2006/09/22 by Marc Pradas, M. Pradas, A. Hernández‐Machado +1
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Solidification and crystal growth phenomena #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.74.041608
published as Phys. Rev. E 74, 041608 (2006) · Accepted for publication in Physical Review E
arxiv created 2006/09/22 · openalex publication_date 2006/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study spontaneous imbibition using a phase field model in a two-dimensional system with a dichotomic quenched noise. By imposing a constant pressure \ensuremathμa<0 at the origin, we study the case when the interface advances at low velocities, obtaining the scaling exponents z=3.0\ifmmode±\else\textpm\fi0.1, \ensuremathα=1.50\ifmmode±\else\textpm\fi0.02, and \ensuremathαloc=0.95\ifmmode±\else\textpm\fi0.03 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\ifmmode±\else\textpm\fi0.1, \ensuremathα=1.25\ifmmode±\else\textpm\fi0.02, and \ensuremathαloc=0.95\ifmmode±\else\textpm\fi0.03. 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.