On the Short Wave Instability of the Liquid/Gas Contact Surface in Porous Media

We consider a problem of hydrodynamic stability of the liquid displacement by gas in a porous medium in the case when a light gas is located above the liquid. The onset of instability and the evolution of the small shortwave perturbations are investigated. We show that when using the Darcy filtration law, the onset of instability may take place at an infinitely large wavenumber when the normal modes method is inapplicable. The results of numerical simulation of the nonlinear problem indicate that the anomalous growth of the amplitude of shortwave small perturbations persists, but the growth rate of amplitude decreases significantly compared to the results of linear analysis. An analysis of the stability of the gas/liquid interface is also carried out using a network model of a porous medium. It is shown that the results of surface evolution calculations obtained using the network model are in qualitative agreement with the results of the continual approach, but the continual model predicts a higher velocity of the interfacial surfaces in the capillaries. The growth rate of perturbations in the network model also increases with decreasing perturbation wavelength at a constant amplitude.