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by P. A. Ramachandran
Mass Transfer Processes: Modeling, Computations, and Design, First Edition
Cover Page
About This E-Book
Title Page
Copyright Page
Contents
Preface
Key Distinguishing Features
Intended Audience
Style of Presentation
Topical Outline
Part I
Part II
Part III
For Instructors
Acknowledgments
About the Author
Notation
Greek Letters
Common Subscripts
Acronyms
Part I: Fundamentals of Mass Transfer Modeling
Chapter 1. Introduction to Modeling of Mass Transfer Processes
1.1 What Is Mass Transfer?
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 Flux Vector
1.3.1 Molar and Mass Flux: Definition
1.3.2 Convection Flux
1.3.3 Diffusion Flux
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 Application Examples
1.5.1 Reacting Systems
1.5.2 Unit Operations
1.5.3 Bioseparations
1.5.4 Semiconductor and Solar Devices
1.5.5 Biomedical Applications
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
1.7 Conservation Principle
1.8 Differential Models
1.9 Macroscopic Scale
1.9.1 Stirred Tank Reactor: Mixing Model
1.9.2 Sublimation of a Solid Sphere: Mass Transfer Coefficient
1.9.3 Model for Mixer-Settler
1.9.4 Equilibrium Stage Model
1.10 Mesoscopic or Cross-Section Averaged Models
1.10.1 Solid Dissolution from a Wall
1.10.2 Tubular Flow Reactor
1.11 Compartmental Models
Summary
Review Questions
Problems
Chapter 2. Examples of Differential (1-D) Balances
2.1 Cartesian Coordinates
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 Cylindrical Coordinates
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 Spherical Coordinates
2.3.1 Steady State Diffusion across a Spherical Shell
2.3.2 Diffusion and Reaction
2.3.3 Transient Diffusion in Spherical Coordinates
Summary
Review Questions
Problems
Chapter 3. Examples of Macroscopic Models
3.1 Macroscopic Balance
3.1.1 In and Out Terms from Flow
3.1.2 Wall or Interface Transfer Term
3.1.3 Rate Term
3.1.4 Accumulation Term
3.2 The Batch Reactor
3.2.1 Differential Equations for the Reactor
3.2.2 ODE45 with CHEBFUN
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
3.6.1 First-Order Reaction
3.6.2 Second-Order Reaction
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 Liquid–Liquid Extraction
3.8.1 Mass Transfer Rate
3.8.2 Backmixed–Backmixed Model
3.8.3 Equilibrium Stage Model
3.8.4 Stage Efficiency
Summary
Review Questions
Problems
Chapter 4. Examples of Mesoscopic Models
4.1 Solid Dissolution from a Wall
4.1.1 Model Details
4.1.2 Mass Transfer Correlations in Pipe Flow
4.2 Tubular Flow Reactor
4.2.1 Plug Flow Closure
4.2.2 Dispersion Closure
4.3 Mass Exchangers
4.3.1 Single Stream
4.3.2 Two Streams
4.3.3 NTU and HTU Representation
Summary
Review Questions
Problems
Chapter 5. Equations of Mass Transfer
5.1 Flux Form
5.1.1 Mole Basis
5.1.2 Mass Basis
5.2 Frame of Reference
5.2.1 Mass Fraction Averaged Velocity
5.2.2 Mole Fraction Averaged Velocity
5.3 Properties of Diffusion Flux
5.4 Pseudo-Binary Diffusivity
5.5 Concentration Form
5.5.1 Mass Basis
5.5.2 Constant-Density Systems
5.5.3 Overall Continuity: Mass Basis
5.5.4 Mole Basis
5.5.5 Overall Continuity: Mole Basis
5.5.6 Common Simplifications
5.6 Common Boundary Conditions
5.7 Macroscopic Models: Single-Phase Systems
5.8 Multiphase Systems: Local Volume Averaging
Summary
Review Questions
Problems
Chapter 6. Diffusion-Dominated Processes and the Film Model
6.1 Steady State Diffusion: No Reaction
6.1.1 Combined Flux Equation
6.1.2 Diffusion-Induced Convection
6.1.3 Determinacy Condition
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
6.2.2 Analysis for UMD
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
Summary
Review Questions
Problems
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
7.2.1 Stokes-Einstein Model
7.2.2 Wilke-Chang Equation
7.3 Non-Ideal Liquids
7.3.1 Activity Correction Factor
7.3.2 Activity Coefficient Models
7.4 Solid–Solid Diffusion
7.4.1 Vacancy Diffusion
7.4.2 Interstitial Diffusion
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
7.6 Heterogeneous Media
7.7 Polymeric Membranes
7.8 Other Complex Effects
