Chapter 0 The Subject of Transport Phenomena

Part Ⅰ Momentum TransportChapter 1 Viscosity and the Mechanisms of Momentum Transport

1.1 Newton's Law of Viscosity（Molecular Momentum Transport）

Ex.1.1-1 Calculation of Momentum Flux

1.2 Generalization of Newton's Law of Viscosity

1.3 Pressure and Temperature Dependence of Viscosity

Ex.1.3-1 Estimation of Viscosity from Critical Properties

1.4 Molecular Theory of the Viscosity of Gases at Low Density

Ex.1.4-1 Computation of the Viscosity of a Gas Mixture at Low Density

Ex.1.4-2 Prediction of the Viscosity of a Gas Mixture at Low Density

1.5 Molecular Theory of the Viscosity of Liquids

Ex.1.5-1 Estimation of the Viscosity of a Pure Liquid

1.6 Viscosity of Suspensions and Emulsions

1.7 Convective Momentum Transport

Questions for Discussion

Problems

Chapter 2 Shell Momentum Balances and Velocity Distributions in Laminar Flow

2.1 Shell Momentum Balances and Boundary Conditions

2.2 Flow of a Falling Film

Ex.2.2-1 Calculation of Film Velocity

Ex.2.2-2 Falling Film with Variable Viscosity

2.3 Flow Through a Circular Tube

Ex.2.3-1 Determination of Viscosity from Capillary Flow Data

Ex.2.3-2 Compressible Flow in a Horizontal Circular Tube

2.4 Flow through an Annulus

2.5 Flow of Two Adjacent Immiscible Fluids

2.6 Creeping Flow around a Sphere

Ex.2.6-1 Determination of Viscosity from the Terminal Velocity of a Falling Sphere

Questions for Discussion

Problems

Chapter 3 The Equations of Change for Isothermal Systems

3.1 The Equation of Continuity

Ex.3.1-1 Normal Stresses at Solid Surfaces for Incompressible Newtonian Fluids

3.2 The Equation of Motion

3.3 The Equation of Mechanical Energy

3.4 The Equation of Angular Momentum

3.5 The Equations of Change in Terms of the Substantial Derivative

Ex.3.5-1 The Bernoulli Equation for the Steady Flow of Inviscid Fluids

3.6 Use of the Equations of Change to Solve Flow Problems

Ex.3.6-1 Steady Flow in a Long Circular Tube

Ex.3.6-2 Falling Film with Variable Viscosity

Ex.3.6-3 Operation ofa Couette Viscometer

Ex.3.6-4 Shape of the Surface of a Rotating Liquid

Ex.3.6-5 Flow near a Slowly Rotating Sphere

3.7 Dimensional Analysis of the Equations of Change

Ex.3.7-1 Transverse Flow around a Circular Cylinder

Ex.3.7-2 Steady Flow in an Agitated Tank

Ex.3.7-3 Pressure Drop for Creeping Flow in a Packed Tube

Questions for Discussion

Problems

Chapter 4 Velocity Distributions with More than One Independent Variable

4.1 Time-Dependent Flow of Newtonian Fluids

Ex.4.1-1 Flow near a Wall Suddenly Set in Motion

Ex.4.1-2 Unsteady Laminar Flow between Two Parallel Plates

Ex.4.1-3 Unsteady Laminar Flow near an Oscillating Plate

4.2 Solving Flow Problems Using a Stream Function

Ex.4.2-1 Creeping Flow around a Sphere

4.3 Flow of Inviscid Fluids by Use of the Velocity Potential

Ex.4.3-1 Potential Flow around a Cylinder

Ex.4.3-2 Flow into a Rectangular Channel

Ex.4.3-3 Flow near a Corner

4.4 Flow near Solid Surfaces by Boundary-Layer Theory

Ex.4.4-1 Laminar Flow along a Flat Plate（Approximate Solution）

Ex.4.4-2 Laminar Flow along a Flat Plate（Exact Solution）

Ex.4.4-3 Flow near a Corner

Questions for Discussion

Problems

Chapter 5 Velocity Distributions in Turbulent Flow

5.1 Comparisons of Laminar and Turbulent Flows

5.2 Time-Smoothed Equations of Change for Incompressible Fluids

5.3 The Time-Smoothed Velocity Profile near a Wall

5.4 Empirical Expressions for the Turbulent Momentum Flux

Ex.5.4-1 Development of the Reynolds Stress Expression in the Vicinity of the Wall

