Mass transfer

Preface. 1 Introduction. 1.1 The Beginnings of Mass Transfer. 1.2 Characteristics of Mass Transfer. 1.3 Three Fundamental Laws of Transport Phenomena. 1.3.1 Newton's Law of Viscosity. 1.3.2 Fourier's Law of Heat Conduction. 1.3.3 Fick's Law of Diffusion. 1.4 Summary of Phase Equilibria in Gas-Liquid Systems. References. 2 Diffusion and Mass Transfer. 2.1 Motion of Molecules and Diffusion. 2.1.1 Diffusion Phenomena. 2.1.2 Definition of Diffusional Flux and Reference Velocity of Diffusion. 2.1.3 Binary Diffusion Flux. 2.2 Diffusion Coefficients. 2.2.1 Binary Diffusion Coefficients in the Gas Phase. 2.2.2 Multicomponent Diffusion Coefficients in the Gas Phase. Example 2.1. Solution. 2.3 Rates of Mass Transfer. 2.3.1 Definition of Mass Flux. 2.3.2 Unidirectional Diffusion in Binary Mass Transfer. 2.3.3 Equimolal Counterdiffusion. 2.3.4 Convective Mass Flux for Mass Transfer in a Mixture of Vapors. Example 2.2. Solution. 2.4 Mass Transfer Coefficients. Example 2.3. Solution. 2.5 Overall Mass Transfer Coefficients. References. 3 Governing Equations of Mass Transfer. 3.1 Laminar and Turbulent Flow. 3.2 Continuity Equation and Diffusion Equation. 3.2.1 Continuity Equation. 3.2.2 Diffusion Equation in Terms of Mass Fraction. 3.2.3 Diffusion Equation in Terms of Mole Fraction. 3.3 Equation of Motion and Energy Equation. 3.3.1 The Equation of Motion (Navier-Stokes Equation). 3.3.2 The Energy Equation. 3.3.3 Governing Equations in Cylindrical and Spherical Coordinates. 3.4 Some Approximate Solutions of the Diffusion Equation. 3.4.1 Film Model. 3.4.2 Penetration Model. 3.4.3 Surface Renewal Model. Example 3.1. Solution. 3.5 Physical Interpretation of Some Important Dimensionless Numbers. 3.5.1 Reynolds Number. 3.5.2 Prandtl Number and Schmidt Number. 3.5.3 Nusselt Number. 3.5.4 Sherwood Number. 3.5.5 Dimensionless Numbers Commonly Used in Heat and Mass Transfer. Example 3.2. Solution. 3.6 Dimensional Analysis. 3.6.1 Principle of Similitude and Dimensional Homogeneity. 3.6.2 Finding Dimensionless Numbers and Pi Theorem. References. 4 Mass Transfer in a Laminar Boundary Layer. 4.1 Velocity Boundary Layer. 4.1.1 Boundary Layer Equation. 4.1.2 Similarity Transformation. 4.1.3 Integral Form of the Boundary Layer Equation. 4.1.4 Friction Factor. 4.2 Temperature and Concentration Boundary Layers. 4.2.1 Temperature and Concentration Boundary Layer Equations. 4.2.2 Integral Form of Thermal and Concentration Boundary Layer Equations. Example 4.1. Solution. 4.3 Numerical Solutions of the Boundary Layer Equations. 4.3.1 Quasi-Linearization Method. 4.3.2 Correlation of Heat and Mass Transfer Rates. Example 4.2. Solution. 4.4 Mass and Heat Transfer in Extreme Cases. 4.4.1 Approximate Solutions for Mass Transfer in the Case of Extremely Large Schmidt Numbers. 4.4.2 Approximate Solutions for Heat Transfer in the Case of Extremely Small Prandtl Numbers. 4.5 Effect of an Inactive Entrance Region on Rates of Mass Transfer. 4.5.1 Polynomial Approximation of Velocity Profiles and Thickness of the Velocity Boundary Layer. 4.5.2 Polynomial Approximation of Concentration Profiles and Thickness of the Concentration Boundary Layer. 4.6 Absorption of Gases by a Falling Liquid Film. 4.6.1 Velocity Distribution in a Falling Thin Liquid Film According to Nusselt. 4.6.2 Gas Absorption for Short Contact Times. 4.6.3 Gas Absorption for Long Exposure Times. Example 4.3. Solution. 4.7 Dissolution of a Solid Wall by a Falling Liquid Film. 4.8 High Mass Flux Effect in Heat and Mass Transfer in Laminar Boundary Layers. 4.8.1 High Mass Flux Effect. 4.8.2 Mickley's Film Model Approach to the High Mass Flux Effect. 