Growing interfaces in quenched disordered media

We present the microscopic equation of growing interface with quenched nois e for the Tang and Leschhorn model (Phys. Rev. A 45 (1992) R8309). The evol ution equations for the mean height and the roughness are reached in a simp le way. Also, an equation for the interface activity density (i.e. interfac e density of free sites) as function of time is obtained. The microscopic e quation allows us to express these equations in two contributions: the diff usion and the substratum one. All the equation shows the strong interplay b etween both contributions in the dynamics. A macroscopic evolution equation for the roughness is presented for this model for the critical pressure p = 0.461. The dynamical exponent beta = 0.629 is analytically obtained in a simple way. Theoretical results are in excellent agreement with the Monte C arlo simulation. (C) 1999 Elsevier Science B.V. All rights reserved.