Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2000-08-30
Eur. Phys. J. B 15, 701 (2000)
Physics
Condensed Matter
Disordered Systems and Neural Networks
14 pages, 13 figures
Scientific paper
10.1007/s100510051175
The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field $\alpha({\bf x})$. The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation $H \sim t^{1/2}$ for the slowing down motion of the average interface position $H$. The interface is found to be superrough, with global roughness exponent $\chi \approx 1.25$, indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale $\xi_{\times} \sim H^{1/2}$ arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv\a'ath and Stanley [Phys. Rev. E {\bf 52} 5166 (1995)] on the temporal scaling of the interface.
Ala-Nissila Tapio
Alava Mikko
Dube Martin
Elder K. R.
Majaniemi Sami
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