Eur. Phys. J. B 46, 553-561 (2005)
https://doi.org/10.1140/epjb/e2005-00288-x

Dynamics and kinetic roughening of interfaces in two-dimensional forced wetting

¹ Laboratory of Physics, P.O. Box 1100, Helsinki University of Technology, 02015 HUT, Espoo, Finland
² Department of Physics, McGill University, 3600 rue University, Montreal, QC, Canada H3A 2T8
³ Department of Physics, P.O. Box 1843, Brown University, Providence, RI 02912–1843, USA

Corresponding author: ^a teemu.laurila@hut.fi

Received: 21 April 2005
Published online: 7 September 2005

Abstract

We consider the dynamics and kinetic roughening of wetting fronts in the case of forced wetting driven by a constant mass flux into a 2D disordered medium. We employ a coarse-grained phase field model with local conservation of density, which has been developed earlier for spontaneous imbibition driven by capillary forces. The forced flow creates interfaces that propagate at a constant average velocity. We first derive a linearized equation of motion for the interface fluctuations using projection methods. From this we extract a time-independent crossover length , which separates two regimes of dissipative behavior and governs the kinetic roughening of the interfaces by giving an upper cutoff for the extent of the fluctuations. By numerically integrating the phase field model, we find that the interfaces are superrough with a roughness exponent of , a growth exponent of , and as a function of the velocity. These results are in good agreement with recent experiments on Hele-Shaw cells. We also make a direct numerical comparison between the solutions of the full phase field model and the corresponding linearized interface equation. Good agreement is found in spatial correlations, while the temporal correlations in the two models are somewhat different.