5.5 Turbulent Flow in Ducts

Ex.5.5-1 Estimation of the Average Velocity in a Circular Tube

Ex.5.5-2 Application of Prandtl's Mixing Length Formula to Turbulent Flow in a Circular Tube

Ex.5.5-3 Relative Magnitude of Viscosity and Eddy Viscosity

5.6 Turbulent Flow in Jets

Ex.5.6-1 Time-Smoothed Velocity Distribution in a Circular Wall Jet

Questions for Discussion

Problems

Chapter 6 Interphase Transport in Isothermal Systems

6.1 Definition of Friction Factors

6.2 Friction Factors for Flow in Tubes

Ex.6.2-1 Pressure Drop Required for a Given Flow Rate

Ex.6.2-2 Flow Rate for a Given Pressure Drop

6.3 Friction Factors for Flow around Spheres

Ex.6.3-1 Determination of the Diameter of a Falling Sphere

6.4 Friction Factors for Packed Columns

Questions for Discussion

Problems

Chapter 7 Macroscopic Balances for Isothermal Flow Systems

7.1 The Macroscopic Mass Balance

Ex.7.1-1 Draining of a Spherical Tank

7.2 The Macroscopic Momentum Balance

Ex.7.2-1 Force Exerted by a 1et （Part a）

7.3 The Macroscopic Angular Momentum Balance

Ex.7.3-1 Torque on a Mixing Vessel

7.4 The Macroscopic Mechanical Energy Balance

Ex.7.4-1 Force Exerted by a Jet（Part b）

7.5 Estimation of the Viscous Loss

Ex.7.5-1 Power Requirement for Pipeline Flow

7.6 Use of the Macroscopic Balances for Steady-State Problems

Ex.7.6-1 Pressure Rise and Friction Loss in a Sudden Enlargement

Ex.7.6-2 Performance of a Liquid-Liquid Ejector

Ex.7.6-3 Thrust on a Pipe Bend

Ex.7.6-4 The Impinging Jet

Ex.7.6-5 Isothermal Flow of a Liquid through an Orifice

7.7 Use of the Macroscopic Balances for Unsteady-State Problems

Ex.7.7.1 Acceleration Effects in Unsteady Flow from a Cylindrical Tank

Ex.7.7-2 Manometer Oscillations

7.8 Derivation of the Macroscopic Mechanical Energy Balance

Questions for Discussion

Problems

Chapter 8 Polymeric Liquids

8.1 Examples of the Behavior of Polymeric Liquids

8.2 Rheometry and Material Functions

8.3 Non-Newtonian Viscosity and the Generalized Newtonian Models

Ex.8.3-1 Laminar Flow of an Incompressible Power-Law Fluid in a Circular Tube

Ex.8.3-2 Flow of a Power-Law Fluid in a Narrow Slit

Ex.8.3-3 Tangential Annular Flow of a Power-Law Fluid

8.4 Elasticity and the Linear Viscoelastic Models

Ex.8.4-1 Small-Amplitude Oscillatory Motion

Ex.8.4-2 Unsteady Viscoelastic Flow near an Oscillating Plate

8.5 The Corotational Derivatives and the Nonlinear Viscoelastic Models

Ex.8.5-1 Material Functions for the Oldroyd 6-Constant Model

8.6 Molecular Theories for Polymeric Liquids

Ex.8.6-1 Material Functions for the FENE-P Model

Questions for Discussion

Problems

Part Ⅱ Energy Transport

Chapter 9 Thermal Conductivity and the Mechanisms of Energy Transport

9.1 Fouriers Law of Heat Conduction（Molecular Energy Transport）

Ex.9.1-1 Measurement of Thermal Conductivity

9.2 Temperature and Pressure Dependence of Thermal Conductivity

Ex.9.2-1 Effect of Pressure on Thermal Conductivity

9.3Theory of Thermal Conductivity of Gases at Low Density

Ex.9.3-1 Computation of the Thermal Conductivity of a Monatomic Gas at Low Density