4.8.3 Correlation of High Mass Flux Effect for Heat and Mass Transfer. Example 4.4. Solution. References. 5 Heat and Mass Transfer in a Laminar Flow inside a Circular Pipe. 5.1 Velocity Distribution in a Laminar Flow inside a Circular Pipe. 5.2 Graetz Numbers for Heat and Mass Transfer. 5.2.1 Energy Balance over a Small Volume Element of a Pipe. 5.2.2 Material Balance over a Small Volume Element of a Pipe. 5.3 Heat and Mass Transfer near the Entrance Region of a Circular Pipe. 5.3.1 Heat Transfer near the Entrance Region at Constant Wall Temperature. 5.3.2 Mass Transfer near the Entrance Region at Constant Wall Concentration. 5.4 Heat and Mass Transfer in a Fully Developed Laminar Flow inside a Circular Pipe. 5.4.1 Heat Transfer at Constant Wall Temperature. 5.4.2 Mass Transfer at Constant Wall Concentration. 5.5 Mass Transfer in Wetted-Wall Columns. Example 5.1. Solution. References. 6 Motion, Heat and Mass Transfer of Particles. 6.1 Creeping Flow around a Spherical Particle. 6.2 Motion of Spherical Particles in a Fluid. 6.2.1 Numerical Solution of the Drag Coefficients of a Spherical Particle in the Intermediate Reynolds Number Range. 6.2.2 Correlation of the Drag Coefficients of a Spherical Particle. 6.2.3 Terminal Velocity of a Particle. Example 6.1. Solution. 6.3 Heat and Mass Transfer of Spherical Particles in a Stationary Fluid. 6.4 Heat and Mass Transfer of Spherical Particles in a Flow Field. 6.4.1 Numerical Approach to Mass Transfer of a Spherical Particle in a Laminar Flow. 6.4.2 The Ranz-Marshall Correlation and Comparison with Numerical Data. Example 6.2. Solution. 6.4.3 Liquid-Phase Mass Transfer of a Spherical Particle in Stokes' Flow. 6.5 Drag Coefficients, Heat and Mass Transfer of a Spheroidal Particle. 6.6 Heat and Mass Transfer in a Fluidized Bed. 6.6.1 Void Function. 6.6.2 Interaction of Two Spherical Particles of the Same Size in a Coaxial Arrangement. 6.6.3 Simulation of the Void Function. References. 7 Mass Transfer of Drops and Bubbles. 7.1 Shapes of Bubbles and Drops. 7.2 Drag Force of a Bubble or Drop in a Creeping Flow (Hadamard's Flow). 7.2.1 Hadamard's Stream Function. 7.2.2 Drag Coefficients and Terminal Velocities of Small Drops and Bubbles. 7.2.3 Motion of Small Bubbles in Liquids Containing Traces of Contaminants. 7.3 Flow around an Evaporating Drop. 7.3.1 Effect of Mass Injection or Suction on the Flow around a Spherical Particle. 7.3.2 Effect of Mass Injection or Suction on Heat and Mass Transfer of a Spherical Particle. Example 7.1. Solution. 7.4 Evaporation of Fuel Sprays. 7.4.1 Drag Coefficients, Heat and Mass Transfer of an Evaporating Drop. 7.4.2 Behavior of an Evaporating Drop Falling Freely in the Gas Phase. Example 7.2. Solution. 7.5 Absorption of Gases by Liquid Sprays. Example 7.3. Solution. 7.6 Mass Transfer of Small Bubbles or Droplets in Liquids. 7.6.1 Continuous-Phase Mass Transfer of Bubbles and Droplets in Hadamard Flow. 7.6.2 Dispersed-Phase Mass Transfer of Drops in Hadamard Flow. 7.6.3 Mass Transfer of Bubbles or Drops of Intermediate Size in the Liquid Phase. Example 7.4. Solution. References. 8 Turbulent Transport Phenomena. 8.1 Fundamentals of Turbulent Flow. 8.1.1 Turbulent Flow. 8.1.2 Reynolds Stress. 8.1.3 Eddy Heat Flux and Diffusional Flux. 8.1.4 Eddy Transport Properties. 8.1.5 Mixing Length Model. 8.2 Velocity Distribution in a Turbulent Flow inside a Circular Pipe and Friction Factors. 8.2.1 1/n-th Power Law. 8.2.2 Universal Velocity Distribution Law for Turbulent Flow inside a Circular Pipe. 8.2.3 Friction Factors for Turbulent Flow inside a Smooth Circular Pipe. Example 8.1. Solution. 8.3 Analogy between Momentum, Heat, and Mass Transfer. 8.3.1 Reynolds Analogy. 