## Description

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 for the engineering perspective, this book can be used as a text for reference and 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.

**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

**644 Pages – 100 B/W Illustrations. Published in 2012**

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**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