Diffusion and Mass Transfer

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Features

  • Provides a comprehensive summary of the theoretical aspects of diffusion and mass transfer
  • Analyzes a wide variety of mass transfer problems
  • Explains and shows the use of solution methods such as Green’s functions, perturbation methods, and similarity transformations
  • Considers various aspects of polymer behavior, including polymer diffusion, sorption in polymers, and volumetric behavior of polymer–solvent systems
  • Discusses the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems

Summary

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.

Table of Contents

Introduction
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
Definitions
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
Antiplasticization
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
Vectors
Tensors
Results for Curvilinear Coordinates
Material and Spatial Representations
Reynolds’ Transport Theorem

Author Bio(s)

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. Vrentas received 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.

Editorial Reviews

"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