Transport Phenomena, 2nd Edition

by R. Byron Bird; Warren E. Stewart; Edwin N. Lightfoot

• ISBN13: 9780471410775
• ISBN10: 0471410772
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-08-01
• Publisher: Wiley

Summary

"Transport Phenomena" has been revised to include deeper and more extensive coverage of heat transfer, enlarged discussion of dimensional analysis, a new chapter on flow of polymers, systematic discussions of convective momentum, and energy. Topics also include mass transport, momentum transport and energy transport, which are presented at three different scales: molecular, microscopic and macroscopic. If this is your first look at Transport Phenomena you'll quickly learn that its balanced introduction to the subject of transport phenomena is the foundation of its long-standing success.

Table of Contents

Preface
The Subject of Transport Phenomena	1	(10)
Part 1 Momentum Transport
Viscosity and the Mechanisms of Momentum Transport	11	(29)
Newton's Law of Viscosity (Molecular Momentum Transport)	11	(5)
Calculation of Momentum Flux	15	(1)
Generalization of Newton's Law of Viscosity	16	(5)
Pressure and Temperature Dependence of Viscosity	21	(2)
Estimation of Viscosity from Critical Properties	23	(1)
Molecular Theory of the Viscosity of Gases at Low Density	23	(6)
Computation of the Viscosity of Gas Mixture at Low Density	28	(1)
Prediction of the Viscosity of a Gas Mixture at Low Density	28	(1)
Molecular Theory of the Viscosity of Liquids	29	(2)
Estimation of the Viscosity of a Pure Liquid	31	(1)
Viscosity of Suspensions and Emulsions	31	(3)
Convective Momentum Transport	34	(6)
Questions for Discussion	37	(1)
Problems	37	(3)
Shell Momentum Balances and Velocity Distributions in Laminar Flow	40	(35)
Shell Momentum Balances and Boundary Conditions	41	(1)
Flow of a Falling Film	42	(6)
Calculation of Film Velocity	47	(1)
Falling Film with Variable Viscosity	47	(1)
Flow Through a Circular Tube	48	(5)
Determination of Viscosity from Capillary Flow Data	52	(1)
Compressible Flow in a Horizontal Circular Tube	53	(1)
Flow Through an Annulus	53	(3)
Flow of Two Adjacent Immiscible Fluids	56	(2)
Creeping Flow around a Sphere	58	(17)
Determination of Viscosity from the Terminal Velocity of a Falling Sphere	61	(1)
Questions for Discussion	61	(1)
Problems	62	(13)
The Equations of Change for Isothermal Systems	75	(39)
The Equation of Continuity	77	(1)
Normal Stresses at Solid Surfaces for Incompressible Newtonian Fluids	78	(1)
The Equation of Motion	78	(3)
The Equation of Mechanical Energy	81	(1)
The Equation of Angular Momentum	82	(1)
The Equation of Change in Terms of the Substantial Derivative	83	(3)
The Bernoulli Equation for the Steady Flow of Inviscid Fluids	86	(1)
Use of the Equations of Change to Solve Flow Problems	86	(11)
Steady Flow in a Long Circular Tube	88	(1)
Falling Film with Variable Viscosity	89	(1)
Operation of a Couette Viscometer	89	(4)
Shape of the Surface of a Rotating Liquid	93	(2)
Flow near a Slowly Rotating Sphere	95	(2)
Dimensional Analysis of the Equations of Change	97	(17)
Transverse Flow around a Circular Cylinder	98	(3)
Steady Flow in an Agitated Tank	101	(2)
Pressure Drop for Creeping Flow in a Packed Tube	103	(1)
Questions for Discussion	104	(1)
Problems	104	(10)
Velocity Distributions with More than One Independent Variable	114	(38)
Time-Dependent Flow of Newtonian Fluids	114	(7)
Flow near a Wall Suddenly Set in Motion	115	(2)
Unsteady Laminar Flow between Two Parallel Plates	117	(3)
Unsteady Laminar Flow near an Oscillating Plate	120	(1)