Summary
Review Questions
Problems
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
8.2.2 Series Solution
8.2.3 Evaluation of the Series Coefficient
8.2.4 Illustrative Results
8.2.5 Average Concentration
8.3 Solutions for Slab: Robin Condition
8.4 Solution for Cylinders and Spheres
8.4.1 Long Cylinder
8.4.2 Sphere
8.4.3 One-Term Approximation
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
8.7.2 Integral Method
8.7.3 Pulse Response
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
Summary
Review Questions
Problems
Chapter 9. Basics of Convective Mass Transport
9.1 Definitions for External and Internal Flows
9.2 Relation to Differential Model
9.3 Key Dimensionless Groups
9.3.1 Other Derived Dimensionless Groups
9.4 Mass Transfer in Flows in Pipes and Channels
9.4.1 Laminar Flow
9.4.2 Turbulent Flow
9.4.3 Channel Flow
9.5 Mass Transfer in Flow over a Flat Plate
9.5.1 Laminar Flow
9.5.2 Turbulent Flow
9.5.3 The j-Factor
9.6 Mass Transfer for Film Flow
9.6.1 Solid to Liquid
9.6.2 Gas to Liquid
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
9.10.2 Gas Side Coefficient
9.10.3 Transfer Area
Summary
Review Questions
Problems
Chapter 10. Convective Mass Transfer: Theory for Internal Laminar Flow
10.1 Mass Transfer in Laminar Flow in a Pipe
10.1.1 Dimensionless Form
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
10.2.1 Solution Using CHEBFUN
10.2.2 Illustrative Results
10.3 Entry Region Analysis
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
Summary
Review Questions
Problems
Chapter 11. Mass Transfer in Laminar Boundary Layers
11.1 Flat Plate with Low Flux Mass Transfer
11.1.1 Concentration Equation
11.1.2 Velocity Equations
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 High Flux Analysis
11.3.1 Film Model
11.3.2 Integral Balance Method
11.3.3 Blasius Approach
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
11.4.7 Flow past a Sphere
11.5 Bubbles and Drops
11.5.1 Rigid Bubbles
11.5.2 Spherical Cap Bubbles
Summary
Review Questions
Problems
Chapter 12. Convective Mass Transfer in Turbulent Flow
12.1 Properties of Turbulent Flow
12.1.1 Transition Criteria
12.1.2 Characteristics of Fully Turbulent Flow
12.1.3 Stochastic Nature
12.2 Properties of Time Averaging
12.3 Time-Averaged Equation of Mass Transfer
12.3.1 Turbulent Mass Flux
12.3.2 Reynolds Stresses
12.3.3 Reaction Contribution
12.4 Closure Models
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
12.8.1 Damping of Turbulence
12.8.2 Marangoni Effect
12.8.3 Interfacial Turbulence
Summary
Review Questions
Problems
Chapter 13. Macroscopic and Compartmental Models
13.1 Stirred Reactor: The Backmixing Assumption
13.2 Transient Balance: Tracer Studies
13.2.1 Step Input
13.2.2 Pulse or Bolus Input
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
13.5 Macrofluid Models
13.5.1 Second-Order Reaction
13.5.2 Zero-Order Reaction
13.6 Variance-Based Models for Partial Micromixing
13.7 Compartmental Models
13.7.1 Matrix Representation
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 Fluid–Fluid Systems
13.9.1 Backmixed–Backmixed Model
13.9.2 Equilibrium Model
13.9.3 Mixing Cell Model
13.10 Models for Multistage Cascades
13.10.1 Equilibrium Model
Summary
Review Questions
Problems
Chapter 14. Mesoscopic Models and the Concept of Dispersion
14.1 Plug Flow Idealization
14.2 Dispersion Model
14.2.1 Boundary Conditions
14.2.2 Solution for a First-Order Reaction
14.2.3 Nonlinear Reactions
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
14.3.3 Time Domain Solution
14.4 Taylor Model for Dispersion in Laminar Flow
14.5 Segregated Flow Model
14.6 Dispersion Coefficient Values for Some Common Cases
14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns
14.7.1 Plug-Backmixed Model
14.7.2 Non-Idealities in Two-Phase Flow
14.8 Tracer Response in Two-Phase Systems
14.8.1 Single Flowing Phase
14.8.2 Two Flowing Phases
Summary
Review Questions
Problems
Chapter 15. Mass Transfer: Multicomponent Systems
15.1 Constitutive Model for Multicomponent Transport
15.1.1 Binary Revisited
15.1.2 Generalization: The Stefan-Maxwell Model
