book

Mass Transfer Processes: Modeling, Computations, and Design

Name: Mass Transfer Processes: Modeling, Computations, and Design
Author: P. A. Ramachandran
ISBN: 9780134675640

by P. A. Ramachandran

February 2018

Intermediate to advanced

1072 pages

28h 4m

English

Pearson

Read now

Unlock full access

Cover Page
About This E-Book
Title Page
Copyright Page
Contents
Preface
Key Distinguishing FeaturesIntended AudienceStyle of PresentationTopical OutlinePart IPart IIPart IIIFor InstructorsAcknowledgments
About the Author
Notation
Greek LettersCommon SubscriptsAcronyms
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 Concentration1.2.1 The Continuum Assumption1.2.2 Concentration: Mole Units1.2.3 Concentration: Mass Units1.2.4 Concentration: Partial Pressure Units1.3 Flux Vector1.3.1 Molar and Mass Flux: Definition1.3.2 Convection Flux1.3.3 Diffusion Flux1.4 Concentration Jump at Interface1.4.1 Gas–Liquid Interface: Henry’s Law1.4.2 Vapor–Liquid Interface: Raoult’s Law1.4.3 Liquid–Liquid Interface: Partition Constant1.4.4 Fluid–Solid Interface: Adsorption Isotherm1.4.5 Nonlinear Equilibrium Models1.5 Application Examples1.5.1 Reacting Systems1.5.2 Unit Operations1.5.3 Bioseparations1.5.4 Semiconductor and Solar Devices1.5.5 Biomedical Applications1.5.6 Application to Metallurgy and Metal Winning1.5.7 Product Development and Product Engineering1.5.8 Electrochemical Processes1.5.9 Environmental Applications1.6 Basic Methodology of Model Development1.7 Conservation Principle1.8 Differential Models1.9 Macroscopic Scale1.9.1 Stirred Tank Reactor: Mixing Model1.9.2 Sublimation of a Solid Sphere: Mass Transfer Coefficient1.9.3 Model for Mixer-Settler1.9.4 Equilibrium Stage Model1.10 Mesoscopic or Cross-Section Averaged Models1.10.1 Solid Dissolution from a Wall1.10.2 Tubular Flow Reactor1.11 Compartmental ModelsSummaryReview QuestionsProblems