Solving Flow Problems Using a Stream Function	121	(5)
Creeping Flow around a Sphere	122	(4)
Flow of Inviscid Fluids by Use of the Velocity Potential	126	(7)
Potential Flow around a Cylinder	128	(2)
Flow into a Rectangular Channel	130	(1)
Flow near a Corner	131	(2)
Flow near Solid Surfaces by Boundary-Layer Theory	133	(19)
Laminar Flow along a Flat Plate (Approximate Solution)	136	(1)
Laminar Flow along a Flat Plate (Exact Solution)	137	(2)
Flow near a Corner	139	(1)
Questions for Discussion	140	(1)
Problems	141	(11)
Velocity Distributions in Turbulent Flow	152	(25)
Comparisons of Laminar and Turbulent Flows	154	(2)
Time-Smoothed Equations of Change for Incompressible Fluids	156	(3)
The Time-Smoothed Velocity Profile near a Wall	159	(3)
Empirical Expressions for the Turbulent Momentum Flux	162	(3)
Development of the Reynolds Stress Expression in the Vicinity of the Wall	164	(1)
Turbulent Flow in Ducts	165	(3)
Estimation of the Average Velocity in a Circular Tube	166	(1)
Application of Prandtl's Mixing Length Formula to Turbulent Flow in a Circular Tube	167	(1)
Relative Magnitude of Viscosity and Eddy Viscosity	167	(1)
Turbulent Flow in Jets	168	(9)
Time-Smoothed Velocity Distribution in a Circular Wall Jet	168	(4)
Questions for Discussion	172	(1)
Problems	172	(5)
Interphase Transport in Isothermal Systems	177	(20)
Definition of Friction Factors	178	(1)
Friction Factors for Flow in Tubes	179	(6)
Pressure Drop Required for a Given Flow Rate	183	(1)
Flow Rate for a Given Pressure Drop	183	(2)
Friction Factors for Flow around Spheres	185	(3)
Determination of the Diameter of a Falling Sphere	187	(1)
Friction Factors for Packed Columns	188	(9)
Questions for Discussion	192	(1)
Problems	193	(4)
Macroscopic Balances for Isothermal Flow Systems	197	(34)
The Macroscopic Mass Balance	198	(2)
Draining of a Spherical Tank	199	(1)
The Macroscopic Momentum Balance	200	(2)
Force Exerted by a Jet (Part a)	201	(1)
The Macroscopic Angular Momentum Balance	202	(1)
Torque on a Mixing Vessel	202	(1)
The Macroscopic Mechanical Energy Balance	203	(2)
Force Exerted by a Jet (Part b)	205	(1)
Estimation of the Viscous Loss	205	(4)
Power Requirement for Pipeline Flow	207	(2)
Use of the Macroscopic Balances for Steady-State Problems	209	(7)
Pressure Rise and Friction Loss in a Sudden Enlargement	209	(1)
Performance of a Liquid-Liquid Ejector	210	(2)
Thrust on a Pipe Bend	212	(2)
The Impinging Jet	214	(1)
Isothermal Flow of a Liquid through an Orifice	215	(1)
Use of the Macroscopic Balances for Unsteady-State Problems	216	(5)
Acceleration Effects in Unsteady Flow from a Cylindrical Tank	217	(2)
Manometer Oscillations	219	(2)
Derivation of the Macroscopic Mechanical Energy Balance	221	(10)
Questions for Discussion	223	(1)
Problems	224	(7)
Polymeric Liquids	231	(32)
Examples of the Behavior of Polymeric Liquids	232	(4)
Rheometry and Material Functions	236	(4)
Non-Newtonian Viscosity and the Generalized Newtonian Models	240	(4)
Laminar Flow of an Incompressible Power-Law Fluid in a Circular Tube	242	(1)
Flow of a Power-Law Fluid in a Narrow Slit	243	(1)
Tangential Annular Flow of a Power-Law Fluid	244	(1)
Elasticity and the Linear Viscoelastic Models	244	(5)
Small-Amplitude Oscillatory Motion	247	(1)
Unsteady Viscoelastic Flow near an Oscillating Plate	248	(1)
The Corotational Derivatives and the Nonlinear Viscoelastic Models	249	(4)
Material Functions for the Oldroyd 6-Constant Model	251	(2)
Molecular Theories for Polymeric Liquids	253	(10)
Material Functions for the FENE-P Model	255	(3)
