Dynamics of viscous-fingering fractals in porous media

Publisher Website
Google Scholar
Abstract
A gas displacing a high-viscosity liquid in a porous medium generates a fractal finger structure similar to that obtained in diffusion-limited aggregation (DLA). This structure is controlled by the surface dynamics of the growing active zone. The dynamics of viscous fingering in a two-dimensional porous model has been investigated. We have studied the radius of the active zone and the screening length of the active zone as a function of time in the DLA regime. In this regime the fingering structure grows mainly at the tips, and the inner region is screened by the outer fingers. The length of the longest finger as a function of time is accurately described by the results of a new form of DLA simulation which in addition to DLA structures gives the time dependence in a form suitable for comparison with experiments.