Basic equations of the mass transport through a membrane layer / Endre Nagy.

Format:

Book

Author/Creator:

Nagy, Endre, 1946- author.

Series:

Elsevier insights.

Elsevier insights

Language:

English

Subjects (All):

Biological transport.

Membranes (Biology).

Physical Description:

1 online resource (xii, 329 pages) : illustrations.

Edition:

2nd ed.

Place of Publication:

Amsterdam, Netherlands ; Oxford, England ; Cambriadge, Massachusetts : Elsevier, [2019]

Summary:

Basic Equations of Mass Transport Through a Membrane Layer, Second Edition, has been fully updated to deliver the latest research in the field. This volume covers the essentials of compound separation, product removal, concentration, and production in the chemical, biochemical, pharmaceutical, and food industries. It outlines the various membrane processes and their applications, offering a detailed mathematical description of mass transport and defining basic mass transport and concentration distribution expressions. Additionally, this book discusses the process parameters and application of the expressions developed for a variety of industrial applications. Comprehensive explanations of convective/diffusive mass transport are provided, both with and without polarization layers, that help predict and process performance and facilitate improvements to operation conditions and efficiency.Basic Equations of Mass Transport Through a Membrane Layer is an ideal resource for engineers and technologists in the chemical, biochemical, and pharmaceutical industries, as well as researchers, professors, and students in these areas at both an undergraduate and graduate level.- Cites and analyzes mass transport equations developed for different membrane processes.- Examines the effect of biochemical/chemical reactions in the presence of convective and diffusive flows in plane and cylindrical spaces.- Defines the mass transfer rate for first- and zero-order reactions and analytical approaches are given for other-order reactions in closed mathematical forms.- Analyzes the simultaneous convective and diffusive transports with same or different directions.

Contents:

Front Cover

Basic Equations of Mass Transport Through a Membrane Layer

Basic Equations of MassTransport Through a Membrane Layer

Copyright

Dedication

Contents

Preface to the Second Edition

1 - Membrane Materials, Characterization, and Transport Properties

1.1 INTRODUCTION

1.2 MEMBRANE MATERIALS

1.2.1 Organic Membranes

1.2.2 Inorganic Membranes

1.2.3 Inorganic/Organic Hybrid Membranes

1.3 MEMBRANE CHARACTERIZATION METHODS

1.3.1 Physical and Chemical Characterization Modes

1.3.2 Microscopy Methods for Membrane Characterization

1.3.3 Spectroscopy Methods for Membrane Characterization

1.4 THE EFFECT OF POLYMER MEMBRANES' PHYSICAL/CHEMICAL PROPERTIES ON TRANSPORT

1.5 CONCLUDING REMARKS

REFERENCES

FURTHER READING

2 - Membrane Materials, Structures, and Modules

2.1 INTRODUCTION

2.2 MEMBRANE OPERATION PROCESSES

2.3 MEMBRANE MODULES

2.4 FLOW GEOMETRIES

2.5 CONCLUDING REMARKS

3 - Mass Transport Through a Membrane Layer

3.1 INTRODUCTION

3.2 GENERAL CONSIDERATIONS

3.2.1 State Properties and Equation

3.2.2 Typical Expressions According to the Solution/Diffusion Model

3.2.3 Nonequilibrium (Irreversible) Thermodynamic Approach

3.2.4 On Transport Mechanisms in General

3.3 SURVEY OF THE BASIC MASS FLUX EXPRESSIONS

3.3.1 Solution/Diffusion Mass Transport Through a Dense Membrane

3.3.1.1 Transport of Uncharged Species in Dilute Solution

3.3.1.2 Diffusive Transport of Charged Species

3.3.2 Convective Transport Through a Porous Membrane Layer

3.3.2.1 Viscous Flow

3.3.3 Gas Transport in Meso- (and Macro-) Porous Membranes

3.3.4 Molecular Sieving Transport

3.3.5 Transfer Rate of Concentrated Feed Solution

3.3.6 Application of the Maxwell-Stefan Equations.

3.3.6.1 The Maxwell-Stefan Approach to Mass Transfer in a Polymeric, Dense Membrane

3.3.6.2 The Maxwell-Stefan Approach to Mass Transfer in a Ceramic (Zeolite) Membrane

3.3.6.3 The Maxwell-Stefan Approach for Mass Transfer in Porous Media

3.3.7 Flory-Huggins Theory for Prediction of Activity

3.3.8 Maxwell-Stefan Equation With the Flory-Huggins' Theory

3.3.9 UNIQUAC Model

3.4 CONCLUDING REMARKS

NOTATION

GREEK

SUBSCRIPT

SUPERSCRIPT

4 - Molecular Diffusion

4.1 INTRODUCTION

4.2 GAS DIFFUSIVITIES

4.3 PREDICTION OF DIFFUSIVITIES IN LIQUIDS

4.4 DIFFUSION OF ELECTROLYTE SOLUTION

4.5 DIFFUSION IN A MEMBRANE

4.5.1 Diffusion in a Dense Membrane

4.5.1.1 Steady-State Diffusion

4.5.1.1.1 Diffusion Through a Composite Membrane

4.5.1.1.2 Diffusion Through a Composite Membrane With Different Solubility in the Sublayers

4.5.1.2 Unsteady-State Diffusion

4.5.1.2.1 Time-Lag Prediction in Special Cases

4.5.1.2.1.1 Concentration-Dependent Diffusion Coefficient

4.5.1.2.1.2 Two-Layer Composite Membrane

4.5.1.2.1.3 Time Lag for Dual-Mode Sorption

4.5.1.3 Diffusive Transport Through a Cylindrical Membrane

4.5.1.3.1 Nonsteady-State Solution

4.5.1.4 Solubility Coefficient in a Polymeric Membrane

4.5.2 Diffusion in a Porous Membrane

4.5.2.1 Knudsen-Limited Diffusion

4.5.2.2 Knudsen-Viscous Transition Diffusion

4.5.2.3 Knudsen-Molecular Diffusion

4.6 TRANSPORT WITH CONVECTIVE VELOCITY DUE TO THE COMPONENTS' DIFFUSION

4.7 ION TRANSPORT AND HINDRANCE FACTORS

4.8 CONCLUDING REMARKS

NOTATIONS

APPENDIX 4

5 - Diffusion Through a Plane Membrane Layer

5.1 INTRODUCTION

5.2 STEADY-STATE DIFFUSION

5.2.1 Concentration-Dependent Diffusion Coefficient.

5.2.1.1 Exponential Concentration Dependency, D=Doexp(αφ)≡Doexp(α˜Φ)

5.2.1.2 Linear Concentration Dependency, D=Do(1+αφ)≡Do(1+α˜Φ)

5.2.1.3 Optional Concentration Dependency of the Diffusion Coefficient

5.3 CONCENTRATION-DEPENDENT SOLUBILITY COEFFICIENT, H=H(C)

5.3.1 Linear Solubility Dependency

5.3.2 Langmuir-Type Dependency

5.3.3 Dual-Sorption Model

5.3.4 ENSIC Model

5.3.5 Flory-Huggins Model

5.4 MASS TRANSFER THROUGH A COMPOSITE MEMBRANE

5.5 BINARY COUPLED COMPONENT DIFFUSION TRANSPORT

5.5.1 Modeling of the Coupled Diffusion

5.6 CASE STUDIES

5.6.1 Binary Gas Separation by a Zeolite Membrane

5.6.2 Binary Transport for Pervaporation

5.7 NONSTEADY-STATE DIFFUSION

5.7.1 Mass Transport With External Mass Transfer Resistance on the Feed Side

5.7.2 Solution of Fickian Diffusion by Boltzmann's Transformation

5.7.3 Solution With Variable Diffusion Coefficient

5.8 CONCLUDING REMARKS

6 - Diffusion Accompanied by Chemical Reaction Through a Plane Sheet

6.1 INTRODUCTION

6.1.1 Important Characteristics and Performance of Chemical (Biochemical) Reactions