15.2 Computations for a Reacting System
15.3 Heterogeneous Reactions
15.4 Non-Reacting Systems
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 D 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
16.1.2 Nernst-Planck Equation
16.2 Charge Neutrality
16.3 General Expression for the Electric Field
16.3.1 Laplace Equation for the Potential
16.3.2 Transference Number
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
16.5.2 Transport Rate
16.6 Transfer Rate in Diffusion Film near an Electrode
Summary
Review Questions
Problems
Part II: Reacting Systems
Chapter 17. Laminar Flow Reactor
17.1 Model Equations and Key Dimensionless Groups
17.1.1 Dimensionless Model Equations
17.1.2 Boundary Conditions
17.2 Two Limiting Cases
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
17.4.1 Channel Flow
17.4.2 Non-Newtonian Fluids
17.4.3 Heat Transfer Effects
17.4.4 Turbulent Flow Reactor: 2-D Model
17.4.5 Axial Dispersion Model for the Turbulent Case
Summary
Review Questions
Problems
Chapter 18. Mass Transfer with Reaction: Porous Catalysts
18.1 Catalyst Properties and Applications
18.1.1 Catalyst Properties
18.2 Diffusion-Reaction Model
18.2.1 First-Order Reaction
18.2.2 Zero-Order Reaction
18.2.3 nth-Order Reaction
18.3 Multiple Species
18.4 Three-Phase Catalytic Reactions
18.4.1 Application Examples
18.4.2 Mass Transfer Effects
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
18.6.1 Basis of the Method
18.6.2 Two-Point Collocation
18.7 Finite Difference Methods
18.7.1 Central Difference Equations
18.7.2 Zero-Order Reaction
18.7.3 Nonlinear Kinetics
18.7.4 Neumann and Robin Conditions
18.8 Linking with Reactor Models
18.8.1 First-Order Reaction
18.8.2 Second-Order Reaction
18.8.3 Zero-Order Reaction
Summary
Review Questions
Problems
Chapter 19. Reacting Solids
19.1 Shrinking Core Model
19.1.1 No Solid Product
19.1.2 Solid Product: Ash Layer Effects
19.2 Volume Reaction Model
19.2.1 Kinetic Model
19.2.2 Concentration Profile for Gas and Solid
19.2.3 First-Order Reaction in B
19.2.4 Zero-Order Reaction
19.3 Other Models for Gas–Solid Reactions
19.3.1 Effect of Structural Changes
19.4 Solid–Solid Reactions
19.4.1 Classical Models
19.4.2 Dalvi-Suresh Contact Point Model
Summary
Review Questions
Problems
Chapter 20. Gas–Liquid Reactions: Film Theory Models
20.1 First-Order Reaction of Dissolved Gas
20.1.1 Boundary Conditions
20.1.2 Dimensionless Version
20.1.3 Flux Values at the Interface and into the Bulk
20.1.4 Enhancement Factor
20.2 Bulk Concentration and Bulk Reactions
20.2.1 Bulk Concentration
20.2.2 Absorption Rate Calculation for Ha < 0.2
20.3 Bimolecular Reactions
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
20.4.1 Model Equations
20.4.2 Dimensionless Representation
20.4.3 CHEBFUN Solution
20.5 Coupling with Reactor Models
20.5.1 Semibatch Reactor
20.5.2 Packed Column Absorber
20.6 Absorption in Slurries
20.6.1 Particle Size Effect
20.6.2 Instantaneous Reaction Case
20.7 Liquid–Liquid Reactions
Summary
Review Questions
Problems
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 Bimolecular Reaction
21.2.1 Dimensionless Form of the Model
21.2.2 Illustrative Results
21.3 Instantaneous Reaction Case
21.4 Ideal Contactors
21.4.1 Laminar Jet Apparatus
21.4.2 Wetted Wall Column
21.4.3 Wetted Sphere
21.4.4 Stirred Cells
Summary
Review Questions
Problems
Chapter 22. Reactive Membranes and Facilitated Transport
22.1 Single Solute Diffusion
22.1.1 Model Equations
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
22.2.2 Model for Co-Transport
22.3 Equilibrium Model: A Computational Scheme
22.3.1 Illustrative Results
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
Summary
Review Questions
Problems
Chapter 23. Biomedical Applications
23.1 Oxygen Uptake in Lungs
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
23.3.1 Basic Framework
23.3.2 Physiologically Based Compartments
23.4 Model for a Hemodialyzer
23.4.1 Model Formulation
23.4.2 Model for Patient-Dialyzer System
Summary
Review Questions
Problems
Chapter 24. Electrochemical Reaction Engineering
24.1 Basic Definitions
24.1.1 Anodic and Cathodic Reactions