Questions for Discussion	258	(1)
Problems	258	(5)
Part II Energy Transport
Thermal Conductivity and the Mechanisms of Energy Transport	263	(27)
Fourier's Law of Heat Conduction (Molecular Energy Transport)	266	(6)
Measurement of Thermal Conductivity	270	(2)
Temperature and Pressure Dependence of Thermal Conductivity	272	(2)
Effect of Pressure on Thermal Conductivity	273	(1)
Theory of Thermal Conductivity of Gases at Low Density	274	(5)
Computation of the Thermal Conductivity of a Monatomic Gas at Low Density	277	(1)
Estimation of the Thermal Conductivity of a Polyatomic Gas at Low Density	278	(1)
Prediction of the Thermal Conductivity of a Gas Mixture at Low Density	278	(1)
Theory of Thermal Conductivity of Liquids	279	(1)
Prediction of the Thermal Conductivity of a Liquid	280	(1)
Thermal Conductivity of Solids	280	(1)
Effective Thermal Conductivity of Composite Solids	281	(2)
Convective Transport of Energy	283	(1)
Work Associated with Molecular Motions	284	(6)
Questions for Discussion	286	(1)
Problems	287	(3)
Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow	290	(43)
Shell Energy Balances; Boundary Conditions	291	(1)
Heat Conduction with an Electrical Heat Source	292	(4)
Voltage Required for a Given Temperature Rise in a Wire Heated by an Electric Current	295	(1)
Heated Wire with Specified Heat Transfer Coefficient and Ambient Air Temperature	295	(1)
Heat Conduction with a Nuclear Heat Source	296	(2)
Heat Conduction with a Viscous Heat Source	298	(2)
Heat Conduction with a Chemical Heat Source	300	(3)
Heat Conduction through Composite Walls	303	(4)
Composite Cylindrical Walls	305	(2)
Heat Conduction in a Cooling Fin	307	(3)
Error in Thermocouple Measurement	309	(1)
Forced Convection	310	(6)
Free Convection	316	(17)
Questions for Discussion	319	(1)
Problems	320	(13)
The Equations of Change for Nonisothermal Systems	333	(41)
The Energy Equation	333	(3)
Special Forms of the Energy Equation	336	(2)
The Boussinesq Equation of Motion for Forced and Free Convection	338	(1)
Use of the Equations of Change to Solve Steady-State Problems	339	(14)
Steady-State Forced-Convection Heat Transfer in Laminar Flow in a Circular Tube	342	(1)
Tangential Flow in an Annulus with Viscous Heat Generation	342	(1)
Steady Flow in a Nonisothermal Film	343	(1)
Transpiration Cooling	344	(2)
Free Convection Heat Transfer from a Vertical Plate	346	(3)
Adiabatic Frictionless Processes in an Ideal Gas	349	(1)
One-Dimensional Compressible Flow: Velocity, Temperature, and Pressure Profiles in a Stationary Shock Wave	350	(3)
Dimensional Analysis of the Equations of Change for Nonisothermal Systems	353	(21)
Temperature Distribution about a Long Cylinder	356	(2)
Free Convection in a Horizontal Fluid Layer; Formation of Benard Cells	358	(2)
Surface Temperature of an Electrical Heating Coil	360	(1)
Questions for Discussion	361	(1)
Problems	361	(13)
Temperature Distributions with More than One Independent Variable	374	(33)
Unsteady Heat Conduction in Solids	374	(7)
Heating of a Semi-Infinite Slab	375	(1)
Heating of a Finite Slab	376	(3)
Unsteady Heat Conduction near a Wall with Sinusoidal Heat Flux	379	(1)
Cooling of a Sphere in Contact with a Well-Stirred Fluid	379	(2)
Steady Heat Conduction in Laminar, Incompressible Flow	381	(4)
Laminar Tube Flow with Constant Heat Flux at the Wall	383	(1)
Laminar Tube Flow with Constant Heat Flux at the Wall: Asymptotic Solution for the Entrance Region	384	(1)
Steady Potential Flow of Heat in Solids	385	(2)
Temperature Distribution in a Wall	386	(1)
