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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