BREAKDOWN OF SCALE-INVARIANCE IN THE PHASE ORDERING OF FRACTAL CLUSTERS

Numerical simulations with the Cahn-Hilliard equation show that coarse ning of fractal clusters (FCs) is not a scale-invariant process. On th e other hand, a typical coarsening length scale and interfacial area o f the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formulated that can follow t he whole dynamics of a diffusion controlled growth, coarsening, fragme ntation, and approach to equilibrium in a system with conserved order parameter.