Chapter 2. Examples of Differential (1-D) Balances
2.1 Cartesian Coordinates2.1.1 Steady State Diffusion across a Slab2.1.2 Steady State Diffusion with Reaction in a Slab2.1.3 Transient Diffusion in a Slab2.1.4 Diffusion with Convection2.2 Cylindrical Coordinates2.2.1 Steady State Radial Diffusion2.2.2 Steady State Mass Transfer with Reaction2.2.3 Transient Diffusion in a Cylinder2.3 Spherical Coordinates2.3.1 Steady State Diffusion across a Spherical Shell2.3.2 Diffusion and Reaction2.3.3 Transient Diffusion in Spherical CoordinatesSummaryReview QuestionsProblems
Chapter 3. Examples of Macroscopic Models
3.1 Macroscopic Balance3.1.1 In and Out Terms from Flow3.1.2 Wall or Interface Transfer Term3.1.3 Rate Term3.1.4 Accumulation Term3.2 The Batch Reactor3.2.1 Differential Equations for the Reactor3.2.2 ODE45 with CHEBFUN3.3 Reactor–Separator Combination3.4 Sublimation of a Spherical Particle3.4.1 Correlation for Mass Transfer Coefficient3.5 Dissolved Oxygen Concentration in a Stirred Tank3.6 Continuous Stirred Tank Reactor3.6.1 First-Order Reaction3.6.2 Second-Order Reaction3.7 Tracer Experiments: Test for Backmixed Assumption3.7.1 Interconnected Cells Model3.7.2 Model Composed of Active and Dead Zone3.8 Liquid–Liquid Extraction3.8.1 Mass Transfer Rate3.8.2 Backmixed–Backmixed Model3.8.3 Equilibrium Stage Model3.8.4 Stage EfficiencySummaryReview QuestionsProblems
Chapter 4. Examples of Mesoscopic Models
4.1 Solid Dissolution from a Wall4.1.1 Model Details4.1.2 Mass Transfer Correlations in Pipe Flow4.2 Tubular Flow Reactor4.2.1 Plug Flow Closure4.2.2 Dispersion Closure4.3 Mass Exchangers4.3.1 Single Stream4.3.2 Two Streams4.3.3 NTU and HTU RepresentationSummaryReview QuestionsProblems
Chapter 5. Equations of Mass Transfer
5.1 Flux Form5.1.1 Mole Basis5.1.2 Mass Basis5.2 Frame of Reference5.2.1 Mass Fraction Averaged Velocity5.2.2 Mole Fraction Averaged Velocity5.3 Properties of Diffusion Flux5.4 Pseudo-Binary Diffusivity5.5 Concentration Form5.5.1 Mass Basis5.5.2 Constant-Density Systems5.5.3 Overall Continuity: Mass Basis5.5.4 Mole Basis5.5.5 Overall Continuity: Mole Basis5.5.6 Common Simplifications5.6 Common Boundary Conditions5.7 Macroscopic Models: Single-Phase Systems5.8 Multiphase Systems: Local Volume AveragingSummaryReview QuestionsProblems
Chapter 6. Diffusion-Dominated Processes and the Film Model
6.1 Steady State Diffusion: No Reaction6.1.1 Combined Flux Equation6.1.2 Diffusion-Induced Convection6.1.3 Determinacy Condition6.1.4 Low Flux Model: The Laplace Equation6.2 Diffusion-Induced Convection6.2.1 Conditions for the Validity of the Low Flux Model6.2.2 Analysis for UMD6.2.3 Drift Flux Correction Factor6.2.4 Mole Fraction Profiles in UMD6.3 Film Concept in Mass Transfer Analysis6.3.1 Boundary Layer Concept for Fluid–Solid Mass Transfer6.3.2 Film Model Approximation6.3.3 Film Model: Determinacy Correction Factor6.4 Surface Reactions: Role of Mass Transfer6.4.1 Low Flux Model: First-Order Reaction6.4.2 Low Flux Model: Nonlinear Reactions6.4.3 High Flux Model: Effect of Product Counter-Diffusion6.5 Gas–Liquid Interface: Two-Film Model6.5.1 Mass Transfer Coefficients6.5.2 Overall Mass Transfer CoefficientSummaryReview QuestionsProblems
Chapter 7. Phenomena of Diffusion