8.3.2 Chilton-Colburn Analogy. Example 8.2. Solution. 8.3.3 Von Ka'rman Analogy. 8.3.4 Deissler Analogy. Example 8.3. Solution. 8.4 Friction Factor, Heat, and Mass Transfer in a Turbulent Boundary Layer. 8.4.1 Velocity Distribution in a Turbulent Boundary Layer. 8.4.2 Friction Factor. 8.4.3 Heat and Mass Transfer in a Turbulent Boundary Layer. 8.5 Turbulent Boundary Layer with Surface Mass Injection or Suction. Example 8.4. Solution. References. 9 Evaporation and Condensation. 9.1 Characteristics of Simultaneous Heat and Mass Transfer. 9.1.1 Mass Transfer with Phase Change. 9.1.2 Surface Temperatures in Simultaneous Heat and Mass Transfer. 9.2 Wet-Bulb Temperatures and Psychrometric Ratios. Example 9.1. Solution. Example 9.2. Solution. 9.3 Film Condensation of Pure Vapors. 9.3.1 Nusselt's Model for Film Condensation of Pure Vapors. 9.3.2 Effect of Variable Physical Properties. Example 9.3. Solution. 9.4 Condensation of Binary Vapor Mixtures. 9.4.1 Total and Partial Condensation. 9.4.2 Characteristics of the Total Condensation of Binary Vapor Mixtures. 9.4.3 Rate of Condensation of Binary Vapors under Total Condensation. 9.5 Condensation of Vapors in the Presence of a Non-Condensable Gas. 9.5.1 Accumulation of a Non-Condensable Gas near the Interface. 9.5.2 Calculation of Heat and Mass Transfer. 9.5.3 Experimental Approach to the Effect of a Non-Condensable Gas. Example 9.4. Solution. 9.6 Condensation of Vapors on a Circular Cylinder. 9.6.1 Condensation of Pure Vapors on a Horizontal Cylinder. 9.6.2 Heat and Mass Transfer in the case of a Cylinder with Surface Mass Injection or Suction. 9.6.3 Calculation of the Rates of Condensation of Vapors on a Horizontal Tube in the Presence of a Non-Condensable Gas. Example 9.5. Solution. References. 10 Mass Transfer in Distillation. 10.1 Classical Approaches to Distillation and their Paradox. 10.1.1 Tray Towers and Packed Columns. 10.1.2 Tray Efficiencies in Distillation Columns. 10.1.3 HTU as a Measure of Mass Transfer in Packed Distillation Columns. 10.1.4 Paradox in Tray Efficiency and HTU. Example 10.1. Solution. 10.2 Characteristics of Heat and Mass Transfer in Distillation. 10.2.1 Physical Picture of Heat and Mass Transfer in Distillation. 10.2.2 Rate-Controlling Process in Distillation. 10.2.3 Effect of Partial Condensation of Vapors on the Rates of Mass Transfer in Binary Distillation. 10.2.4 Dissimilarity of Mass Transfer in Gas Absorption and Distillation. Example 10.2. Solution. Example 10.3. Solution. 10.3 Simultaneous Heat and Mass Transfer Model for Packed Distillation Columns. 10.3.1 Wetted Area of Packings. 10.3.2 Apparent End Effect. 10.3.3 Correlation of the Vapor-Phase Diffusional Fluxes in Binary Distillation. 10.3.4 Correlation of Vapor-Phase Diffusional Fluxes in Ternary Distillation. 10.3.5 Simulation of Separation Performance in Ternary Distillation on a Packed Column under Total Reflux Conditions. Example 10.4. Solution. Example 10.5. Solution. 10.4 Calculation of Ternary Distillations on Packed Columns under Finite Reflux Ratio. 10.4.1 Material Balance for the Column. 10.4.2 Convergence of Terminal Composition. Example 10.6. Solution. 10.5 Cryogenic Distillation of Air on Packed Columns. 10.5.1 Air Separation Plant. 10.5.2 Mass and Diffusional Fluxes in Cryogenic Distillation. 10.5.3 Simulation of Separation Performance of a Pilot-Plant-Scale Air Separation Plant. 10.6 Industrial Separation of Oxygen-18 by Super Cryogenic Distillation. 10.6.1 Oxygen-18 as Raw Material for PET Diagnostics. 10.6.2 A New Process for Direct Separation of Oxygen-18 from Natural Oxygen. 10.6.3 Construction and Operation of the Plant. References. Subject Index.