DIFFUSION-LIMITED-AGGREGATION-LIKE DISPLACEMENT STRUCTURES IN A 3-DIMENSIONAL POROUS-MEDIUM

We have studied the structure that arises when a low-viscosity fluid displaces a high-viscosity fluid in a transparent three-dimensional porous medium. The viscosity ratio m is not far from 1 (m14) in this system. The fluids we use have equal densities so that there are no gravity effects. The injected fluid forms a ramified structure when an intermediate displacement rate is used (NCa10-4). We have measured the projected area A of these growing structures. The cluster mass M is found to scale with a characteristic length RA obtained from this area, as MRAAD. We find the exponent to be DA=2.50.1. The physical model was simulated on the computer using the three-dimensional off-lattice diffusion-limited aggregation (DLA) algorithm. Projections of these clusters show features in common with the experimentally generated patterns. Quantitatively we find reasonably good agreement in terms of the exponent DA, although the experiments are outside the DLA regime of viscous fingering. © 1990 The American Physical Society.