Time dependence of stability of the water-vapor phase transition front in high-temperature rocks

We investigate the stability of a water boiling front in high-temperature rocks, which separates a water-saturated region from a region saturated with superheated vapor. Such flows arise both during the exploitation of geothermal reservoirs and in natural processes. We conduct the stability analysis using the modified method of normal modes, where the amplitude of pressure perturbation depends on time, and the water-saturated region is bounded.We studied resulting dispersion equation numerically and asymptotically. We found that the stability criterion depends on time and asymptotically approaches the solution for an infinite water-saturated region.We show that the transition to instability occurs at finite wavenumbers, and the characteristic scale of the most unstable perturbations remains almost unchanged over time.