Diffusion and Mass Transfer: 1st Edition (Hardback) book cover

Diffusion and Mass Transfer

1st Edition

By James S. Vrentas, Christine M. Vrentas

CRC Press

644 pages | 100 B/W Illus.

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Hardback: 9781466515680
pub: 2012-12-12
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A proper understanding of diffusion and mass transfer theory is critical for obtaining correct solutions to many transport problems. Diffusion and Mass Transfer presents a comprehensive summary of the theoretical aspects of diffusion and mass transfer and applies that theory to obtain detailed solutions for a large number of important problems. Particular attention is paid to various aspects of polymer behavior, including polymer diffusion, sorption in polymers, and volumetric behavior of polymer–solvent systems.

The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedimentation, drying of polymer films, and chromatography.

Presenting diffusion and mass transfer from both engineering and fundamental science perspectives, this book can be used as a text for a graduate-level course as well as a reference text for research in diffusion and mass transfer. The book includes mass transfer effects in polymers, which are very important in many industrial processes. The attention given to the proper setup of numerous problems along with the explanations and use of mathematical solution methods will help readers in properly analyzing mass transfer problems.


"Finally a text which integrates in an easily understandable and logical fashion the coupled nature of the equations of change with respect to multicomponent mass transfer and its constitutive equations."

—William H. Velander, University of Nebraska, Lincoln

"The book begins with a description of conservation laws, boundary conditions and constitutive equations…presents a mathematical treatment not covered in other similar books. This is a modern approach to transport phenomena. The unique feature of the book is the treatment of several topics, such as sorption, chromatography, and viscoelastic diffusion."

—Darsh T. Wasan, Dimitri Gidaspow, Illinois Institute of Technology

Table of Contents


Generalized Transport Phenomena Approach to Problem Analysis

General Content

Conservation Laws and Field Equations

Concentrations, Velocities, and Fluxes

Thermodynamics of Purely Viscous Fluid Mixtures

Conservation of Mass for a One-Component System

Conservation of Mass for a Mixture

Modification of Field Equations for Mass Transfer

Conservation of Linear Momentum for One-Component Systems

Conservation of Linear Momentum for a Mixture

Conservation of Moment of Momentum for One-Component Systems

Conservation of Moment of Momentum for a Mixture

Strategies for the Solution of Mass Transfer Problems

Boundary Conditions


Jump Balances for Mass Conservation

Jump Balances for Linear Momentum Conservation

Postulated Boundary Conditions at Phase Interfaces

Boundary Conditions in the Absence of Mass Transfer

Utilization of Jump Balances

Additional Comments on Boundary Conditions

Boundary Conditions and Uniqueness of Solutions

Constitutive Equations

Constitutive Principles

First-Order Theory for Binary Systems

Combined Field and Constitutive Equations for First-Order Binary Theory

First-Order Theory for Ternary Systems

Special Second-Order Theory for Binary Systems

Viscoelastic Effects in Flow and Diffusion

Validity of Constitutive Equations

Parameters in Constitutive Equations

General Approach in Parameter Determination

Diffusion in Polymer–Solvent Mixtures

Diffusion in Infinitely Dilute Polymer Solutions

Diffusion in Dilute Polymer Solutions

Diffusion in Concentrated Polymer Solutions – Free-Volume Theory for Self-Diffusion

Diffusion in Concentrated Polymer Solutions – Mutual Diffusion Process

Diffusion in Crosslinked Polymers

Additional Properties of Diffusion Coefficients

Special Behaviors of Polymer–Penetrant Systems

Volumetric Behavior of Polymer–Penetrant Systems

Sorption Behavior of Polymer–Penetrant Systems


Nonequilibrium at Polymer–Penetrant Interfaces

Mathematical Apparatus

Basic Definitions

Classification of Second-Order Partial Differential Equations

Specification of Boundary Conditions

Sturm–Liouville Theory

Series and Integral Representations of Functions

Solution Methods for Partial Differential Equations

Separation of Variables Method

Separation of Variables Solutions

Integral Transforms

Similarity Transformations

Green’s Functions for Ordinary Differential Equations

Green’s Functions for Elliptic Equations

Green’s Functions for Parabolic Equations

Perturbation Solutions

Weighted Residual Method

Solution Strategy for Mass Transfer Problems

Proposed Solution Methods

Induced Convection

Solutions of a General Set of Mass Transfer Problems

Mixing of Two Ideal Gases

Steady Evaporation of a Liquid in a Tube

Unsteady-State Evaporation

Analysis of Free Diffusion Experiments

Dissolution of a Rubbery Polymer

Bubble Growth from Zero Initial Size

Stability Behavior and Negative Concentrations in Ternary Systems

Analysis of Impurity Migration in Plastic Containers

Efficiency of Green’s Function Solution Method

Mass Transfer in Tube Flow

Time-Dependent Interfacial Resistance

Laminar Liquid Jet Diffusion Analysis

Analysis of the Diaphragm Cell

Dissolved Organic Carbon Removal from Marine Aquariums

Unsteady Diffusion in a Block Copolymer

Drying of Solvent-Coated Polymer Films

Flow and Diffusion Past a Flat Plate with Solid Dissolution

Gas Absorption in Vertical Laminar Liquid Jet

Utilization of Polymers in Drug Delivery

Gas Absorption and Diffusion into a Falling Liquid Film

Perturbation Solutions of Mass Transfer Moving Boundary Problems

Dissolution of a Plane Surface of a Pure Gas Phase

Bubble Dissolution

Singular Perturbations in Moving Boundary Problems

Dropping Mercury Electrode

Sorption in Thin Films

Numerical Analysis of Mass Transfer Moving Boundary Problems

Diffusion and Reaction

Design of a Tubular Polymerization Reactor

Transport Effects in Low-Pressure CVD Reactors

Solution of Reaction Problems with First-Order Reactions

Plug Flow Reactors with Variable Mass Density

Bubble Dissolution and Chemical Reaction

Danckwerts Boundary Conditions for Chemical Reactors

Transport in Nonporous Membranes

Assumptions Used in the Theory for Membrane Transport

Steady Mass Transport in Binary Membranes

Steady Mass Transport in Ternary Membranes

Unsteady Mass Transport in Binary Membranes

Phase Inversion Process for Forming Asymmetric Membranes

Pressure Effects in Membranes

Analysis of Sorption and Desorption

Derivation of a Short-Time Solution Form for Sorption in Thin Films

Sorption to a Film from a Pure Fluid of Finite Volume

A General Analysis of Sorption in Thin Films

Analysis of Step-Change Sorption Experiments

Integral Sorption in Glassy Polymers

Integral Sorption in Rubbery Polymers

Oscillatory Diffusion and Diffusion Waves

Dispersion and Chromatography

Formulation of Taylor Dispersion Problem

Dispersion in Laminar Tube Flow for Low Peclet Numbers

Dispersion in Laminar Tube Flow for Long Times

Dispersion in Laminar Tube Flow for Short Times

Analysis of an Inverse Gas Chromatography Experiment

Effects of Pressure Gradients on Diffusion: Wave Behavior and Sedimentation

Wave Propagation in Binary Fluid Mixtures

Hyperbolic Waves

Dispersive Waves

Time Effects for Parabolic and Hyperbolic Equations

Sedimentation Equilibrium

Viscoelastic Diffusion

Experimental Results for Sorption Experiments

Viscoelastic Effects in Step-Change Sorption Experiments

Slow Bubble Dissolution in a Viscoelastic Fluid

Transport with Moving Reference Frames

Relationships Between Fixed and Moving Reference Frames

Field Equations in Moving Reference Frames

Steady Diffusion in an Ultracentrifuge

Material Time Derivative Operators

Frame Indifference of Material Time Derivatives

Frame Indifference of Velocity Gradient Tensor

Rheological Implications

Appendix: Vector and Tensor Notation

General Notation Conventions



Results for Curvilinear Coordinates

Material and Spatial Representations

Reynolds’ Transport Theorem

About the Authors

James S. Vrentas received his B.S. degree in chemical engineering from the University of Illinois and his M.Ch.E. and Ph.D. degrees in chemical engineering from the University of Delaware. As the Dow Professor of Chemical Engineering at the Pennsylvania State University, he teaches and conducts research in the fundamental aspects of diffusion and fluid mechanics. He is the recipient of two national AIChE awards, the William H. Walker Award for Excellence in Contributions to the Chemical Engineering Literature and the Charles M. A. Stine Award for Materials Engineering and Science. At Penn State, he has received the College of Engineering’s Premier Research Award and several teaching awards.

Christine M. Vrentasreceived her B.S. degree in chemical engineering from the Illinois Institute of Technology and her M.S. and Ph.D. degrees in chemical engineering from Northwestern University where she studied the dynamic and transient properties of polymer solutions. She has served as an instructor at the Pennsylvania State University and is currently an adjunct professor in the chemical engineering department working in the areas of diffusion and fluid mechanics. As a public school volunteer and supporter of science education, she helped coach State College Area Middle and High School Science Olympiad teams to national gold medals and served as a regional and state event supervisor at Science Olympiad competitions.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Chemistry / Industrial & Technical
SCIENCE / Mechanics / Dynamics / Thermodynamics