Dynamics of front-like water evaporation phase transition interfaces

We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other.