Ex.9.3-2 Estimation of the Thermal Conductivity of a Polyatomic Gas at Low Density

Ex.9.3-3 Prediction of the Thermal Conductivity of a Gas Mixture at Low Density

9.4 Theory of Thermal Conductivity of Liquids

Ex.9.4-1 Prediction of the Thermal Conductivity of a Liquid

9.5 Thermal Conductivity of Solids

9.6 Effective Thermal Conductivity of Composite Solids

9.7 Convective Transport of Energy

9.8 Work Associated with Molecular Motions

Questions for Discussion

Problems

Chapter 10 Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow

10.1 Shell Energy Balances;Boundary Conditions

10.2 Heat Conduction with an Electrical Heat Source

Ex.10.2-1 Voltage Required for a Given Temperature Rise in a Wire Heated by an Electric Current

Ex.10.2-2 Heated Wire with Specified Heat Transfer Coefficient and Ambient Air Temperature

10.3 Heat Conduction with a Nuclear Heat Source

10.4 Heat Conduction with a Viscous Heat Source

10.5 Heat Conduction with a Chemical Heat Source

10.6 Heat Conduction through Composite Walls

Ex.10.6-1 Composite Cylindrical Walls

10.7 Heat Conduction in a Cooling Fin

Ex.10.7-1 Error in Thermocouple Measurement

10.8 Forced Convection

10.9 Free Convection

Questions for Discussion

Problems

Chapter 11 The Equations of Change for Nonisothermal Systems

11.1 The Energy Equation

11.2 Special Forms of the Energy Equation

11.3 The Boussinesq Equation of Motion for Forced and Free Convection

11.4 Use of the Equations of Change to Solve Steady-State Problems

Ex.11.4-1 Steady-State Forced-Convection Heat Transfer in Laminar Flow in a Circular Tube

Ex.11.4-2 Tangential Flow in an Annulus with Viscous Heat Generation

Ex.11.4-3 Steady Flow in a Nonisothermal Film

Ex.11.4-4 Transpiration Cooling

Ex.11.4-5 Free Convection Heat Transfer from a Vertical Plate

Ex.11.4-6 Adiabatic Frictionless Processes in an Ideal Gas

Ex.11.4-7 One-Dimensional Compressible Flow：Velocity,Temperature,and Pressure Profiles in a Stationary Shock Wave

11.5 Dimensional Analysis of the Equations of Change for Nonisothermal Systems

Ex.11.5-1 Temperature Distribution about a Long Cylinder

Ex.11.5-2 Free Convection in a Horizontal Fluid Layer;Formation of Bénard Cells

Ex.11.5-3 Surface Temperature of an Electrical Heating Coil

Questions for Discussion

Problems

Chapter 12 Temperature Distributions with More than One Independent Variable

12.1 Unsteady Heat Conduction in Solids

Ex.12.1-1 Heatingofa Semi-Infinite Slab

Ex.12.1-2 Heatingofa Finite Slab

Ex.12.1-3 Unsteady Heat Conduction near a Wall with Sinusoidal Heat Flux

Ex.12.1-4 Coolingofa Sphere in Contact with a Well-Stirred Fluid

12.2Steady Heat Conduction in Laminar,Incompressible Flow

Ex.12.2-1 Laminar Tube Flow with Constant Heat Flux at the Wall

Ex.12.2-2 Laminar Tube Flow with Constant Heat Flux at the Wall：Asymptotic Solution for the Entrance Region

12.3Steady Potential Flow of Heat in Solids

Ex.12.3-1 Temperature Distribution in a Wall

12.4Boundary Layer Theory for Nonisothermal Flow

Ex.12.4-1 Heat Transfer in Laminar Forced Convection along a Heated Flat Plate（the von Kármán Integral Method）

