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Rayleigh-Taylor instability of an interface in a nonwettable porous medium. (English. Russian original) Zbl 1200.76076
Fluid Dyn. 42, No. 1, 83-90 (2007); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2007, No. 1, 96-104 (2007).
Summary: The diffusion of vapor through the roof of an underground structure located beneath an aquifer is considered. In the process of evaporation, an interface between the upper water-saturated layer and the lower layer containing an air-vapor mixture is formed. A mathematical model of the evaporation process is proposed and a solution of the steady-state problem is found. It is shown that in the presence of capillary forces in the case of a nonwettable medium the solution is not unique. Using the normal mode method, it is shown that Rayleigh-Taylor instability of the interface can develop in the nonwettable porous medium. It is found that there are two scenarios of loss of stability corresponding to the occurrence of the most unstable wavenumber at zero and at infinity, respectively. It is shown that for zero wavenumber the stability limit is reached at the same time as the solution of the steady-state problem disappears.

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
76T10 Liquid-gas two-phase flows, bubbly flows
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References:
[1] V.Zh. Arens, A.P. Dmitriev, and Yu.D. Dyad’kin, Thermophysical Aspects of Subsoil Resource Development (Nedra, Leningrad, 1988) [in Russian].
[2] G. G. Tsypkin and L. Brevdo, ”A Phenomenological Model of the Increase in Solute Concentration in Ground Water due to the Evaporation,” Transport Porous Media 37(2), 129–151 (1999).
[3] P.G. Drazin, Introduction to Hydrodynamic Stability (Cambridge University Press, Cambridge, 2002). · Zbl 0997.76001
[4] A.T. Il’ichev, Solitary Waves in Hydromechanical Models (Fizmatlit, Moscow, 2003) [in Russian].
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