7.1 Diffusion Coefficients in Gases7.1.1 Model Based on Kinetic Theory7.1.2 Frictional Interpretation7.1.3 Multicomponent Diffusion7.2 Diffusion Coefficients in Liquids7.2.1 Stokes-Einstein Model7.2.2 Wilke-Chang Equation7.3 Non-Ideal Liquids7.3.1 Activity Correction Factor7.3.2 Activity Coefficient Models7.4 Solid–Solid Diffusion7.4.1 Vacancy Diffusion7.4.2 Interstitial Diffusion7.5 Diffusion of Fluids in Porous Solids7.5.1 Single-Pore Gas Diffusion: Effect of Pore Size7.5.2 Liquid-Filled Pores: Hindered Diffusion7.5.3 Porous Catalysts: Effective Diffusivity7.6 Heterogeneous Media7.7 Polymeric Membranes7.8 Other Complex EffectsSummaryReview QuestionsProblems
Chapter 8. Transient Diffusion Processes
8.1 Transient Diffusion Problems in 1-D8.2 Solution for Slab: Dirichlet Case8.2.1 Dimensionless Representation8.2.2 Series Solution8.2.3 Evaluation of the Series Coefficient8.2.4 Illustrative Results8.2.5 Average Concentration8.3 Solutions for Slab: Robin Condition8.4 Solution for Cylinders and Spheres8.4.1 Long Cylinder8.4.2 Sphere8.4.3 One-Term Approximation8.5 Transient Non-Homogeneous Problems8.5.1 D-D Problem in Slab Geometry8.5.2 Transient Diffusion with Reaction8.6 2-D Problems: Product Solution Method8.7 Semi-Infinite Slab Analysis8.7.1 Constant Surface Concentration8.7.2 Integral Method8.7.3 Pulse Response8.8 Penetration Theory of Mass Transfer8.9 Transient Diffusion with Variable Diffusivity8.10 Eigenvalue Computations with CHEBFUN8.11 Computations with PDEPE Solver8.11.1 Sample Code for 1-D Transient Diffusion with ReactionSummaryReview QuestionsProblems
Chapter 9. Basics of Convective Mass Transport
9.1 Definitions for External and Internal Flows9.2 Relation to Differential Model9.3 Key Dimensionless Groups9.3.1 Other Derived Dimensionless Groups9.4 Mass Transfer in Flows in Pipes and Channels9.4.1 Laminar Flow9.4.2 Turbulent Flow9.4.3 Channel Flow9.5 Mass Transfer in Flow over a Flat Plate9.5.1 Laminar Flow9.5.2 Turbulent Flow9.5.3 The j-Factor9.6 Mass Transfer for Film Flow9.6.1 Solid to Liquid9.6.2 Gas to Liquid9.7 Mass Transfer from a Solid Sphere9.8 Mass Transfer from a Gas Bubble9.8.1 Bubble Swarms and Bubble Columns9.9 Mass Transfer in Mechanically Agitated Tanks9.10 Gas–Liquid Mass Transfer in a Packed Bed Absorber9.10.1 Liquid Side Coefficient9.10.2 Gas Side Coefficient9.10.3 Transfer AreaSummaryReview QuestionsProblems
Chapter 10. Convective Mass Transfer: Theory for Internal Laminar Flow
10.1 Mass Transfer in Laminar Flow in a Pipe10.1.1 Dimensionless Form10.1.2 Constant Wall Concentration: The Dirichlet Problem10.1.3 Concentration, Wall Mass Flux, and Sherwood Number10.2 Wall Reaction: The Robin Problem10.2.1 Solution Using CHEBFUN10.2.2 Illustrative Results10.3 Entry Region Analysis10.4 Channel Flows with Mass Transfer10.5 Mass Transfer in Film Flow10.5.1 Solid Dissolution at a Wall in Film Flow10.5.2 Gas Absorption from Interface in Film Flow10.6 Numerical Solution with PDEPESummaryReview QuestionsProblems
Chapter 11. Mass Transfer in Laminar Boundary Layers
11.1 Flat Plate with Low Flux Mass Transfer11.1.1 Concentration Equation11.1.2 Velocity Equations11.1.3 Scaling Results and the Analogies11.1.4 Exact or Blasius Analysis11.2 Integral Balance Approach11.2.1 Integral Momentum Balance11.2.2 Integral Species Mass Balance11.2.3 Solution for No Reaction Case11.2.4 Solution for Homogeneous Reaction11.3 High Flux Analysis11.3.1 Film Model11.3.2 Integral Balance Method11.3.3 Blasius Approach11.4 Mass Transfer for Flow over Inclined and Curved Surfaces11.4.1 Pressure Variation Term11.4.2 Integral Balance Method for Inclined and Curved Surfaces11.4.3 Inclined Plates: Use of Similarity Variable11.4.4 Wedge Flow: Falkner-Skan Equation11.4.5 Stagnation Point (Hiemenz) Flow11.4.6 Flow over a Rotating Disk11.4.7 Flow past a Sphere11.5 Bubbles and Drops11.5.1 Rigid Bubbles11.5.2 Spherical Cap BubblesSummaryReview QuestionsProblems
