Etienne Guyon

Permeability of a random array of fractures of widely varying apertures

We modelize a fractured rock by a random array of plane cracks of finite extent having a very broad distribution of apertures (or of hydraulic conductances). If the rock is permeable, the flow will essentially take place along a ‘subnetwork’ made of the less resistant cracks. Using an analogy with the treatment of variable range transport in semiconductors, we evaluate the homogenization length and the permeability of this disordered network. This evaluation makes use of the notion of the critical bonds which are the weakest cracks among the good ones necessary for percolation; the remaining weaker bonds make a negligible contribution to the permeability. The method is applicable to other examples of transport in very heterogeneous macroscopic random materials.

Superconductivity in ''normal'' metals

The superconducting transition temperature (T) of a film of a given metal, which is in contact with a superconducting film, is discussed. The given metal is assumed to exhibit no superconductivity in the bulk state. It is shown that an analysis of the dependence of T on the thickness of the normal-metal film can be used to evaluate one of the superconducting parameters (in the Bardeen- CooperSchrieffer model) of the given metal. (T.F.H.)

Disorder and fracture

Sixteen papers (lectures) from the June 1989 Institute are grouped in sections covering tools, diffusion-limited aggregation model, statistical models of fracture, rheology and fracture, and materials and applications. The papers range from theoretical concepts to practical applications. Each sectio

Rupture of heterogeneous media in the limit of infinite disorder

We consider a random fuse or random fragile element model. We show that, in the limit of infinite disorder in the bond-breaking thresholds, the rupture of a lattice is a “disguised” percolation process. Therefore, just before the final overall rupture of the lattice, we obtain scaling relations of various physical properties as a function of the number of bonds broken.

Dispersion in the presence of recirculation zones

Abstract Hydrodynamic effects are of prime importance in understanding the effects of dispersion of passive tracers in a porous geometry, beyond the simple random lattice description. We consider here the role of recirculation zones of the flow field which is somewhat intermediate between pure geometric dispersion and hold-up dispersion in stagnant zones. We illustrate the problem by proposing a scaling analysis of the dispersion in a convective pattern of rolls in the absence of D.C flow.

Fractals and percolation in porous media and flows

Abstract We review a body of recent work, related to the research interests of our group, on the channel structure of disordered porous media, or fractured systems, where concepts of percolation and fractal geometry have proved useful in characterizing, or explaining, features of the transport properties of single and multiphase flow, or of the “dynamics” of invasion percolation.

The viscous catenary revisited: experiments and theory

Detailed observations have been performed on the evolution of a viscous catenary, a rope of high-viscosity fluid suspended from two points falling under gravity. Stroboscopic imaging techniques are used to obtain the position and shape of the strand as a function of time. Depending on their initial thickness and profile, the filaments are observed to evolve into either a quasi-catenary, or other, more complex shapes. A conceptually simple, energy-based theory is developed and compared with observations. It is shown to describe reasonably, except for a scaling in the time scale, the catenary-like regime.

Critical behaviors of central-force lattices

Around the concept of central-force lattices, various mechanical critical behaviors can be investigated, that always exhibit non-locality and sometimes non-linearity: •- Linear behavior of randomly diluted, or reinforced, structures (percolation type problems).•- Non-linear behavior due to large deformation.•- Non-linear behavior due to contacts.•- Growth of a single crack…

Propagation of order in the dilute antiferromagnetic three-state Potts model

A recent analysis of the propagation of order in a dilute 3-state Potts antiferromagnetic model on a triangular lattice at zero temperature by Adleret al. has shown the importance of nonlocality in the propagation of order. We study a linearized continuous version of this model, which can be mapped onto three independent percolation problems. We discuss the respective roles of nonlocality and nonlinearity, in particular in connection with central-force percolation.

Transport Exponents in Percolation

This meeting has been devoted to “Growth and Form” Here, we would like to investigate how forms and, more specifically, randomness in geometry as found in percolative structures, govern the macroscopic transport behavior. In the first part, we show how in the node-link-and-blob picture of the percolation infinite cluster, one can derive bounds for critical exponents. This method can be used for scalar transport, for elasticity, or for the specific problem (discussed by P. N. Sen in this book) of “continuous percolation.” In the second part, we give an upper bound for the elastic critical exponent which may well be an exact relation (conjecture).