Ex.12.4-2 Heat Transfer in Laminar Forced Convection along a Heated Flat Plate（Asymptotic Solution for Large Prandtl Numbers）

Ex.12.4-3 Foreed Convection in Steady Three-Dimensional Flow at High Prandtl Numbers

Questions for Discussion

Problems

Chapter 13 Temperature Distributions in Turbulent Flow

13.1 Time-Smoothed Equations of Change for Incompressible Nonisothermal Flow

13.2 The Time-Smoothed Temperature Profile near a Wall

13.3 Empirical Expressions for the Turbulent Heat Flux

Ex.13.3-1 An Approximate Relation for the Wall Heat Flux for Turbulent Flow in a Tube

13.4 Temperature Distribution for Turbulent Flow in Tubes

13.5 Temperature Distribution for Turbulent Flow in Jets

13.6 Fourier Analysis of Energy Transport in Tube Flow at Large Prandtl Numbers

Questions for Discussion

Problems

Chapter 14 Interphase Transport in Nonisothermal Systems

14.1 Definitions of Heat Transfer Coefficients

Ex.14.1-1 Calculation of Heat Transfer Coefficients from Experimental Data

14.2 Analytical Calculations of Heat Transfer Coefficients for Forced Convection through Tubes and Slits

14.3 Heat Transfer Coefficients for Forced Convection in Tubes

Ex.14.3-1 Design of a Tubular Heater

14.4 Heat Transfer Coefficients for Forced Convection around Submerged Objects

14.5 Heat Transfer Coefficients for Forced Convection through Packed Beds

14.6 Heat Transfer Coefficients for Free and Mixed Convection

Ex14.6-1 Heat Loss bu Free Convection from a Horizontal Pipe

14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces

Ex.14.7-1 Condensation of Steam on a Vertical Surface

Questions for Discussion

Problems

Chapter 15 Macroscopic Balances for Nonisothermal Systems

15.1 The Macroscopic Energy Balance

15.2 The Macroscopic Mechanical Energy Balance

15.3 Use of the Macroscopic Balances to Solve Steady-State Problems with Flat Velocity Profiles

Ex.15.3-1 The Cooling of an Ideal Gas

Ex.15.3-2 Mixing of Tuo Ideal Gas Streams

15.4 The d-Forms of the Macroscopic Balances

Ex.15.4-1 Parallel-or Counter-Flow Heat Exchangers

Ex.15.4-2 Power Requirement for Pumping a Compressible Fluid through a Long Pipe

15.5 Use of the Macroscopic Balances to Solve Unsteady-State Problems and Problems with Nonflat Velocity Profiles

Ex.15.5-1 Heating ofa Liquid in an Agitated Tank

Ex.15.5-2 Operation ofa Simple Temperature Controller

Ex.15.5-3 Flow of Compressible Fluids through Heat Meters

Ex.15.5-4 Free Batch Expansion of a Compressible Fluid

Questions for Discussion

Problems

Chapter 16 Energy Transport by Radiation

16.1 The Spectrum of Electromagnetic Radiation

16.2 Absorption and Emission at Solid Surfaces

16.3 Planck's Distribution Law,Wien's Displacement Law,and the Stefan-Boltzmann Law

Ex.16.3-1 Temperature and Radiation-Energy Emission of the Sun

16.4 Direct Radiation between Black Bodies in Vacuo at Different Temperatures

Ex.16.4-1 Estimation of the Solar Constant

Ex.16.4-2 Radiant Heat Transfer between Disks

16.5 Radiation between Nonblack Bodies at Different Temperatures

Ex.16.5-1 Radiation Shields

Ex.16.5-2 Radiation and Free-Convection Heat Losses from a Horizontal Pipe

Ex.16.5-3 Combined Radiation and Convection

16.6 Radiant Energy Transport in Absorbing Media