24.1.2 Half Reactions and Overall Reaction
24.1.3 Classification of Electrode Reactions
24.1.4 Primary Variables
24.2 Thermodynamic Considerations: Nernst Equation
24.2.1 Equilibrium Cell Potential
24.3 Kinetic Model for Electrochemical Reactions
24.3.1 Butler-Volmer Equation
24.3.2 Tafel Equation
24.4 Mass Transfer Effects
24.4.1 Concentration Overpotential
24.5 Voltage Balance
24.6 Copper Electrowinning
24.6.1 Operating Current Density
24.6.2 Voltage Balance
24.6.3 Meso-Model for the Electrolyzer
24.7 Hydrogen Fuel Cell
24.8 Li-Ion Battery Modeling
24.8.1 Charging
24.8.2 Discharging
Summary
Review Questions
Problems
Part III: Mass Transfer–Based Separations
Chapter 25. Humidification and Drying
25.1 Wet and Dry Bulb Temperature
25.1.1 The Lewis Relation
25.2 Humidification: Cooling Towers
25.2.1 Classification
25.2.2 General Design Considerations
25.3 Model for Counterflow
25.3.1 Mass Balance Equations
25.3.2 Enthalpy Balance Equations
25.3.3 Merkel Equation
25.4 Cross-Flow Cooling Towers
25.5 Drying
25.5.1 Types of Dryers
25.5.2 Types of Solids
25.5.3 Constant and Falling Rates
25.6 Constant Rate Period
25.7 Falling Rate Period
25.7.1 Empirical Models
25.7.2 Diffusion Type of Models
25.7.3 Capillary Flow Models
25.7.4 Choosing a Model
Summary
Review Questions
Problems
Chapter 26. Condensation
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
26.2.1 Mass Transfer Rate
26.2.2 Heat Transfer Rate and Ackermann Correction Factor
26.2.3 Interface Temperature Calculations
26.2.4 Condenser Model
26.3 Fog Formation
26.4 Condensation of Binary Gas Mixture
26.4.1 Condensation Rates: Unmixed Model
26.4.2 Calculation of the Interface Temperature
26.5 Condenser Model
26.5.1 Liquid and Vapor Phase Balances
26.6 Ternary Systems
26.6.1 Stefan-Maxwell Model
26.6.2 Condensation with Reaction
Summary
Review Questions
Problems
Chapter 27. Gas Transport in Membranes
27.1 Gas Separation Membranes
27.1.1 Membrane Classification
27.1.2 Transport Rate: Permeability
27.1.3 Transport Rate: Permeance
27.1.4 Selectivity
27.1.5 Sievert’s Law: Dissociative Diffusion
27.1.6 Nonlinear Effects in Membrane Transport
27.2 Gas Translation Model
27.3 Gas Permeator Models
27.3.1 Flux Relations
27.3.2 Local Concentration
27.3.3 Backmixed-Backmixed Model
27.3.4 Countercurrent Flow
27.3.5 Cross-Flow Pattern
27.4 Reactor Coupled with a Membrane Separator
Summary
Review Questions
Problems
Chapter 28. Liquid Separation Membranes
28.1 Classification Based on Pore Size
28.2 Transport in Semi-Permeable Membranes
28.2.1 Osmotic Pressure
28.2.2 Reverse Osmosis
28.2.3 Concentration Polarization Effects
28.2.4 Kedem-Katchalski Model
28.2.5 Equipment-Level Model
28.3 Forward Osmosis
28.4 Pervaporation
28.4.1 Illustrative Applications
28.4.2 Model for Permeate Flux
28.4.3 Local Permeate Composition
Summary
Review Questions
Problems
Chapter 29. Adsorption and Chromatography
29.1 Applications and Adsorbent Properties
29.2 Isotherms
29.2.1 Langmuir Model
29.2.2 Competitive Adsorption Isotherm
29.2.3 Freundlich Isotherms
29.2.4 BET Isotherm
29.3 Model for Batch Slurry Adsorber
29.3.1 Model Equations
29.3.2 Particle-Level Model
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 Fixed Bed Adsorption
29.4.1 Equilibrium Model
29.4.2 Axial Dispersion Effects
29.4.3 Heterogeneous Model
29.4.4 Klinkenberg Equation
29.4.5 Scale-Up Aspects
29.5 Chromatography
Summary
Review Questions
Problems
Chapter 30. Electrodialysis and Electrophoresis
30.1 Technological Aspects
30.1.1 When to Use Electrodialysis
30.1.2 Membranes
30.1.3 Electrodialysis Reversal Process
30.1.4 Electrodialysis with Bipolar Membranes
30.2 Preliminary Design of an Electrodialyzer
30.2.1 Current and Voltage
30.2.2 Limiting Current
30.2.3 Detailed Models
30.3 Principle of Electrophoresis
30.3.1 Solutes with Fixed Type of Charge
30.3.2 Solutes with Charge Dependent on pH
30.4 Electrophoretic Separation Devices
30.4.1 Philpot Design
30.4.2 Hannig Design
30.4.3 Rotating Annular Bed
Summary
Review Questions
Problems
References
Index
Code Snippets
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