  We present the microscopic equation for the growing interface with quenched
noise for the model first presented by Buldyrev et al. [Phys. Rev. A 45, R8313
(1992)]. The evolution equation for the height, the mean height, and the
roughness are reached in a simple way. The microscopic equation allows us to
express these equations in two contributions: the contact and the local one. We
compare this two contributions with the ones obtained for the Tang and
Leschhorn model [Phys. Rev A 45, R8309 (1992)] by Braunstein et al. [Physica A
266, 308 (1999)]. Even when the microscopic mechanisms are quiet different in
both model, the two contribution are qualitatively similar. An interesting
result is that the diffusion contribution, in the Tang and Leschhorn model, and
the contact one, in the Buldyrev model, leads to an increase of the roughness
near the criticality.
