Diffusion and Mass Transfer

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.

IntroductionGeneralized Transport Phenomena Approach to Problem AnalysisGeneral ContentConservation Laws and Field EquationsConcentrations, Velocities, and FluxesThermodynamics of Purely Viscous Fluid MixturesConservation of Mass for a One-Component SystemConservation of Mass for a MixtureModification of Field Equations for Mass TransferConservation of Linear Momentum for One-Component SystemsConservation of Linear Momentum for a MixtureConservation of Moment of Momentum for One-Component SystemsConservation of Moment of Momentum for a MixtureStrategies for the Solution of Mass Transfer ProblemsBoundary ConditionsDefinitionsJump Balances for Mass ConservationJump Balances for Linear Momentum ConservationPostulated Boundary Conditions at Phase InterfacesBoundary Conditions in the Absence of Mass TransferUtilization of Jump BalancesAdditional Comments on Boundary ConditionsBoundary Conditions and Uniqueness of SolutionsConstitutive EquationsConstitutive PrinciplesFirst-Order Theory for Binary SystemsCombined Field and Constitutive Equations for First-Order Binary TheoryFirst-Order Theory for Ternary SystemsSpecial Second-Order Theory for Binary SystemsViscoelastic Effects in Flow and DiffusionValidity of Constitutive EquationsParameters in Constitutive EquationsGeneral Approach in Parameter DeterminationDiffusion in Polymer–Solvent MixturesDiffusion in Infinitely Dilute Polymer SolutionsDiffusion in Dilute Polymer SolutionsDiffusion in Concentrated Polymer Solutions – Free-Volume Theory for Self-DiffusionDiffusion in Concentrated Polymer Solutions – Mutual Diffusion ProcessDiffusion in Crosslinked PolymersAdditional Properties of Diffusion CoefficientsSpecial Behaviors of Polymer–Penetrant SystemsVolumetric Behavior of Polymer–Penetrant SystemsSorption Behavior of Polymer–Penetrant SystemsAntiplasticizationNonequilibrium at Polymer–Penetrant InterfacesMathematical ApparatusBasic DefinitionsClassification of Second-Order Partial Differential EquationsSpecification of Boundary ConditionsSturm–Liouville TheorySeries and Integral Representations of FunctionsSolution Methods for Partial Differential EquationsSeparation of Variables MethodSeparation of Variables SolutionsIntegral TransformsSimilarity TransformationsGreen’s Functions for Ordinary Differential Equations Green’s Functions for Elliptic EquationsGreen’s Functions for Parabolic EquationsPerturbation SolutionsWeighted Residual MethodSolution Strategy for Mass Transfer ProblemsProposed Solution MethodsInduced ConvectionSolutions of a General Set of Mass Transfer ProblemsMixing of Two Ideal GasesSteady Evaporation of a Liquid in a TubeUnsteady-State EvaporationAnalysis of Free Diffusion ExperimentsDissolution of a Rubbery PolymerBubble Growth from Zero Initial SizeStability Behavior and Negative Concentrations in Ternary SystemsAnalysis of Impurity Migration in Plastic ContainersEfficiency of Green’s Function Solution MethodMass Transfer in Tube FlowTime-Dependent Interfacial ResistanceLaminar Liquid Jet Diffusion AnalysisAnalysis of the Diaphragm CellDissolved Organic Carbon Removal from Marine AquariumsUnsteady Diffusion in a Block CopolymerDrying of Solvent-Coated Polymer FilmsFlow and Diffusion Past a Flat Plate with Solid DissolutionGas Absorption in Vertical Laminar Liquid Jet Utilization of Polymers in Drug DeliveryGas Absorption and Diffusion into a Falling Liquid FilmPerturbation Solutions of Mass Transfer Moving Boundary ProblemsDissolution of a Plane Surface of a Pure Gas PhaseBubble DissolutionSingular Perturbations in Moving Boundary ProblemsDropping Mercury ElectrodeSorption in Thin FilmsNumerical Analysis of Mass Transfer Moving Boundary ProblemsDiffusion and Reaction Design of a Tubular Polymerization ReactorTransport Effects in Low-Pressure CVD ReactorsSolution of Reaction Problems with First-Order ReactionsPlug Flow Reactors with Variable Mass DensityBubble Dissolution and Chemical ReactionDanckwerts Boundary Conditions for Chemical ReactorsTransport in Nonporous MembranesAssumptions Used in the Theory for Membrane TransportSteady Mass Transport in Binary MembranesSteady Mass Transport in Ternary MembranesUnsteady Mass Transport in Binary MembranesPhase Inversion Process for Forming Asymmetric MembranesPressure Effects in MembranesAnalysis of Sorption and DesorptionDerivation of a Short-Time Solution Form for Sorption in Thin FilmsSorption to a Film from a Pure Fluid of Finite VolumeA General Analysis of Sorption in Thin FilmsAnalysis of Step-Change Sorption ExperimentsIntegral Sorption in Glassy PolymersIntegral Sorption in Rubbery PolymersOscillatory Diffusion and Diffusion WavesDispersion and ChromatographyFormulation of Taylor Dispersion ProblemDispersion in Laminar Tube Flow for Low Peclet NumbersDispersion in Laminar Tube Flow for Long TimesDispersion in Laminar Tube Flow for Short TimesAnalysis of an Inverse Gas Chromatography ExperimentEffects of Pressure Gradients on Diffusion: Wave Behavior and SedimentationWave Propagation in Binary Fluid MixturesHyperbolic WavesDispersive WavesTime Effects for Parabolic and Hyperbolic EquationsSedimentation EquilibriumViscoelastic DiffusionExperimental Results for Sorption ExperimentsViscoelastic Effects in Step-Change Sorption ExperimentsSlow Bubble Dissolution in a Viscoelastic FluidTransport with Moving Reference FramesRelationships Between Fixed and Moving Reference FramesField Equations in Moving Reference FramesSteady Diffusion in an UltracentrifugeMaterial Time Derivative OperatorsFrame Indifference of Material Time DerivativesFrame Indifference of Velocity Gradient TensorRheological ImplicationsAppendix: Vector and Tensor NotationGeneral Notation ConventionsVectorsTensorsResults for Curvilinear CoordinatesMaterial and Spatial RepresentationsReynolds’ Transport Theorem

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.