EFFECT OF QUENCHED AND CORRELATED DISORDER ON GROWTH PHENOMENA

We investigate the effect of quenched disorder with long-range correla tions on two growth phenomena, namely, diffusion-limited aggregation ( DLA) and the dielectric-breakdown model (DBM). The motivation for this study arises from experimental observations indicating that the perme ability and hydraulic conductivity of heterogeneous rock masses seem t o follow a fractional Brownian motion (FBM), a distribution that induc es correlations that are essentially of infinite-extent. A two-dimensi onal FBM is used to generate the conductivities of the medium in which DLA and DBM clusters are grown. A cutoff is also introduced into FBM that allows one to tune the length scale over which the conductivities are correlated. The results indicate that long-range correlations pla y a dominant role in the growth of the clusters, and the effect of all other factors, which could be important if there were no long-range c orrelations, is negligible. The results are completely different from those of disordered but uncorrelated media, and also reveal large diff erences between the DBM and DLA models. Thus any realistic modeling of transport in heterogeneous rocks must take into account the effect of such correlations.