Boundary Layer Theory for Nonisothermal Flow	387	(20)
Heat Transfer in Laminar Forced Convection along a Heated Flat Plate (the von Karman Integral Method)	388	(3)
Heat Transfer in Laminar Forced Convection along a Heated Flat Plate (Asymptotic Solution for Large Prandtl Numbers)	391	(1)
Forced Convection in Steady Three-Dimensional Flow at High Prandtl Numbers	392	(2)
Questions for Discussion	394	(1)
Problems	395	(12)
Temperature Distributions in Turbulent Flow	407	(15)
Time-Smoothed Equations of Change for Incompressible Nonisothermal Flow	407	(2)
The Time-Smoothed Temperature Profile near a Wall	409	(1)
Empirical Expressions for the Turbulent Heat Flux	410	(1)
An Approximate Relation for the Wall Heat Flux for Turbulent Flow in a Tube	411	(1)
Temperature Distribution for Turbulent Flow in Tubes	411	(4)
Temperature Distribution for Turbulent Flow in Jets	415	(1)
Fourier Analysis of Energy Transport in Tube-Flow at Large Prandtl Numbers	416	(6)
Questions for Discussion	421	(1)
Problems	421	(1)
Interphase Transport in Nonisothermal Systems	422	(32)
Definitions of Heat Transfer Coefficients	423	(5)
Calculation of Heat Transfer Coefficients from Experimental Data	426	(2)
Analytical Calculation of Heat Transfer Coefficients for Forced Convection through Tubes and Slits	428	(5)
Heat Transfer Coefficients for Forced Convection in Tubes	433	(5)
Design of a Tubular Heater	437	(1)
Heat Transfer Coefficients for Forced Convection around Submerged Objects	438	(3)
Heat Transfer Coefficients for Forced Convection through Packed Beds	441	(1)
Heat Transfer Coefficients for Free and Mixed Convection	442	(4)
Heat Loss by Free Convection from a Horizontal Pipe	445	(1)
Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces	446	(8)
Condensation of Steam on a Vertical Surface	449	(1)
Questions for Discussion	449	(1)
Problems	450	(4)
Macroscopic Balances for Nonisothermal Systems	454	(33)
The Macroscopic Energy Balance	455	(1)
The Macroscopic Mechanical Energy Balance	456	(2)
Use of the Macroscopic Balances to Solve Steady-State Problems with Flat Velocity Profiles	458	(3)
The Cooling of an Ideal Gas	459	(1)
Mixing of Two Ideal Gas Streams	460	(1)
The d-Forms of the Macroscopic Balances	461	(4)
Parallel- or Counter-Flow Heat Exchangers	462	(2)
Power Requirement for Pumping a Compressible Fluid through a Long Pipe	464	(1)
Use of the Macroscopic Balances to Solve Unsteady-State Problems and Problems with Nonflat Velocity Profiles	465	(22)
Heating of a Liquid in an Agitated Tank	466	(2)
Operation of a Simple Temperature Controller	468	(3)
Flow of Compressible Fluids through Heat Meters	471	(1)
Free Batch Expansion of a Compressible Fluid	472	(2)
Questions for Discussion	474	(1)
Problems	474	(13)
Energy Transport by Radiation	487	(26)
The Spectrum of Electromagnetic Radiation	488	(2)
Absorption and Emission at Solid Surfaces	490	(3)
Planck's Distribution Law, Wien's Displacement Law, and the Stefan-Boltzmann Law	493	(4)
Temperature and Radiation-Energy Emission of the Sun	496	(1)
Direct Radiation between Black Bodies in Vacuo at Different Temperatures	497	(5)
Estimation of the Solar Constant	501	(1)
Radiant Heat Transfer between Disks	501	(1)
Radiation between Nonblack Bodies at Different Temperatures	502	(4)
Radiation Shields	503	(1)
Radiation and Free-Convection Heat Losses from a Horizontal Pipe	504	(1)
Combined Radiation and Convection	505	(1)
Radiant Energy Transport in Absorbing Media	506	(7)
Absorption of a Monochromatic Radiant Beam	507	(1)
Questions for Discussion	508	(1)
