This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free Path Statistics . 8 1. 5. Void Point-Surface Statistics . 11 1. 6. Variational Principles Applied to the Diffusion Equation. 12 1. 7. Notation. 16 Chapter 2. Diffusion Through a Porous Medium . 18 2. 1. Introduction 18 2. 2. Diffusion Through an Isotropic Porous Medium 18 2. 3. Variational Formulation for De . 20 2. 4. Bounds on De for an Isotropic Suspension 22 2. 5.

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1. Introduction and Preliminaries.- 1.1. General Survey.- 1.2. Phenomenological Descriptions of Diffusion and Reaction..- 1.3. Correlation Functions for Random Suspensions..- 1.4. Mean Free Path Statistics.- 1.5. Void Point-Surface Statistics.- 1.6. Variational Principles Applied to the Diffusion Equation...- 1.7. Notation.- 2. Diffusion Through a Porous Medium.- 2.1. Introduction.- 2.2. Diffusion Through an Isotropic Porous Medium..- 2.3. Variational Formulation for De.- 2.4. Bounds on De for an Isotropic Suspension.- 2.5. Best Possible Bounds on De.- 2.6. Bounds on De for a Random Bed of Solid Spheres..- 2.7. Knudsen Diffusion Through a Porous Medium.- 2.8. Variational Formulation for Knudsen Diffusion..- 2.9. Upper Bounds on the Knudsen Permeability.- 3. Diffusion Limited Reaction.- 3.1. Introduction.- 3.2. Diffusion Limited Precipitation.- 3.3. The Spherical Cell Approximation.- 3.4. Variational Principle and Upper Bound on the Precipitation Rate.- 3.5. Diffusion Controlled Quenching.- 3.6. Upper Bound on ke.- 3.7. Lower Bound on ke.- 3.8. Random Quencher Particles.- 4. Heterogeneous Catalysis.- 4.1. Introduction.- 4.2. Variational Principles for Heterogeneous Catalysis: the Homogeneous Model.- 4.3. Application to First Order Kinetics in a Slab.- 4.4. Application to Langmuir-Hinshelwood Kinetics in a Slab..- 4.5. Effects of Pellet Shape on the Effectiveness Factor..- 4.6. Variational Principles for Heterogeneous Catalysis: the Discrete Model.- 4.7. Application to Linear Kinetics in a Slab: Discrete Model.- 4.8. Analysis of Experimental Data.- 4.9. Non-monotonic Kinetics.- Notation.- Author Index.