Chapter 12. Convective Mass Transfer in Turbulent Flow
12.1 Properties of Turbulent Flow12.1.1 Transition Criteria12.1.2 Characteristics of Fully Turbulent Flow12.1.3 Stochastic Nature12.2 Properties of Time Averaging12.3 Time-Averaged Equation of Mass Transfer12.3.1 Turbulent Mass Flux12.3.2 Reynolds Stresses12.3.3 Reaction Contribution12.4 Closure Models12.4.1 Turbulent Schmidt Number12.4.2 Prandtl’s Model for Eddy Viscosity12.5 Velocity and Turbulent Diffusivity Profiles12.5.1 Universal Velocity Profiles12.5.2 Eddy Diffusivity Profiles12.5.3 Wall Shear Stress Relations12.6 Turbulent Mass Transfer in Channels and Pipes12.6.1 Simplified Analysis: Constant Wall Flux12.6.2 Stanton Number Calculation for Boundary Layers12.6.3 Analogy with Momentum Transfer12.6.4 Stanton Number for Pipe Flows12.7 Van Driest Model for Large Sc12.8 Turbulent Mass Transfer at Gas–Liquid Interface12.8.1 Damping of Turbulence12.8.2 Marangoni Effect12.8.3 Interfacial TurbulenceSummaryReview QuestionsProblems
Chapter 13. Macroscopic and Compartmental Models
13.1 Stirred Reactor: The Backmixing Assumption13.2 Transient Balance: Tracer Studies13.2.1 Step Input13.2.2 Pulse or Bolus Input13.2.3 Age Distribution Functions13.2.4 Tracer Response for Tanks in Series Model13.3 Moment Analysis of Tracer Data13.3.1 Moments from Laplace Transform of Response13.4 Tanks in Series Models: Reactor Performance13.5 Macrofluid Models13.5.1 Second-Order Reaction13.5.2 Zero-Order Reaction13.6 Variance-Based Models for Partial Micromixing13.7 Compartmental Models13.7.1 Matrix Representation13.8 Compartmental Models for Environmental Transport13.8.1 Fugacity of Pollutants in Each Compartment13.8.2 Level I or Equilibrium Model13.8.3 Level II Model: Advection Effects13.8.4 Level III Model: Intermedia Transport Effects13.8.5 Level IV Model: Transient Effects13.9 Fluid–Fluid Systems13.9.1 Backmixed–Backmixed Model13.9.2 Equilibrium Model13.9.3 Mixing Cell Model13.10 Models for Multistage Cascades13.10.1 Equilibrium ModelSummaryReview QuestionsProblems
Chapter 14. Mesoscopic Models and the Concept of Dispersion
14.1 Plug Flow Idealization14.2 Dispersion Model14.2.1 Boundary Conditions14.2.2 Solution for a First-Order Reaction14.2.3 Nonlinear Reactions14.2.4 Dispersion Model: Numerical Code Using CHEBFUN14.2.5 Criteria for Negligible Dispersion14.3 Dispersion Coefficient: Tracer Response Method14.3.1 Laplace Domain Solution14.3.2 Moments of the Response Curve14.3.3 Time Domain Solution14.4 Taylor Model for Dispersion in Laminar Flow14.5 Segregated Flow Model14.6 Dispersion Coefficient Values for Some Common Cases14.7 Two-Phase Flow: Models Based on Ideal Flow Patterns14.7.1 Plug-Backmixed Model14.7.2 Non-Idealities in Two-Phase Flow14.8 Tracer Response in Two-Phase Systems14.8.1 Single Flowing Phase14.8.2 Two Flowing PhasesSummaryReview QuestionsProblems
Chapter 15. Mass Transfer: Multicomponent Systems
15.1 Constitutive Model for Multicomponent Transport15.1.1 Binary Revisited15.1.2 Generalization: The Stefan-Maxwell Model15.2 Computations for a Reacting System15.3 Heterogeneous Reactions15.4 Non-Reacting Systems15.4.1 Evaporation of a Liquid in a Ternary Mixture15.4.2 Evaporation of a Binary Liquid Mixture15.4.3 Equimolar Counter-Diffusion15.5 Multicomponent Diffusivity Matrix15.5.1 D Matrix Relation to Binary Pair Diffusivity
Chapter 16. Mass Transport in Electrolytic Systems