Problems	508	(5)
Part III Mass Transport
Diffusivity and the Mechanisms of Mass Transport	513	(30)
Fick's Law of Binary Diffusion (Molecular Mass Transport)	514	(7)
Diffusion of Helium through Pyrex Glass	519	(1)
The Equivalence of D and D	520	(1)
Temperature and Pressure Dependence of Diffusivities	521	(4)
Estimation of Diffusivity at Low Density	523	(1)
Estimation of Self-Diffusivity at High Density	523	(1)
Estimation of Binary Diffusivity at High Density	524	(1)
Theory of Diffusion in Gases at Low Density	525	(3)
Computation of Mass Diffusivity for Low-Density Monatomic Gases	528	(1)
Theory of Diffusion in Binary Liquids	528	(3)
Estimation of Liquid Diffusivity	530	(1)
Theory of Diffusion in Colloidal Suspensions	531	(1)
Theory of Diffusion in Polymers	532	(1)
Mass and Molar Transport by Convection	533	(3)
Summary of Mass and Molar Fluxes	536	(2)
The Maxwell-Stefan Equations for Multicomponent Diffusion in Gases at Low Density	538	(5)
Questions for Discussion	538	(1)
Problems	539	(4)
Concentration Distributions in Solids and Laminar Flow	543	(39)
Shell Mass Balances; Boundary Conditions	545	(1)
Diffusion through a Stagnant Gas Film	545	(6)
Diffusion with a Moving Interface	549	(1)
Determination of Diffusivity	549	(1)
Diffusion through a Nonisothermal Spherical Film	550	(1)
Diffusion with a Heterogeneous Chemical Reaction	551	(3)
Diffusion with a Slow Heterogeneous Reaction	553	(1)
Diffusion with a Homogeneous Chemical Reaction	554	(4)
Gas Absorption with Chemical Reaction in an Agitated Tank	555	(3)
Diffusion into a Falling Liquid Film (Gas Absorption)	558	(4)
Gas Absorption from Rising Bubbles	560	(2)
Diffusion into a Falling Liquid Film (Solid Dissolution)	562	(1)
Diffusion and Chemical Reaction inside a Porous Catalyst	563	(4)
Diffusion in a Three-Component Gas System	567	(15)
Questions for Discussion	568	(1)
Problems	568	(14)
Equations of Change for Multicomponent Systems	582	(30)
The Equations of Continuity for a Multicomponent Mixture	582	(4)
Diffusion, Convection, and Chemical Reaction	585	(1)
Summary of the Multicomponent Equations of Change	586	(4)
Summary of the Multicomponent Fluxes	590	(2)
The Partial Molar Enthalpy	591	(1)
Use of the Equations of Change for Mixtures	592	(7)
Simultaneous Heat and Mass Transport	592	(3)
Concentration Profile in a Tubular Reactor	595	(1)
Catalytic Oxidation of Carbon Monoxide	596	(2)
Thermal Conductivity of a Polyatomic Gas	598	(1)
Dimensional Analysis of the Equations of Change for Nonreacting Binary Mixtures	599	(13)
Concentration Distribution about a Long Cylinder	601	(1)
Fog Formation during Dehumidification	602	(2)
Blending of Miscible Fluids	604	(1)
Questions for Discussion	605	(1)
Problems	606	(6)
Concentration Distributions with More than One Independent Variable	612	(45)
Time-Dependent Diffusion	613	(10)
Unsteady-State Evaporation of a Liquid (the ``Arnold Problem'')	613	(4)
Gas Absorption with Rapid Reaction	617	(2)
Unsteady Diffusion with First-Order Homogeneous Reaction	619	(2)
Influence of Changing Interfacial Area on Mass Transfer at an Interface	621	(2)
Steady-State Transport in Binary Boundary Layers	623	(10)
Diffusion and Chemical Reaction in Isothermal Laminar Flow along a Soluble Flat Plate	625	(2)
Forced Convection from a Flat Plate at High Mass-Transfer Rates	627	(5)
Approximate Analogies for the Flat Plate at Low Mass-Transfer Rates	632	(1)
Steady-State Boundary-Layer Theory for Flow around Objects	633	(4)
Mass Transfer for Creeping Flow around a Gas Bubble	636	(1)
