First-Order Partial Differential Equations, Vol. 2 (eBook)

Preface1. Pairs of Quasilinear Hyperbolic Equations of First-Order 1.1 Equations for the Chromatography of Two Solutes 1.2 Hyperbolic Systems of Two First-Order Equations 1.3 Reducible Equations and Simple Waves 1.4 Characteristic Directions for Two-Solute Chromatography 1.5 Characteristic Initial Value Problem and Riemann Problem 1.6 Compression Waves and the Formation of Shocks 1.7 Discontinuities in Solutions and the Entropy Condition 1.8 Analysis of Polymer Flooding 1.9 Riemann Invariants and Their Application 1.10 Development of Singularities, Weak Solution, and the Entropy Condition 1.11 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions References2. Two-Solute chromatography with the Langmuir Isotherm 2.1 Langmuir Isotherm and Characteristic Parameters 2.2 Directions of C-Characteristics and Shock Paths 2.3 Riemann Problems 2.4 The Formation of Shocks 2.5 Fundamentals of Wave Interaction 2.6 Interactions between Waves of the Same Family 2.7 Interactions between Waves of Different Families 2.8 Chromatographic Cycle for Two Solutes 2.9 Introduction to Displacement Development 2.10 Shock Layer Analysis References3. Hyperbolic Systems of First-Order Quasilinear Equations and Multicomponent Chromatography 3.1 Equations for the Equilibrium Chromatography of Many Solutes 3.2 Hyperbolic Systems of More than Two First-Order Equations 3.3 Generalized Riemann Invariants and Simple Waves 3.4 Riemann Problem and Fundamental Differential Equations 3.5 Langmuir Isotherm for Multicomponent Adsorption 3.6 Riemann Invariants for Multicomponent Chromatography with the Langmuir Isotherm 3.7 Characteristic Parameters and the space OMEGA(m) 3.8 Characteristic and Simple Waves 3.9 Discontinuities: Shocks 3.10 Entropy Change across a Shock 3.11 Solution of the Riemann Problem 3.12 Illustrations References4. Wave Interactions in Multicomponent Chromatography 4.1 Piecewise Constant Data and Patterns of Interaction 4.2 Interactions between Waves of the Same Family 4.3 Interactions between Waves of Different Families 4.4 Chromatographic Cycle for m Solutes 4.5 Multicomponent Separation by Displacement Development 4.6 An Example: Three Solute Separation by Displacement Development References5. Multicomponent Adsorption in Continuous Countercurrent Moving-Bed Adsorber 5.1 Basic Formulation 5.2 Theoretical Development for the Langmuir Isotherm 5.3 Analysis of Semi-Infinite Columns 5.4 Analysis of a Finite Column 5.5 Analysis of Wave Interactions 5.6 Illustrations References6. More on Hyperbolic Systems of Quasilinear Equations and Analysis of Adiabatic Adsorption Column 6.1 Equations for the Adiabatic Adsorption Column 6.2 Formulation for the Riemann Problem 6.3 Construction of a Continuous Solution 6.4 Discontinuities, Weak Solutions, and the Entropy Condition 6.5 Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions 6.6 Solution Scheme for a Moving-Bed Problem 6.7 Adiabatic Adsorption of Single Solute 6.8 Adiabatic Adsorption of Two Solutes 6.9 Adiabatic Adsorption with Adsorptivity Reversal 6.10 Shock Layer Analysis of Adiabatic Adsorption References7. Chemical Reaction in a countercurrent Reactor 7.1 General Formulation 7.2 Case of Two Reactants 7.3 Characteristics and Discontinuities for the Case of Two Reactants with Adsorption Equilibrium 7.4 The Steady State 7.5 General Procedure for Mapping Out the Steady-State Solution 7.6 Further Developments References Author Index; Subject Index