Ex.16.6-1 Absorption ofa Monochromatic Radiant Beam

Questions for Discussion

Problems

Part Ⅲ Mass Transport

Chapter 17 Diffusivity and the Mechanisms of Mass Transport

17.1 Fick's Law of Binary Diffusion（Molecular Mass Transport）

Ex.17.1-1 Diffusion ofHelium through Pyrex Glass

Ex.17.1-2 The Equivalence of DAB and DBA

17.2 Temperature and Pressure Dependence of Diffusivities

Ex.17.2-1 Estimation of Diffusivity at Low Density

Ex.17.2-2 Estimation of Self-Diffusivity at High Density

Ex.17.2-3 Estimation of Binary Diffusivity at High Density

17.3 Theory of Diffusion in Gases at Low Density

Ex.17.3-1 Computation of Mass Diffusivity for Low-Density Monatomic Gases

17.4 Theory of Diffusion in Binary Liquids

Ex.17.4-1 Estimation of Liquid Diffusivity

17.5 Theory of Diffusion in Colloidal Suspensions

17.6 Theory of Diffusion in Polymers

17.7 Mass and Molar Transport by Convection

17.8 Summary of Mass and Molar Fluxes

17.9 The Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density

Questions for Discussion

Problems

Chapter 18 Concentration Distributions in Solids and Laminar Flow

18.1 Shell Mass Balances;Boundary Conditions

18.2 Diffusion through a Stagnant Gas Film

Ex.18.2-1 Diffusion with a Moving Interface

Ex.18.2-2 Determination of Diffusivity

Ex.18.2-3 Diffusion through a Nonisothermal Spherical Film

18.3 Diffusion with a Heterogeneous Chemical Reaction

Ex.18.3-1 Diffusion with a Slow Heterogeneous Reaction

18.4 Diffusion with a Homogeneous Chemical Reaction

Ex.18.4-1 Gas Absorption with Chemical Reaction in an Agitated Tank

18.5 Diffusion into a Falling Liquid Film（Gas Absorption）

Ex.18.5-1 Gas Absorption from Rising Bubbles

18.6 Diffusion into a Falling Liquid Film（Solid Dissolution）

18.7 Diffusion and Chemical Reaction inside a Porous Catalyst

18.8 Diffusion in a Three-Component Gas System

Questions for Discussion

Problems

Chapter 19 Equations of Change for Multicomponent Systems

19.1 The Equations of Continuity for a Multicomponent Mixture

Ex.19.1-1 Diffusion,Convection,and Chemical Reaction

19.2 Summary of the Multicomponent Equations of Change

19.3 Summary of the Multicomponent Fluxes

Ex.19.3-1 The Partial Molar Enthalpy

19.4 Use of the Equations of Change for Mixtures

Ex.19.4-1 Simultaneous Heat and Mass Transport

Ex.19.4-2 Concentration Profile in a Tubular Reactor

Ex.19.4-3 Catalytic Oxidation of Carbon Monoxide

Ex.19.4-4 Thermal Conductivity of a Polyatomic Gas

19.5 Dimensional Analysis of the Equations of Change for Nonreacting Binary Mixtures

Ex.19.5-1 Concentration Distribution about a Long Cylinder

Ex.19.5-2 Fog Formation during Dehumidification

Ex.19.5-3 Blending of Miscible Fluids

Questions for Discussion

Problems

Chapter 20 Concentration Distributions with More than One Independent Variable

20.1 Time-Dependent Diffusion

Ex.20.1-1 Unsteady-State Evaporation of a Liquid（the“Arnold Problem”）

Ex.20.1-2 Gas Absorption with Rapid Reaction

Ex.20.1-3 Unsteady Diffusion with First-Order Homogeneous Reaction

Ex.20.1-4 Influence of Changing Interfacial Area on Mass Transferat an Interface

20.2 Steady-State Transport in Binary Boundary Layers

Ex.20.2-1 Diffusion and Chemical Reaction in Isothermal Laminar Flow along a Soluble Flat Plate

