A review on dynamics of growing interfaces in quenched disordered media

L. A. BRAUNSTEIN; R. C. BUCETA; N. GIOVAMBATTISTA; A. DÍAZ-SÁNCHEZ

MATERIALS INSTABILITIES - Proceedings of the First Latin American Summer School

World Scientific

Año: 2000; p. 281 - 303

We make a review of the two principal models that allows to explain the imbibition of fluid in porous media. These models, that belong to the directed percolation depining (DPD) universality class, where introduced simultaneously by Tang and Leschhorn [Phys. Rev. A 45, R8309 (1992)] and Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)] and reviewed by Btraunstein et al. [J. Phys. A 32, 1801 (1999); Phys. Rev E 59, 4243 (1999)]. Even these models have been classified in the same universality class than the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] with quenched noise (QKPZ), the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. These results suggest that the QKPZ equation not describe properly the DPD models even when the exponents derived from this equation are similar to the one obtained from the simulations of this models. These fact is confirmed through the deduced analytical equation for the Tang and Leschhorn model. This equation has the same symmetries than the QKPZ one but its coefficients depend on the balance between the driving force and the quenched noise.