Brenner Macrotransport Processes

1. Auflage 2013
ISBN: 978-0-08-051059-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 744 Seiten, Web PDF

This unique book, the first published on the subject, provides an introduction to the theory of macrotransport processes, a comprehensive effective-medium theory of transport phenomena in heterogeneous systems. The text begins with a relatively simple approach to the basic theory before turning to a more formal theoretical treatment which is extended in scope in each successive chapter. Many detailed examples, as well as questions appearing at the end of each chapter, are included to demonstrate the practical implementation of the theory. Macrotransport Processes is aimed at an audience already familiar with conventional theories of transport phenomena. This audience especially includes graduate students in chemical, mechanical, and civil engineering departments, as well as applied mathematicians, biomechanicists, and soil physics, particularly those with interests in problems of flow and dispersion in porous media.

Autoren/Hrsg.

Brenner, Howard

Inhaltsverzeichnis

1;Front Cover;1
2;Macrotransport Processes;6
3;Copyright Page;7
4;Table of Contents;8
5;PART I: MATERIAL DISPERSION THEORY;28
5.1;CHAPTER 1. Introduction to Macrotransport Processes ;30
5.1.1;1.1 Historical Review;32
5.1.2;1.2 Dispersion and its Kinematical Description;36
5.1.3;1.3 Examples of (Material) Macrotransport Processes;38
5.1.4;1.4 Examples of Nonmaterial Macrotransport Processes;51
5.1.5;1.5 Summary;53
5.2;CHAPTER 2. Unidirectional Dispersion of a Nonreactive Solute;58
5.2.1;2.1 Capillary Dispersion: The Intuitive Arguments of G.I. Taylor;59
5.2.2;2.2 Brownian Motion and the Conditional Probability Density;66
5.2.3;2.3 Dispersion in a Capillary Tube: Aris' Method of Moments;73
5.2.4;2.4 Summary;82
5.3;CHAPTER 3. Dispersion of Nonreactive Solutes in Continuous Media;92
5.3.1;3.1 Kinematics;93
5.3.2;3.2 Method of Moments;105
5.3.3;3.3Macrotransport Equation;116
5.3.4;3.4Macrotransport Paradigm;120
5.3.5;3.5 Examples of Unidirectional Dispersion;123
5.3.6;3.6 Examples of Nonspherical, Brownian Particles Sedimenting in Unbounded, Quiescent Fluids;132
5.3.7;3.7 Examples of the Hindered Motion of Brownian Particles;156
5.3.8;3.8 Summary;165
5.4;CHAPTER 4.Dispersion of Nonreactive Solutes in Discontinuous Media;184
5.4.1;4.1Geometrical Properties of Spatially Periodic Media;187
5.4.2;4.2 Average, Darcy-Scale Fields;208
5.4.3;4.3 Kinematics of Fluid Motion in Spatially Periodic Porous Media;220
5.4.4;4.4 Convective-Diffusive Phenomena;232
5.4.5;4.5 Macrotransport (Darcy-Scale) Equation;257
5.4.6;4.6 Macrotransport Paradigm;259
5.4.7;4.7Examples;263
5.4.8;4.8 Summary;278
5.5;CHAPTER 5.Surface and Interfacial Transport Processes;292
5.5.1;5.1 Generic Development for Continuous Systems;293
5.5.2;5.2 Macrotransport Paradigm for Continuous Systems;301
5.5.3;5.3 Examples;304
5.5.4;5.4 Generic Development for Discontinuous Systems;309
5.5.5;5.5 Macrotransport Paradigm for Discontinuous Systems;314
5.5.6;5.6 Examples;317
5.5.7;5.7 Entrained Colloidal Particles with Adsorbing Constituents in Continuous Systems;321
5.5.8;5.8 Summary;326
5.6;CHAPTER 6. Time Periodic Processes;338
5.6.1;6.1 Generic Development for Continuous Systems;339
5.6.2;6.2 Macrotransport Paradigm for Continuous Systems;345
5.6.3;6.3 Examples;347
5.6.4;6.4 Generic Development for Discontinuous Systems;363
