Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

Details Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

2003-12-19

arxiv.org/abs/nlin/0312041v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 4 eps figures; to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.69.031406

We analyze a recent experiment of Sharon \textit{et 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 $t^{1/3}$ at intermediate distances and very slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.

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