Abstract
The displacement of a high viscosity fluid by a low viscosity fluid in a porous medium is a process of both scientific and practical importance. It has recently been shown by Chen and Wilkinson1 and by Maloy et al.2 that viscous fingering in a random porous medium at high capillary numbers, Ca > >10−4, generates structures with a fractal3 geometry. This fractal structure closely resembles that obtained from the diffusion limited aggregation (DLA) model of Witten and Sander4. Similar structures have also been obtained by fluid-fluid displacement in radial HeleShaw cells using non-Newtonian viscous fluids5. The relationship between fluid-fluid displacement in porous media and DLA was first discussed by Paterson6 and a more detailed analysis has been presented by Kadanoff7.
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