J.P. Nadal

Yves Pomeau

E. Guyon

CARGESE INSTITUfE ON DISORDER AND MIXING Convection, diffusion and reaction are the three basic mechanisms in physico-chemical hydrodynamics and chemical engineering. Both convective and diffusive processes are strongly influenced by the effect of disorder of granular matter in porous media, suspensions, fluidized beds or/and by the randomness caused in turbulent flow field. This book has been initiated by a NATO summer institute held in Cargese (Corsica, FRANCE) from June 15 th to 27 th 1987 . Its aim was to associate statistical physicists, fluid mechanicians and specialists of chemical engineering on the problems of the relation between disorder and mixing and, in this respect, this is a " premiere ". This book is made of chapters based on lectures given in the meeting. However we have paid a considerable attention to harmonize the contents and styles of chapters made by scientists trained in different communities and using different languages and techniques to describe similar problems. The Prelude by the editors of the book introduces the different points and is a biased view of some of the important and most active aspects of the subjects developed. We wish to thank all contributors and students of the institute who gave the style of the present interdisciplinary approach. We also greatly thank Elisabeth Charlaix who has shared with us the scientific and practical organisation of the institute, and Marie-France Hanseler for her technical support.

Convection, Diffusion and Reaction in Random Materials and Processes

Disorder and Mixing

J.C. Charmet

Stéphane Roux

Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described.

E. Guyon

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