Boundary Layer Mass Transport with Complex Interfacial Motion	637	(6)
Mass Transfer with Nonuniform Interfacial Deformation	641	(1)
Gas Absorption with Rapid Reaction and Interfacial Deformation	642	(1)
``Taylor Dispersion'' in Laminar Tube Flow	643	(14)
Questions for Discussion	647	(1)
Problems	648	(9)
Concentration Distributions in Turbulent Flow	657	(14)
Concentration Fluctuations and the Time-Smoothed Concentration	657	(1)
Time-Smoothing of the Equation of Continuity of A	658	(1)
Semi-Empirical Expressions for the Turbulent Mass Flux	659	(1)
Enhancement of Mass Transfer by a First-Order Reaction in Turbulent Flow	659	(4)
Turbulent Mixing and Turbulent Flow with Second-Order Reaction	663	(8)
Questions for Discussion	667	(1)
Problems	668	(3)
Interphase Transport in Nonisothermal Mixtures	671	(55)
Definition of Transfer Coefficients in One Phase	672	(4)
Analytical Expressions for Mass Transfer Coefficients	676	(3)
Correlation of Binary Transfer Coefficients in One Phase	679	(8)
Evaporation from a Freely Falling Drop	682	(1)
The Wet and Dry Bulb Psychrometer	683	(2)
Mass Transfer in Creeping Flow through Packed Beds	685	(2)
Mass Transfer to Drops and Bubbles	687	(1)
Definition of Transfer Coefficients in Two Phases	687	(7)
Determination of the Controlling Resistance	690	(1)
Interaction of Phase Resistances	691	(2)
Area Averaging	693	(1)
Mass Transfer and Chemical Reactions	694	(4)
Estimation of the Interfacial Area in a Packed Column	694	(1)
Estimation of Volumetric Mass Transfer Coefficients	695	(1)
Model-Insensitive Correlations for Absorption with Rapid Reaction	696	(2)
Combined Heat and Mass Transfer by Free Convection	698	(1)
Additivity of Grash of Numbers	698	(1)
Free-Convection Heat Transfer as a Source of Forced-Convection Mass Transfer	698	(1)
Effects of Interfacial Forces on Heat and Mass Transfer	699	(4)
Elimination of Circulation in a Rising Gas Bubble	701	(1)
Marangoni Instability in a Falling Film	702	(1)
Transfer Coefficients at High Net Mass Transfer Rates	703	(13)
Rapid Evaporation of a Liquid from a Plane Surface	710	(1)
Correction Factors in Droplet Evaporation	711	(1)
Wet-Bulb Performance Corrected for Mass-Transfer Rate	711	(1)
Comparison of Film and Penetration Models for Unsteady Evaporation in a Long Tube	712	(1)
Concentration Polarization in Ultrafiltration	713	(3)
Matrix Approximations for Multicomponent Mass Transport	716	(10)
Questions for Discussion	721	(1)
Problems	722	(4)
Macroscopic Balances for Multicomponent Systems	726	(38)
The Macroscopic Mass Balances	727	(11)
Disposal of an Unstable Waste Product	728	(2)
Binary Splitters	730	(1)
The Macroscopic Balances and Dirac's ``Separative Capacity'' and ``Value Function''	731	(2)
Compartmental Analysis	733	(3)
Time Constants and Model Insensitivity	736	(2)
The Macroscopic Momentum and Angular Momentum Balances	738	(1)
The Macroscopic Energy Balance	738	(1)
The Macroscopic Mechanical Energy Balance	739	(1)
Use of the Macroscopic Balances to Solve Steady-State Problems	739	(13)
Energy Balances for a Sulfur Dioxide Converter	739	(3)
Height of a Packed-Tower Absorber	742	(4)
Linear Cascades	746	(3)
Expansion of a Reactive Gas Mixture through a Frictionless Adiabatic Nozzle	749	(3)
Use of the Macroscopic Balances to Solve Unsteady-State Problems	752	(12)
Start-Up of a Chemical Reactor	752	(1)
Unsteady Operation of a Packed Column	753	(3)
The Utility of Low-Order Moments	756	(2)
Questions for Discussion	758	(1)
Problems	759	(5)
Other Machanisms for Mass Transport	764	(41)
The Equation of Change for Entropy	765	(2)
