Catastrophic transition to instability of evaporation front in a porous medium

Interaction of stabilizing and destabilizing factors and bifurcations of phase transition fronts

“…В работах [8,9] показано, что при изменении физических пара-метров может возникнуть бифуркация поверхности фазового перехо-да типа точки поворота, когда происходит рождение или исчезнове-ние пары поверхностей, одна из которых подвержена длинноволно-вой неустойчивости через дестабилизацию возмущением с нулевым волновым числом. В этом случае эволюция узкой полосы слабонели-нейных волн вблизи порога неустойчивости описывается веществен-ным диффузионным уравнением Колмогорова -Петровского -Пискунова с невырожденной квадратичной нелинейностью в случае общего положения [10].…”

Dynamics and stability of moving fronts of water evaporation in a porous medium

“…The arising stationary evaporation front separating these two domains can be either stable or non-stable [6,7]. In [6] by the method of normal forms stability of the vertical flow was studied with the stationary phase transition front. This stability analysis concerns the behavior of infinitely small harmonic perturbations of the front.…”

“…number (long-wave instability), and the second implies first destabilization of the mode with infinite wave number (short-wave instability). Analysis when the basic regime with the stationary plane phase transition front is subjected to finite localized perturbations requires the use of sophisticated numerical methods and along with the study of the basic physical effects allows to determine the bounds of application of fundamental physical results of [6] for the case of localized finite amplitude perturbations [8]. In [6,7] it is also shown that a narrow band of weakly unstable modes in some neighborhood of the instability threshold of the existing pair of phase transition fronts are described by the nonlinear diffusion KPP equation [9].…”

Anomaly of spontaneous transition to instability of liquid–vapour front in a porous medium

“…The transitions to instability at fluid-fluid interfaces are of great interest on account of their wide range of applications. These instabilities can often occur at a liquid-vapour interface in a geothermal system [2][3][4][5][6][7][8][9][10]. There is much need for the better understanding of the different physical phenomena involved with liquid-vapour phase changes, and this is the focus of our study.…”