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Dynamics of water evaporation fronts. (Russian, English) Zbl 1299.76075
Zh. Vychisl. Mat. Mat. Fiz. 53, No. 9, 1531-1553 (2013); translation in Comput. Math. Math. Phys. 53, No. 9, 1350-1370 (2013).
Summary: The evolution and shapes of water evaporation fronts caused by long-wave instability of vertical flows with a phase transition in extended two-dimensional horizontal porous domains are analyzed-numerically. The plane surface of the phase transition loses stability when the wave number becomes-infinite or zero. In the latter case, the transition to instability is accompanied with reversible bifurcations-in a subcritical neighborhood of the instability threshold and by the formation of secondary (not necessarily horizontal homogeneous) flows. An example of motion in a porous medium is considered concerning the instability of a water layer lying above a mixture of air and vapor filling a porous layer under-isothermal conditions in the presence of capillary forces acting on the phase transition interface.

76E17 Interfacial stability and instability in hydrodynamic stability
76T10 Liquid-gas two-phase flows, bubbly flows
76S05 Flows in porous media; filtration; seepage
80A22 Stefan problems, phase changes, etc.
Full Text: DOI
[1] Il’ichev, A T; Tsypkin, G G, Weakly linear theory for the instability of long-wave perturbations, Dokl. Phys., 52, 499-501, (2007) · Zbl 1423.76134
[2] Kolmogorov, A N; Petrovskii, I G; Piskunov, N S, Study of diffusion equation with an increase in the quantity of matter and its application to a biological problem, Byull. Mosk. Gos. Univ. Mat. Mekh., 1, 1-26, (1937)
[3] M. Bramson, “Convergence of Solutions of the Kolmogorov Equation to Travelling Waves,” (Am. Math. Soc., Providence, R.I., 1983). · Zbl 0517.60083
[4] Kirchgässner, K, On the nonlinear dynamics of travelling fronts, J. Differ. Equations, 96, 256-278, (1992) · Zbl 0802.35078
[5] V. Zh. Arens, A. P. Dmitriev, and Yu. D. Dyad’kin, Thermophysical Aspects of Subsoil Resource Development (Nedra, Leningrad, 1988) [in Russian].
[6] Il’ichev, A T; Tsypkin, G G, Rayleigh-Taylor instability of an interface in a nonwettable porous medium, Fluid Dyn., 42, 83-90, (2007) · Zbl 1200.76076
[7] Il’ichev, A T; Tsypkin, G G, Catastrophic transition to instability of evaporation front in a porous medium, Eur. J. Mech. B Fluids, 27, 665-677, (2008) · Zbl 1151.76480
[8] Il’ichev, A T; Tsypkin, G G, Instabilities of uniform filtration flows with phase transition, J. Exp. Theor. Phys., 107, 699-711, (2008)
[9] D. R. Lide, Handbook of Chemistry and Physics (CRC, Boca-Raton, 2001-2002).
[10] M. P. Vukalovich, Thermodynamic Properties of Water and Water Vapor (Mashgiz, Moscow, 1955) [in Russian].
[11] C. A. J. Fletcher, Computational Techniques for Fluid Dynamics (Springer-Verlag, Berlin, 1990).
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