16.1 Transport of Charged Species: Preliminaries16.1.1 Mobility and Diffusivity16.1.2 Nernst-Planck Equation16.2 Charge Neutrality16.3 General Expression for the Electric Field16.3.1 Laplace Equation for the Potential16.3.2 Transference Number16.3.3 Mass Balance for Reacting Systems16.4 Electrolyte Transport across Uncharged Membrane16.5 Transport across a Charged Membrane16.5.1 Interfacial Jump: Donnan Equation16.5.2 Transport Rate16.6 Transfer Rate in Diffusion Film near an ElectrodeSummaryReview QuestionsProblems
Part II: Reacting Systems
Chapter 17. Laminar Flow Reactor
17.1 Model Equations and Key Dimensionless Groups17.1.1 Dimensionless Model Equations17.1.2 Boundary Conditions17.2 Two Limiting Cases17.2.1 Small B: Pure Convection Model17.2.2 Large B: Plug Flow Model17.3 Mesoscopic Dispersion Model17.4 Other Examples of Flow Reactors17.4.1 Channel Flow17.4.2 Non-Newtonian Fluids17.4.3 Heat Transfer Effects17.4.4 Turbulent Flow Reactor: 2-D Model17.4.5 Axial Dispersion Model for the Turbulent CaseSummaryReview QuestionsProblems
Chapter 18. Mass Transfer with Reaction: Porous Catalysts
18.1 Catalyst Properties and Applications18.1.1 Catalyst Properties18.2 Diffusion-Reaction Model18.2.1 First-Order Reaction18.2.2 Zero-Order Reaction18.2.3 nth-Order Reaction18.3 Multiple Species18.4 Three-Phase Catalytic Reactions18.4.1 Application Examples18.4.2 Mass Transfer Effects18.5 Temperature Effects in a Porous Catalyst18.5.1 Equations for Heat and Mass Transport18.5.2 Dimensionless Representation18.5.3 Dimensionless Boundary Conditions18.5.4 Estimate of the Temperature Gradients18.6 Orthogonal Collocation Method18.6.1 Basis of the Method18.6.2 Two-Point Collocation18.7 Finite Difference Methods18.7.1 Central Difference Equations18.7.2 Zero-Order Reaction18.7.3 Nonlinear Kinetics18.7.4 Neumann and Robin Conditions18.8 Linking with Reactor Models18.8.1 First-Order Reaction18.8.2 Second-Order Reaction18.8.3 Zero-Order ReactionSummaryReview QuestionsProblems
Chapter 19. Reacting Solids
19.1 Shrinking Core Model19.1.1 No Solid Product19.1.2 Solid Product: Ash Layer Effects19.2 Volume Reaction Model19.2.1 Kinetic Model19.2.2 Concentration Profile for Gas and Solid19.2.3 First-Order Reaction in B19.2.4 Zero-Order Reaction19.3 Other Models for Gas–Solid Reactions19.3.1 Effect of Structural Changes19.4 Solid–Solid Reactions19.4.1 Classical Models19.4.2 Dalvi-Suresh Contact Point ModelSummaryReview QuestionsProblems
Chapter 20. Gas–Liquid Reactions: Film Theory Models
20.1 First-Order Reaction of Dissolved Gas20.1.1 Boundary Conditions20.1.2 Dimensionless Version20.1.3 Flux Values at the Interface and into the Bulk20.1.4 Enhancement Factor20.2 Bulk Concentration and Bulk Reactions20.2.1 Bulk Concentration20.2.2 Absorption Rate Calculation for Ha < 0.220.3 Bimolecular Reactions20.3.1 Dimensionless Representation20.3.2 Invariance Property of the System20.3.3 Analysis for Pseudo-First-Order Case20.3.4 Analysis for Instantaneous Asymptote20.3.5 Second-Order Case: An Approximate Solution20.3.6 Instantaneous Case: Effect of Gas Film Resistance20.3.7 Choice of Contactor Based on the Regimes of Absorption20.4 Simultaneous Absorption of Two Gases20.4.1 Model Equations20.4.2 Dimensionless Representation20.4.3 CHEBFUN Solution20.5 Coupling with Reactor Models20.5.1 Semibatch Reactor20.5.2 Packed Column Absorber20.6 Absorption in Slurries20.6.1 Particle Size Effect20.6.2 Instantaneous Reaction Case20.7 Liquid–Liquid ReactionsSummaryReview QuestionsProblems
