Viscous Fingering Fractals in Porous Media

Abstract

Gas displacing a high-viscosity fluid in a two-dimensional porous disk intrudes in the form of ramified fingers similar to the structures obtained in diffusion-limited aggregation. We find that the resulting finger structures are described by a fractal dimension $D=1.62\ifmmode\pm\else\textpm\fi{}0.04$ consistent with $D$ for diffusion-limited aggregation clusters. This result confirms the analogy between diffusion-limited aggregation and two-fluid displacement in porous media introduced by Paterson.