  We study spontaneous imbibition using a phase field model in a two
dimensional system with a dichotomic quenched noise. By imposing a constant
pressure $\mu_{a}<0$ at the origin, we study the case when the interface
advances at low velocities, obtaining the scaling exponents $z=3.0\pm 0.1$,
$\alpha=1.50\pm 0.02$ and $\alpha_{loc}= 0.95\pm 0.03$ within the intrinsic
anomalous scaling scenario. These results are in quite good agreement with
experimental data recently published. Likewise, when we increase the interface
velocity, the resulting scaling exponents are $z=4.0 \pm 0.1$, $\alpha=1.25\pm
0.02$ and $\alpha_{loc}= 0.95\pm 0.03$. Moreover, we observe that the local
properties of the interface change from a super-rough to an intrinsic anomalous
description when the contrast between the two values of the dichotomic noise is
increased. From a linearized interface equation we can compute analytically the
global scaling exponents which are comparable to the numerical results,
introducing some properties of the quenched noise.

Disordered Systems and Neural Networks