Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

Abstract

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.

arXiv comment4 pages, 4 eps figures; to appear in Phys. Rev. E

References in corpus (5)

• Theory of Phase Ordering Kinetics
• Instability driven fragmentation of nanoscale fractal islands
• Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters
• Normal scaling in globally conserved interface-controlled coarsening of fractal clusters
• Anomalous Dynamic Scaling in Locally-Conserved Coarsening of Fractal Clusters

Cited by in corpus (4)

• Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell
• Self-similar relaxation dynamics of a fluid wedge in a Hele-Shaw cell
• Self-similar asymptotics for a class of Hele-Shaw flows driven solely by surface tension
• How a Long Bubble Shrinks: a Numerical Method for an Unforced Hele-Shaw Flow