6.2 PSEUDOHOMOGENEOUS MODELS FOR FIRST-ORDER REACTIONS UNDER STEADY-STATE CONDITIONS

6.2.1 Mass Transfer Accompanied by a First-Order, Irreversible Reaction

6.2.1.1 Mass Transport Without a Sweeping Phase

6.2.1.2 First-Order Reaction With a Sweeping Phase on the Permeate Side

6.2.2 Mass Transport With a First-Order, Reversible Reaction (A⇄E)

6.2.3 First-Order Irreversible Reaction With a Polarization Layer on the Feed Side

6.2.3.1 Mass Transport Without a Sweeping Phase on the Permeate Side

6.2.3.2 Overall Mass Transfer Rate in the Presence of a Sweeping Phase on the Permeate Side

6.2.3.3 Polarization Layers on Both Sides of the Catalytic Membrane.

6.2.4 First-Order Reversible Reaction With a Polarization Layer

6.3 MASS TRANSFER FOR A ZERO-ORDER REACTION

6.3.1 Mass Transport Without a Sweeping Phase, dφ/dy=0 at y=δ

6.3.2 Mass Transport With a Sweeping Phase on the Permeate Side, dΦ/dY 0

6.3.3 Mass Transport With a Polarization Layer

6.3.3.1 Mass Transport Without a Sweeping Phase on the Permeate Side

6.3.3.2 Mass Transport With a Polarization Layer and With a Sweeping Phase on the Permeate Side

6.3.3.3 Mass Transport With Polarization Layers on Both Sides of a Catalytic Membrane Layer

6.4 MASS TRANSPORT ACCOMPANIED BY SECOND-ORDER IRREVERSIBLE REACTIONS

6.4.1 Mass Transport Accompanied by a Two-Component Reaction, r=k2φAφB

6.4.1.1 Both Reactants Can Leave the Catalytic Membrane by Diffusion

6.4.1.2 Reactant A Cannot Leave the Membrane by Diffusion, dφA/dY=0 at Y=1

6.4.2 Mass Transport With a One-Component, Second-Order Reaction, r=k2φA2

6.4.2.1 Transport of Reactant A Without Diffusion Flow of Reactant A out of the Permeate Side

6.4.2.2 Transport of Reactant A With a Sweeping Phase on the Permeate Side

6.4.3 Mass Transfer Accompanied by Michaelis-Menten (or Monod) Kinetics

6.4.3.1 Mass Transfer Without a Sweeping Phase on the Outlet Membrane Surface

6.4.3.2 Mass Transport With Michaelis-Menten Kinetics With a Sweeping Phase on the Permeate Side

6.4.4 Mass Transport With a First-Order Reaction With Variable Diffusion Coefficient

6.4.4.1 Mass Transport With a Sweeping Phase

6.4.4.1.1 Transport Without a Chemical Reaction With Variable Diffusion Coefficient and With a Sweeping Phase

6.4.4.2 Mass Transport Accompanied by Chemical Reaction, Without a Sweeping Phase

6.4.5 Mass Transport With a First-Order Reaction Through a Two-Layer Catalytic Membrane

6.5 CONCLUDING REMARKS

SUPERSCRIPT.

APPENDIX 6

A.1. Reactants Are Transported With General (at Y=1 dφj/dY 0

j=A, B) Boundary Layers

A.2. One of the Components Cannot Leave the Catalytic Membrane by Diffusion, dφA/dY=0 at Y=1

A.3. The Solution to r=k2A2, Second-Order Reaction by the Finite Difference Method

A.4. Some Remarks for a Solution to the Four-Diagonal Matrix

7 - Diffusive Plus Convective Mass Transport Through a Plane Membrane Layer

7.1 INTRODUCTION

7.2 DIFFUSION/CONVECTION MASS TRANSPORT THROUGH DIFFERENT TRANSPORT PROCESSES

7.2.1 Diffusive and Convective Countercurrent Fluxes

7.2.1.1 Permeate Side Concentration Is the Highest One Within the Transport Layer, φδ∗ φ∗

7.2.1.2 The Permeate Side Concentration Is Lower Than the Inlet Concentration, φδ∗&lt

φ∗

7.2.2 Diffusive and Convective Fluxes Flowing in the Same Direction

7.2.2.1 The Permeate Side (Y=1) Concentration Is Higher Than the Inlet Concentration, φδ∗ φ∗

7.2.2.2 Transfer Flows Have the Same Direction, and the Outlet Concentration Is Lower Than the Inlet Concentration, φδ&amp

lo ...

7.2.3 Mass Transfer Rates as a Function of the Peclet Number

7.3 DIFFUSION/CONVECTION MASS TRANSPORT THROUGH MORE THAN ONE TRANSFER LAYER

7.3.1 Mass Transport Through Two Transport Layers Considering the Membrane as a ``Black Box''

7.3.2 Mass Transport With Two Transport Layers Applying the Transport Expressions for Cases 2.1.1 and 2.2.2 Without a Sweeping Ph ...

7.3.3 Mass Transport Through Layers With Mixed Transport Properties With or Without a Sweeping Phase on the Permeate Side

7.3.3.1 Summarizing the Developed Expressions of E, Eo, and C∗/Co to the Previous Literature Expressions for Their Comparison

7.3.4 Adaptation of the Foregoing Solute Transport for Membrane Processes When φδ∗→0.

7.3.5 Mass Transport With Two Transport Layers Applying the Transport Expressions for Cases 2.1.2 and 2.2.1.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

0-12-813723-1

0-12-813722-3