Chapter 21. Gas–Liquid Reactions: Penetration Theory Approach
21.1 Concepts of Penetration Theory21.1.1 First-Order or Pseudo-First-Order Reaction21.1.2 Laplace Transform Method21.1.3 Flux and the Average Rate of Mass Transfer21.1.4 Relation between Film Theory and Penetration Theory21.2 Bimolecular Reaction21.2.1 Dimensionless Form of the Model21.2.2 Illustrative Results21.3 Instantaneous Reaction Case21.4 Ideal Contactors21.4.1 Laminar Jet Apparatus21.4.2 Wetted Wall Column21.4.3 Wetted Sphere21.4.4 Stirred CellsSummaryReview QuestionsProblems
Chapter 22. Reactive Membranes and Facilitated Transport
22.1 Single Solute Diffusion22.1.1 Model Equations22.1.2 Dimensionless Representation22.1.3 Invariant of the System22.1.4 Instantaneous Reaction Asymptote22.1.5 Pseudo-First-Order Reaction Asymptote22.2 Co- and Counter-Transport22.2.1 Model for Counter-Transport22.2.2 Model for Co-Transport22.3 Equilibrium Model: A Computational Scheme22.3.1 Illustrative Results22.4 Reactive Membranes in Practice22.4.1 Emulsion Liquid Membranes (ELM)22.4.2 Immobilized Liquid Membranes (ILM)22.4.3 Fixed-Site Carrier MembranesSummaryReview QuestionsProblems
Chapter 23. Biomedical Applications
23.1 Oxygen Uptake in Lungs23.1.1 Oxygen-Hemoglobin Equilibrium23.1.2 Transport Steps for Oxygen Uptake23.1.3 Meso-Model for the Capillary23.2 Transport in Tissues: Krogh Model23.2.1 Oxygen Variation in the Capillary23.3 Compartmental Models for Pharmacokinetics23.3.1 Basic Framework23.3.2 Physiologically Based Compartments23.4 Model for a Hemodialyzer23.4.1 Model Formulation23.4.2 Model for Patient-Dialyzer SystemSummaryReview QuestionsProblems
Chapter 24. Electrochemical Reaction Engineering
24.1 Basic Definitions24.1.1 Anodic and Cathodic Reactions24.1.2 Half Reactions and Overall Reaction24.1.3 Classification of Electrode Reactions24.1.4 Primary Variables24.2 Thermodynamic Considerations: Nernst Equation24.2.1 Equilibrium Cell Potential24.3 Kinetic Model for Electrochemical Reactions24.3.1 Butler-Volmer Equation24.3.2 Tafel Equation24.4 Mass Transfer Effects24.4.1 Concentration Overpotential24.5 Voltage Balance24.6 Copper Electrowinning24.6.1 Operating Current Density24.6.2 Voltage Balance24.6.3 Meso-Model for the Electrolyzer24.7 Hydrogen Fuel Cell24.8 Li-Ion Battery Modeling24.8.1 Charging24.8.2 DischargingSummaryReview QuestionsProblems
Part III: Mass Transfer–Based Separations
Chapter 25. Humidification and Drying
25.1 Wet and Dry Bulb Temperature25.1.1 The Lewis Relation25.2 Humidification: Cooling Towers25.2.1 Classification25.2.2 General Design Considerations25.3 Model for Counterflow25.3.1 Mass Balance Equations25.3.2 Enthalpy Balance Equations25.3.3 Merkel Equation25.4 Cross-Flow Cooling Towers25.5 Drying25.5.1 Types of Dryers25.5.2 Types of Solids25.5.3 Constant and Falling Rates25.6 Constant Rate Period25.7 Falling Rate Period25.7.1 Empirical Models25.7.2 Diffusion Type of Models25.7.3 Capillary Flow Models25.7.4 Choosing a ModelSummaryReview QuestionsProblems
Chapter 26. Condensation
26.1 Condensation of Pure Vapor26.1.1 Laminar Regime: Nusselt Model26.1.2 Wavy and Turbulent Regime26.2 Condensation of a Vapor with a Non-Condensible Gas26.2.1 Mass Transfer Rate26.2.2 Heat Transfer Rate and Ackermann Correction Factor26.2.3 Interface Temperature Calculations26.2.4 Condenser Model26.3 Fog Formation26.4 Condensation of Binary Gas Mixture26.4.1 Condensation Rates: Unmixed Model26.4.2 Calculation of the Interface Temperature26.5 Condenser Model26.5.1 Liquid and Vapor Phase Balances26.6 Ternary Systems26.6.1 Stefan-Maxwell Model26.6.2 Condensation with ReactionSummaryReview QuestionsProblems
