Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

We analyze a recent experiment of Sharon $\mathit{\text{et}}\mathit{\text{al.}}$ (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural model for that experiment, belongs to the same universality class as model B of phase ordering. Two series of numerical simulations with model B are performed, with the FVFPs grown in the experiment, and with Diffusion Limited Aggregates, as the initial conditions. We observed Lifshitz-Slyozov scaling $t^{1\mathrm{/}3}$ at intermediate distances and very slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.