Anomalous Scaling - Square IA

Intrinsic versus superrough anomalous scaling in spontaneous imbibition



M. Pradas and A. Hernandez-Machado

We study spontaneous imbibition using a phase field model in a two dimensional system with a dichotomic quenched noise. By imposing a constant pressure μ at the origin, we study the case when the interface advances at low velocities, obtaining the scaling exponents Z ~ 3.0 , α ~ 1.50 and αloc ~ 0.95 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, $α ~ 1.25 and αloc ~ 0.95. 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.

[Phys. Rev. E74, 041608 (2006) ]