Ex.20.2-2 Forced Convection from a Flat Plate at High Mass-Transfer Rates

Ex.20.2-3 Approximate Analogies for the Flat Plate at Low Mass-Transfer Rates

20.3 Steady-State Boundary-Layer Theory for Flow around Objects

Ex.20.3-1 Mass Transfer for Creeping Flow around a Gas Bubble

20.4 Boundary Layer Mass Transport with Complex Interfacial Motion

Ex.20.4-1 Mass Transfer with Nonuniform Interfacial Deformation

Ex.20.4-2 Gas Absorption with Rapid Reaction and Interfacial Deformation

20.5 “Taylor Dispersion”in Laminar Tube Flow

Questions for Discussion

Problems

Chapter 21 Concentration Distributions in Turbulent Flow

21.1 Concentration Fluctuations and the Time-Smoothed Concentration

21.2 Time-Smoothing of the Equation of Continuity of A

21.3 Semi-Empirical Expressions for the Turbulent Mass Flux

21.4 Enhancement of Mass Transfer by a First-Order Reaction in Turbulent Flow

21.5 Turbulent Mixing and Turbulent Flow with Second-Order Reaction

Questions for Discussion

Problems

Chapter 22 Interphase Transport in Nonisothermal Mixtures

22.1 Definition of Transfer Coefficients in One Phase

22.2 Analytical Expressions for Mass Transfer Coefficients

22.3 Correlation of Binary Transfer Coefficients in One Phase

Ex.22.3-1 Evaporation from a Freely Falling Drop

Ex.22.3-2 The Wet and Dry Bulb Psychrometer

Ex.22.3-3 Mass Transfer in Creeping Flow through Packed Beds

Ex.22.3-4 Mass Transfer to Drops and Bubbles

22.4 Definition of Transfer Coefficients in Two Phases

Ex.22.4-1 Determination of the Controlling Resistance

Ex.22.4-2 Interaction of Phase Resistances

Ex.22.4-3 Area Averaging

22.5 Mass Transfer and Chemical Reactions

Ex.22.5-1 Estimation of the Interfacial Area in a Packed Column

Ex.22.5-2 Estimation of Volumetric Mass Transfer Coefficients

Ex.22.5-3 Model-Insensitive Correlations for Absorption with Rapid Reaction

22.6 Combined Heat and Mass Transfer by Free Convection

Ex.22.6-1 Additivity of Grashof Numbers

Ex.22.6-2 Free-Convection Heat Transfer as a Source of Forced-Convection Mass Transfer

22.7 Effects of Interfacial Forces on Heat and Mass Transfer

Ex.22.7-1 Elimination of Circulation in a Rising Gas Bubble

Ex.22.7-2 Marangoni Instability in a Falling Film

22.8 Transfer Coefficients at High Net Mass Transfer Rates

Ex.22.8-1 Rapid Evaporation of a Liquid from a Plane Surface

Ex.22.8-2 Correction Factors in Droplet Evaporation

Ex.22.8-3 Wet-Bulb Performance Corrected for Mass-Transfer Rate

Ex.22.8-4 Comparison of Film and Penetration Models for Unsteady Evaporation in a Long Tube

Ex.22.8-5 Concentration Polarization in Ultrafiltration

22.9 Matrix Approximations for Multicomponent Mass Transport

Questions for Discussion

Problems

Chapter 23 Macroscopic Balances for Multicomponent Systems

23.1 The Macroscopic Mass Balances

Ex.23.1-1 Disposal of an Unstable Waste Product

Ex.23.1-2 Binary Splitters

Ex.23.1-3 The Macroscopic Balances and Dirac's Separative Capacity”and“Value Function”

Ex.23.1-4 Compartmental Analysis

Ex.23.1-5 Time Constants and Model Insensitivity

23.2 The Macroscopic Momentum and Angular Momentum Balances

23.3 The Macroscopic Energy Balance

23.4 The Macroscopic Mechanical Energy Balance

23.5 Use of the Macroscopic Balances to Solve Steady-State Problems

Ex.23.5-1 Energy Balances for a Sulfur Dioxide Converter

Ex.23.5-2 Heighht of a Packed-Tower Absorber

Ex.23.5-3 Linear Cascades

Ex.23.5-4 Expansion ofa Reactive Gas Mixture through a Frictionless Adiabatic Nozzle

