Eur. Phys. J. B 15, 701-714 (2000)
https://doi.org/10.1007/s100510051175

Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

¹ Helsinki Institute of Physics, P.O. Box 9, 00014 University of Helsinki, Helsinki, Finland
² Laboratory of Physics, P.O. Box 1100, Helsinki University of Technology, 02015 HUT, Espoo, Finland
³ Department of Physics, Oakland University, Rochester, MI 48309-4487, U.S.A.
⁴ Department of Physics, Brown University, Providence, RI 029121843, U.S.A.

Received: 24 November 1999
Published online: 15 June 2000

Abstract

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 . 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 for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horváth and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface.