Phase-field modeling of dynamical interface phenomena in fluids

We discuss recent developments and applications of phase-field models to describe interface phenomena far from equilibrium. The basic idea is to coarse-grain over microscopic degrees of freedom which yields an effective description in terms of continuous macro-variables describing different physical phases or states of the system. In principle, and in some cases even in practice, the coefficients in this effective description can be related to the microscopic physical variables. Typically, phase-field models are constructed to describe (non-critical) bulk phases. However, interfaces between phases and non-equilibrium conditions can be easily implemented through appropriate boundary and initial conditions. The main advantages of the phase field models are (i) such models are relatively easy to construct using simple symmetry arguments and conservation laws; (ii) systematic development of the continuum limit which makes mesoscopic and macroscopic time and length scales accessible; (iii) natural emergence of interfaces and non-equilibrium conditions; (iv) relative ease of numerical implementation; (v) possibility for analytic work through projection techniques. In this review, we focus on some recent applications of phase-field models to interface dynamics and kinetic roughening of wetting fronts in random media.