The Flux Expressions for Heat and Mass	767	(7)
Thermal Diffusion and the Clusius-Dickel Column	770	(2)
Pressure Diffusion and the Ultracentrifuge	772	(2)
Concentration Diffusion and Driving Forces	774	(1)
Applications of the Generalized Maxwell-Stefan Equations	775	(10)
Centrifugation of Proteins	776	(3)
Proteins as Hydrodynamic Particles	779	(1)
Diffusion of Salts in an Aqueous Solution	780	(2)
Departures from Local Electroneutrality: Electro-Osmosis	782	(2)
Additional Mass-Transfer Driving Forces	784	(1)
Mass Transport across Selectively Permeable Membranes	785	(8)
Concentration Diffusion between Preexisting Bulk Phases	788	(1)
Ultrafiltration and Reverse Osmosis	789	(2)
Charged Membrance and Donnan Exclusion	791	(2)
Mass Transport in Porous Media	793	(12)
Knudsen Diffusion	795	(2)
Transport from a Binary External Solution	797	(1)
Questions for Discussion	798	(1)
Problems	799	(6)
Postface	805	(67)
Appendices
Appendix A Vector and Tensor Notation	807	(36)
A.1 Vector Operations from a Geometrical Viewpoint	808	(2)
A.2 Vector Operations in Terms of Components	810	(4)
A.2-1 Proof of a Vector Identity	814	(1)
A.3 Tensor Operations in Terms of Components	815	(4)
A.4 Vector and Tensor Differential Operations	819	(3)
A.4-1 Proof of a Tensor Identity	822	(2)
A.5 Vector and Tensor Integral Theorems	824	(1)
A.6 Vector and Tensor Algebra in Curvilinear Coordinates	825	(4)
A.7 Differential Operations in Curvilinear Coordinates	829	(2)
A.7-1 Differential Operations in Cylindrical Coordinates	831	(7)
A.7-2 Differential Operations in Spherical Coordinates	838	(1)
A.8 Integral Operations in Curvilinear Coordinates	839	(2)
A.9 Further Comments on Vector-Tensor Notation	841	(2)
Appendix B Fluxes and the Equations of Change	843	(9)
B.1 Newton's Law of Viscosity	843	(2)
B.2 Fourier's Law of Heat Conduction	845	(1)
B.3 Fick's (First) Law of Binary Diffusion	846	(1)
B.4 The Equation of Continuity	846	(1)
B.5 The Equation of Motion in Terms of τ	847	(1)
B.6 The Equation of Motion for a Newtonian Fluid with Constant p and μ	848	(1)
B.7 The Dissipation Function &thetas; for Newtonian Fluids	849	(1)
B.8 The Equation of Energy in Terms of q	849	(1)
B.9 The Equation of Energy for Pure Newtonian Fluids with Constant p and k	850	(1)
B.10 The Equation of Continuity for Species α in Terms of jα	850	(1)
B.11 The Equation of Continuity for Species A in Terms of ω for Constant pD	851	(1)
Appendix C Mathematical Topics	852	(6)
C.1 Some Ordinary Differential Equations and Their Solutions	852	(1)
C.2 Expansions of Functions in Taylor Series	853	(1)
C.3 Differentiation of Integrals (the Leibniz Formula)	854	(1)
C.4 The Gamma Function	855	(1)
C.5 The Hyperbolic Functions	856	(1)
C.6 The Error Function	857	(1)
Appendix D The Kinetic Theory of Gases	858	(5)
D.1 The Boltzmann Equation	858	(1)
D.2 The Equations of Change	859	(1)
D.3 The Molecular Expressions for the Fluxes	859	(1)
D.4 The Solution to the Boltzmann Equation	860	(1)
D.5 The Fluxes in Terms of the Transport Properties	860	(1)
D.6 The Transport Properties in Terms of the Intermolecular Forces	861	(1)
D.7 Concluding Comments	861	(2)
Appendix E Tables for Prediction of Transport Properties	863	(4)
E.1 Intermolecular Force Parameters and Critical Properties	864	(2)
E.2 Functions for Prediction of Transport Properties of Gases at Low Densities	866	(1)
Appendix F Constants and Conversion Factors	867	(5)
F.1 Mathematical Constants	867	(1)
F.2 Physical Constants	867	(1)
F.3 Conversion Factors	868	(4)
Notation	872	(5)
Author Index	877	(8)
Subject Index	885