23.6 Use of the Macroscopic Balances to Solve Unsteady-State Problems

Ex.23.6-1 Start-Up of a Chemical Reactor

Ex.23.6-2 Unsteady Operation of a Packed Column

Ex.23.6-3 The Utility of Low-Order Moments

Questions for Discussion

Problems

Chapter 24 Other Mechanisms for Mass Transport

24.1 The Equation of Change for Entropy

24.2 The Flux Expressions for Heat and Mass

Ex.24.2-1 Thermal Diffusion and the Clusius-Dickel Column

Ex.24.2-2 Pressure Diffusion and the Ultra-centrifuge

24.3 Concentration Diffusion and Driving Forces

24.4 Applications of the Generalized Maxwell-Stefan Equations

Ex.24.4-1 Centrifugation of Proteins

Ex.24.4-2 Proteins as Hydrodynamic Particles

Ex.24.4-3 Diffusion of Salts in an Aqueous Solution

Ex.24.4-4 Departures from Local Electroneutrality：Electro-Osmosis

Ex.24.4-5 Additional Mass-Transfer Driving Forces

24.5 Mass Transport across Selectively Permeable Membranes

Ex.24.5-1 Concentration Diffusion between Preexisting Bulk Phases

Ex.24.5-2 Ultrafiltration and Reverse Osmosis

Ex.24.5-3 Charged Membranes and Donnan Exclusion

24.6 Mass Transport in Porous Media

Ex.24.6-1 Knudsen Diffusion

Ex.24.6-2 Transport from a Binary External Solution

Questions for Discussion

Problems

Postface

Appendices

Appendix A Vector and Tensor Notation

A.1 Vector Operations from a Geometrical Viewpoint

A.2 Vector Operations in Terms of Components

Ex.A.2-1 Proof of a Vector Identity

A.3 Tensor Operations in Terms of Components

A.4 Vector and Tensor Differential Operations

Ex.A.4-1 Proof of a Tensor Identity

A.5 Vector and Tensor Integral Theorems

A.6 Vector and Tensor Algebra in Curvilinear Coordinates

A.7 Differential Operations in Curvilinear Coordinates

Ex.A.7-1 Differential Operations in Cylindrical Coordinates

Ex.A.7-2 Differential Operations in Spherical Coordinates

A.8 Integral Operations in Curvilinear Coordinates

A.9 Further Comments on Vector-Tensor Notation

Appendix B Fluxes and the Equations of Change

B.1 Newton's Law of Viscosity

B.2 Fourier's Law of Heat Conduction

B.3 Fick's（First）Law of Binary Diffusion

B.4 The Equation of Continuity

B.5 The Equation of Motion in Terms of ？

B.6 The Equation of Motion for a Newtonian Fluid with Constantρandμ

B.7 The Dissipation Functionφv for Newtonian Fluids

B.8 The Equation of Energy in Terms of q

B.9 The Equation of Energy for Pure Newtonian Fluids with Constantρand k

B.10 The Equation of Continuity for Speciesαin Terms of jα

B.11 The Equation of Continuity for Species A in Terms of ωA for ConstantρDAB

Appendix C Mathematical Topics

C.1 Some Ordinary Differential Equations and Their Solutions

C.2 Expansions of Functions in Taylor Series

C.3 Differentiation of Integrals（the Leibniz Formula）

C.4 The Gamma Function

C.5 The Hyperbolic Functions

C.6 The Error Function

Appendix D The Kinetic Theory of Gases

D.1 The Boltzmann Equation

D.2 The Equations of Change

D.3 The Molecular Expressions for the Fluxes

D.4 The Solution to the Boltzmann Equation

D.5 The Fluxes in Terms of the Transport Properties

D.6 The Transport Properties in Terms of the Intermolecular Forces

D.7 Concluding Comments

Appendix E Tables for Prediction of Transport Properties

E.1 Intermolecular Force Parameters and Critical Properties

E.2 Functions for Prediction of Transport Properties of Gases at Low Densities

Appendix F Constants and Conversion Factors

F.1 Mathematical Constants

F.2 Physical Constants

F.3 Conversion Factors

Notation

Author Index

Subject Index