Scaling relations for interface motion through disordered media: Application to two-dimensional fluid invasion
Abstract
We consider the critical transitions that occur as the force driving an interface through a random medium is increased. The total displacement of the interface, and the incremental advance after a small increase in force, diverge as the force approaches a critical depinning threshold. At the critical force there is a power-law distribution of growth sizes. General scaling relations are derived between the critical exponents associated with such transitions. These scaling relations are tested on a model system-fluid invasion of a two-dimensional porous medium. Critical exponents are determined from simulations using finite-size-scaling techniques. Two universality classes are identified: percolation and depinning. In both cases the calculated exponents obey the scaling relations.
- Publication:
-
Physical Review B
- Pub Date:
- December 1991
- DOI:
- 10.1103/PhysRevB.44.12294
- Bibcode:
- 1991PhRvB..4412294M