Chapter 27. Gas Transport in Membranes
27.1 Gas Separation Membranes27.1.1 Membrane Classification27.1.2 Transport Rate: Permeability27.1.3 Transport Rate: Permeance27.1.4 Selectivity27.1.5 Sievert’s Law: Dissociative Diffusion27.1.6 Nonlinear Effects in Membrane Transport27.2 Gas Translation Model27.3 Gas Permeator Models27.3.1 Flux Relations27.3.2 Local Concentration27.3.3 Backmixed-Backmixed Model27.3.4 Countercurrent Flow27.3.5 Cross-Flow Pattern27.4 Reactor Coupled with a Membrane SeparatorSummaryReview QuestionsProblems
Chapter 28. Liquid Separation Membranes
28.1 Classification Based on Pore Size28.2 Transport in Semi-Permeable Membranes28.2.1 Osmotic Pressure28.2.2 Reverse Osmosis28.2.3 Concentration Polarization Effects28.2.4 Kedem-Katchalski Model28.2.5 Equipment-Level Model28.3 Forward Osmosis28.4 Pervaporation28.4.1 Illustrative Applications28.4.2 Model for Permeate Flux28.4.3 Local Permeate CompositionSummaryReview QuestionsProblems
Chapter 29. Adsorption and Chromatography
29.1 Applications and Adsorbent Properties29.2 Isotherms29.2.1 Langmuir Model29.2.2 Competitive Adsorption Isotherm29.2.3 Freundlich Isotherms29.2.4 BET Isotherm29.3 Model for Batch Slurry Adsorber29.3.1 Model Equations29.3.2 Particle-Level Model29.3.3 Linear Driving Force Model29.3.4 Calculation of the Slurry Transients29.3.5 Simulation Using the Collocation Method29.3.6 Additional Complexities29.4 Fixed Bed Adsorption29.4.1 Equilibrium Model29.4.2 Axial Dispersion Effects29.4.3 Heterogeneous Model29.4.4 Klinkenberg Equation29.4.5 Scale-Up Aspects29.5 ChromatographySummaryReview QuestionsProblems
Chapter 30. Electrodialysis and Electrophoresis
30.1 Technological Aspects30.1.1 When to Use Electrodialysis30.1.2 Membranes30.1.3 Electrodialysis Reversal Process30.1.4 Electrodialysis with Bipolar Membranes30.2 Preliminary Design of an Electrodialyzer30.2.1 Current and Voltage30.2.2 Limiting Current30.2.3 Detailed Models30.3 Principle of Electrophoresis30.3.1 Solutes with Fixed Type of Charge30.3.2 Solutes with Charge Dependent on pH30.4 Electrophoretic Separation Devices30.4.1 Philpot Design30.4.2 Hannig Design30.4.3 Rotating Annular BedSummaryReview QuestionsProblems
References
Index
Code Snippets

Content preview from Mass Transfer Processes: Modeling, Computations, and Design

Chapter 19. Reacting Solids

Learning Objectives

After completing this chapter, you will be able to:

Show how mass transfer affects the rate at which a gas reacts with a solid.
Calculate the rate of reaction in a relatively non-porous solid based on the so-called shrinking core model.
Calculate the rate of reaction of a porous solid on the basis of a diffusion-reaction model.
Derive expressions for the conversion of the solid as a function of time.
Characterize the structural changes of the solid due to a reaction and see how it affects transport properties and the rate of conversion of the solid.
Examine the effects of structural changes such as pore plugging/ opening and in some cases, an incomplete conversion of the solid reactant.
Examine ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

Publisher Resources

ISBN: 9780134675640

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

Mass Transfer Processes: Modeling, Computations, and Design

by P. A. Ramachandran

Chapter 19. Reacting Solids

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.