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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+/-0.1, alpha=1.50+/-0.02, and alpha(loc)=0.95+/-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+/-0.1, alpha=1.25+/-0.02, and alpha(loc)=0.95+/-0.03. Moreover, we observe that the local properties of the interface change from a superrough 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.

Intrinsic versus superrough anomalous scaling in spontaneous imbibition