5.6.5;6.5 Macrotransport Paradigm for Discontinuous Systems;367
5.6.6;6.6 Examples;369
5.6.7;6.7 Summary;375
5.7;CHAPTER 7.Direct Hydrodynamic Coupling: Dispersion of Fluctuating Brownian- Particle Clusters;380
5.7.1;7.1 Dispersion in Continuous Systems with Direct Coupling;383
5.7.2;7.2 Flexible-Chain Transport;387
5.7.3;7.3 Macrotransport Paradigm;391
5.7.4;7.4 Examples;397
5.7.5;7.5 Summary;417
5.8;CHAPTER 8. Chemically Reactive Systems;434
5.8.1;8.1 Generic Development for Continuous Systems;435
5.8.2;8.2 Macrotransport Paradigm for Continuous Systems;446
5.8.3;8.3 Examples;449
5.8.4;8.4 Generic Development for Discontinuous Systems;464
5.8.5;8.5 Macrotransport Paradigm for Discontinuous Systems;473
5.8.6;8.6 Example: Dispersion and Reaction in Two-Dimensional Model Porous Media;474
5.8.7;8.7 Summary;492
5.9;CHAPTER 9. Examples of Dispersion Analyses for Spatially Periodic Systems;500
5.9.1;9.1 Effective Diffusivity in Spatially Periodic Emulsions;501
5.9.2;9.2 Convective Dispersion of a Solute Through an Ordered Porous Medium with Surface Adsorption and Diffusion;513
5.9.3;9.3 Dispersion in Cellular Circulatory Flows;523
5.9.4;9.4 Summary;529
6;PART II: NONMATERIAL DISPERSION THEORY;536
6.1;CHAPTER 10. Energy Dispersion;538
6.1.1;10.1 Internal Energy Transport in an Insulated Circular Tube Containing a Flowing Fluid Possessing Cross-Sectionally Varying Thermal Properties;540
6.1.2;10.2 Thermal Dispersion in Continuous Systems;558
6.1.3;10.3 Thermal Dispersion in Discontinuous Systems;578
6.1.4;10.4 Summary;589
6.2;CHAPTER 11. Momentum Dispersion;598
6.2.1;11.1 Microtransport Description;601
6.2.2;11.2 Lagrangian Calculation of Viscosity: The Brownian Motion Analogy;609
6.2.3;11.3 Macrotransport Equation;610
6.2.4;11.4 Macrotransport Paradigm;612
6.2.5;11.5 Example: A Suspension of Rigid Particles;613
6.2.6;11.6 Summary;623
7;PART III: FOUNDATIONS OF MACROTRANSPORT PROCESSES;628
7.1;CHAPTER 12. Derivation of the Smoluchowski Equation via Macrotransport Theory;630
7.1.1;12.1 The Fokker-Planck Equation;632
7.1.2;12.2 The Smoluchowski Equation;641
7.1.3;12.3 Summary;647
7.2;CHAPTER 13. The Langevin Approach to Macrotransport Processes;654
7.2.1;13.1 The (Inertialess) Langevin Description of the Microtransport Process;656
7.2.2;13.2 Macrotransport Phenomenological Coefficients;659
7.2.3;13.3 Derivation of the Smoluchowski Equation From the Langevin Equation;662
7.2.4;13.4 Equivalence Between the Langevin and Smoluchowski Formulations of the Macrotransport Coefficients;665
7.2.5;13.5 Summary;667
7.3;APPENDIX A: Some Fundamental Properties of Spatially Periodic Functions;670
7.3.1;A. 1 Vanishing of the Surface Integrals of Spatially Periodic Functions over the External Surface of a Unit Cell;670
7.3.2;A.2 Lattice Functions and Lattice Constants;671
7.3.3;A.3 Volume Integrals of Spatially Periodic Functions;672
7.3.4;A.4 A Fundamental Decomposition Theorem for Functions Possessing a Spatially Periodic Gradient;678
7.3.5;A.5 Vanishing of the Surface Integrals of Spatially Periodic Functions over the Surface of a Unit Cell;681
7.3.6;A.6 A "Flux" Theorem for Spatially Periodic Functions;684
7.4;APPENDIX B: Invariant Descriptions of Orientation & Rotation;702
7.4.1;B. 1 An Invariant Vector-Dyadic Representation of Orientation Space for Describing the Rotation of an Arbitrarily Shaped Particle;702
8;BIBLIOGRAPHY;712
9;AUTHOR INDEX;732
10;SUBJECT INDEX;738