Field
16.3.1 Laplace Equation for the Potential
16.3.3 Mass Balance for Reacting Systems
16.4 Electrolyte Transport across Uncharged Membrane
16.5 Transport across a Charged Membrane
16.5.1 Interfacial Jump: Donnan Equation
16.6 Transfer Rate in Diffusion Film near an Electrode
CHAPTER 17 LAMINAR FLOW REACTOR
17.1 Model Equations and Key Dimensionless Groups
17.1.1 Dimensionless Model Equations
17.2.1 Small B: Pure Convection Model
17.2.2 Large B: Plug Flow Model
17.3 Mesoscopic Dispersion Model
17.4 Other Examples of Flow Reactors
17.4.4 Turbulent Flow Reactor: 2-D Model
17.4.5 Axial Dispersion Model for the Turbulent Case
CHAPTER 18 MASS TRANSFER WITH REACTION: POROUS CATALYSTS
18.1 Catalyst Properties and Applications
18.4 Three-Phase Catalytic Reactions
18.5 Temperature Effects in a Porous Catalyst
18.5.1 Equations for Heat and Mass Transport
18.5.2 Dimensionless Representation
18.5.3 Dimensionless Boundary Conditions
18.5.4 Estimate of the Temperature Gradients
18.6 Orthogonal Collocation Method
18.7 Finite Difference Methods
18.7.1 Central Difference Equations
18.7.4 Neumann and Robin Conditions
18.8 Linking with Reactor Models
19.1.2 Solid Product: Ash Layer Effects
19.2.2 Concentration Profile for Gas and Solid
19.2.3 First-Order Reaction in B
19.3 Other Models for Gas–Solid Reactions
19.3.1 Effect of Structural Changes
19.4.2 Dalvi-Suresh Contact Point Model
CHAPTER 20 GAS–LIQUID REACTIONS: FILM THEORY MODELS
20.1 First-Order Reaction of Dissolved Gas
20.1.3 Flux Values at the Interface and into the Bulk
20.2 Bulk Concentration and Bulk Reactions
20.2.2 Absorption Rate Calculation for Ha < 0.2
20.3.1 Dimensionless Representation
20.3.2 Invariance Property of the System
20.3.3 Analysis for Pseudo-First-Order Case
20.3.4 Analysis for Instantaneous Asymptote
20.3.5 Second-Order Case: An Approximate Solution
20.3.6 Instantaneous Case: Effect of Gas Film Resistance
20.3.7 Choice of Contactor Based on the Regimes of Absorption
20.4 Simultaneous Absorption of Two Gases
20.4.2 Dimensionless Representation
20.5 Coupling with Reactor Models
20.6.2 Instantaneous Reaction Case
CHAPTER 21 GAS–LIQUID REACTIONS: PENETRATION THEORY APPROACH
21.1 Concepts of Penetration Theory
21.1.1 First-Order or Pseudo-First-Order Reaction
21.1.2 Laplace Transform Method
21.1.3 Flux and the Average Rate of Mass Transfer
21.1.4 Relation between Film Theory and Penetration Theory
21.2.1 Dimensionless Form of the Model
21.3 Instantaneous Reaction Case
CHAPTER 22 REACTIVE MEMBRANES AND FACILITATED TRANSPORT
22.1.2 Dimensionless Representation
22.1.3 Invariant of the System
22.1.4 Instantaneous Reaction Asymptote
22.1.5 Pseudo-First-Order Reaction Asymptote
22.2 Co- and Counter-Transport
22.2.1 Model for Counter-Transport
22.3 Equilibrium Model: A Computational Scheme
22.4 Reactive Membranes in Practice
22.4.1 Emulsion Liquid Membranes (ELM)
22.4.2 Immobilized Liquid Membranes (ILM)
22.4.3 Fixed-Site Carrier Membranes
CHAPTER 23 BIOMEDICAL APPLICATIONS
23.1.1 Oxygen-Hemoglobin Equilibrium
23.1.2 Transport Steps for Oxygen Uptake
23.1.3 Meso-Model for the Capillary
23.2 Transport in Tissues: Krogh Model
23.2.1 Oxygen Variation in the Capillary
23.3 Compartmental Models for Pharmacokinetics
23.3.2 Physiologically Based Compartments
23.4.2 Model for Patient-Dialyzer System
CHAPTER 24 ELECTROCHEMICAL REACTION ENGINEERING
24.1.1 Anodic and Cathodic Reactions
24.1.2 Half Reactions and Overall Reaction
24.1.3 Classification of Electrode Reactions
24.2 Thermodynamic Considerations: Nernst Equation
24.2.1 Equilibrium Cell Potential
24.3 Kinetic Model for Electrochemical Reactions
24.4.1 Concentration Overpotential
24.6.1 Operating Current Density
24.6.3 Meso-Model for the Electrolyzer
PART III MASS TRANSFER–BASED SEPARATIONS
CHAPTER 25 HUMIDIFICATION AND DRYING
25.1 Wet and Dry Bulb Temperature
25.2 Humidification: Cooling Towers
25.2.2 General Design Considerations
25.3.2 Enthalpy Balance Equations
25.4 Cross-Flow Cooling Towers
25.5.3 Constant and Falling Rates
25.7.2 Diffusion Type of Models
26.1 Condensation of Pure Vapor
26.1.1 Laminar Regime: Nusselt Model
26.1.2 Wavy and Turbulent Regime
26.2 Condensation of a Vapor with a Non-Condensible Gas
26.2.2 Heat Transfer Rate and Ackermann Correction Factor
26.2.3 Interface Temperature Calculations
26.4 Condensation of Binary Gas Mixture
26.4.1 Condensation Rates: Unmixed Model
26.4.2 Calculation of the Interface Temperature
26.5.1 Liquid and Vapor Phase Balances
26.6.2 Condensation with Reaction
CHAPTER 27 GAS TRANSPORT IN MEMBRANES
27.1.1 Membrane Classification
27.1.2 Transport Rate: Permeability
27.1.3 Transport Rate: Permeance
27.1.5 Sievert’s Law: Dissociative Diffusion
27.1.6 Nonlinear Effects in Membrane Transport
27.3.3 Backmixed-Backmixed Model
27.4 Reactor Coupled with a Membrane Separator
CHAPTER 28 LIQUID SEPARATION MEMBRANES
28.1 Classification Based on Pore Size
28.2 Transport in Semi-Permeable Membranes
28.2.3 Concentration Polarization Effects
28.4.1 Illustrative Applications
28.4.2 Model for Permeate Flux
28.4.3 Local Permeate Composition
CHAPTER 29 ADSORPTION AND CHROMATOGRAPHY
29.1 Applications and Adsorbent Properties
29.2.2 Competitive Adsorption Isotherm
29.3 Model for Batch Slurry Adsorber
29.3.3 Linear Driving Force Model
29.3.4 Calculation of the Slurry Transients
29.3.5 Simulation Using the Collocation Method
29.3.6 Additional Complexities
29.4.2 Axial Dispersion Effects
CHAPTER 30 ELECTRODIALYSIS AND ELECTROPHORESIS
30.1.1 When to Use Electrodialysis
30.1.3 Electrodialysis Reversal Process
30.1.4 Electrodialysis with Bipolar Membranes
30.2 Preliminary Design of an Electrodialyzer
30.3 Principle of Electrophoresis
30.3.1 Solutes with Fixed Type of Charge
30.3.2 Solutes with Charge Dependent on pH