First-Order Partial Differential Equations, Vol. 2

, by Rhee, Hyun-Ku; Aris, Rutherford; Amundson, Neal R.

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ISBN: 9780486419947 | 0486419940
Cover: Paperback
Copyright: 9/4/2001

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Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order. Examples are drawn from a wide range of scientific and engineering disciplines. The book begins with a consideration of pairs of quasilinear hyperbolic equations of the first order and goes on to explore multicomponent chromatography, complications of counter-current moving-bed adsorbers, the adiabatic adsorption column, and chemical reaction in countercurrent reactors. Exercises appear at the end of most sections. Accessible to anyone with a thorough grounding in undergraduate mathematics-ideally including volume 1 of this set. 1989 edition. 198 black-and-white illus. Author and subject indices.

Preface	p. xi
Pairs of Quasilinear Hyperbolic Equations of First-Order	p. 1
Equations for the Chromatography of Two Solutes	p. 2
Hyperbolic Systems of Two First-Order Equations	p. 9
Reducible Equations and Simple Waves	p. 19
Characteristic Directions for Two-Solute Chromatography	p. 28
Characteristic Initial Value Problem and Riemann Problem	p. 35
Compression Waves and the Formation of Shocks	p. 43
Discontinuities in Solutions and the Entropy Condition	p. 48
Analysis of Polymer Flooding	p. 63
Riemann Invariants and Their Application	p. 72
Development of Singularities, Weak Solution, and the Entropy Condition	p. 84
Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions	p. 96
References	p. 106
Two-Solute Chromatography with the Langmuir Isotherm	p. 113
Langmuir Isotherm and Characteristic Parameters	p. 115
Directions of C-Characteristics and Shock Paths	p. 123
Riemann Problems	p. 131
The Formation of Shocks	p. 144
Fundamentals of Wave Interaction	p. 151
Interactions between Waves of the Same Family	p. 156
Interactions between Waves of Different Families	p. 170
Chromatographic Cycle for Two Solutes	p. 184
Introduction to Displacement Development	p. 196
Shock Layer Analysis	p. 207
References	p. 225
Hyperbolic Systems of First-Order Quasilinear Equations and Multicomponent Chromatography	p. 228
Equations for the Equilibrium Chromatography of Many Solutes	p. 230
Hyperbolic Systems of More than Two First-Order Equations	p. 233
Generalized Riemann Invariants and Simple Waves	p. 240
Riemann Problem and Fundamental Differential Equations	p. 247
Langmuir Isotherm for Multicomponent Adsorption	p. 251
Riemann Invariants for Multicomponent Chromatography with the Langmuir Isotherm	p. 254
Characteristic Parameters and the space [Omega](m)	p. 259
Characteristics and Simple Waves	p. 263
Discontinuities: Shocks	p. 268
Entropy Change across a Shock	p. 274
Solution of the Riemann Problem	p. 278
Illustrations	p. 287
References	p. 299
Wave Interactions in Multicomponent Chromatography	p. 301
Piecewise Constant Data and Patterns of Interaction	p. 302
Interactions between Waves of the Same Family	p. 308
Interactions between Waves of Different Families	p. 313
Chromatographic Cycle for m Solutes	p. 326
Multicomponent Separation by Displacement Development	p. 338
An Example: Three Solute Separation by Displacement Development	p. 348
References	p. 359
Multicomponent Adsorption in Continuous Countercurrent Moving-Bed Adsorber	p. 362
Basic Formulation	p. 364
Theoretical Development for the Langmuir Isotherm	p. 370
Analysis of Semi-Infinite Columns	p. 378
Analysis of a Finite Column	p. 383
Analysis of Wave Interactions	p. 390
Illustration	p. 405
References	p. 413
More on Hyperbolic Systems of Quasilinear Equations and Analysis of Adiabatic Adsorption Column	p. 415
Equations for the Adiabatic Adsorption Column	p. 416
Formulation for the Riemann Problem	p. 420
Construction of a Continuous Solution	p. 424
Discontinuities, Weak Solutions, and the Entropy Condition	p. 429
Existence, Uniqueness, Structure, and Asymptotic Behavior of Weak Solutions	p. 439
Solution Scheme for a Moving-Bed Problem	p. 450
Adiabatic Adsorption of Single Solute	p. 456
Adiabatic Adsorption of Two Solutes	p. 471
Adiabatic Adsorption with Adsorptivity Reversal	p. 484
Shock Layer Analysis of Adiabatic Adsorption	p. 495
References	p. 503
Chemical Reaction in a Countercurrent Reactor	p. 510
General Formulation	p. 510
Case of Two Reactants	p. 512
Characteristics and Discontinuities for the Case of Two Reactants with Adsorption Equilibrium	p. 516
The Steady State	p. 518
General Procedure for Mapping Out the Steady-State Solution	p. 531
Further Developments	p. 537
References	p. 538
Author Index	p. 541
Subject Index	p. 545
Table of Contents provided by Syndetics. All Rights Reserved.

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