Instability of a combustion model with surface vaporization and overheat in the condensed phase

Using numerical modeling, we have revealed the instability of a steady-state combustion regime which was previously obtained using analytical methods in the substance-combustion model with surface vaporization and with exothermic reactions in the condensed phase which are intense enough to form a maximum of temperature underneath the surface. The instability has been studied analytically using the method of small perturbations to eliminate the version of its nonphysical (numerical) character. Steady-state combustion regimes with maxima on the condensed-phase temperature profile are shown to be actually unsteady. It is suggested that convection in a liquid-subsurface layer owing to bubble motion caused by the Marangoni effect should be taken into account to describe correctly the experimentally observed steady-state regimes with a leading role of the condensed phase.