Intrinsic versus superrough anomalous scaling in spontaneous imbibition

We study spontaneous imbibition using a phase field model in a two-dimensional system with a dichotomic quenched noise. By imposing a constant pressure μₐ<0 at the origin, we study the case when the interface advances at low velocities, obtaining the scaling exponents z=3.0±0.1, α=1.50±0.02, and αloc=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, α=1.25±0.02, and αloc=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.