Evolution of a Condensation Surface in a Porous Medium near the Instability Threshold

  • A. T. Il’ichev
  • G. G. Tsypkin


We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov–Petrovskii–Piskunov type equation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    CRC Handbook of Chemistry and Physics, Ed. by D. R. Lide, 82nd ed., 2001–2002 (CRC Press, Boca Raton, 2001).Google Scholar
  2. 2.
    A. T. Il’ichev and G. G. Tsypkin, “Weakly nonlinear theory for the instability of long-wave perturbations,” Dokl. Akad. Nauk 416 (2), 192–194 (2007) [Dokl. Phys. 52 (9), 499–501 (2007)].zbMATHGoogle Scholar
  3. 3.
    A. T. Il’ichev and G. G. Tsypkin, “Catastrophic transition to instability of evaporation front in a porous medium,” Eur. J. Mech. B: Fluids 27, 665–677 (2008).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    A. T. Il’ichev and G. G. Tsypkin, “Instabilities of uniform filtration flows with phase transition,” Zh. Eksp. Teor. Fiz. 134 (4), 815–830 (2008) [J. Exp. Theor. Phys. 107, 699–711 (2008)].Google Scholar
  5. 5.
    A. Kolmogoroff, I. Petrovsky, and N. Piscounoff, “´Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique,” Bull. Univ. État Moscou, Math. Méc. 1 (6), 1–25 (1937).zbMATHGoogle Scholar
  6. 6.
    V. A. Shargatov, “Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 148–159 (2017) [Fluid Dyn. 52, 146–157 (2017)].MathSciNetzbMATHGoogle Scholar
  7. 7.
    N. Shokri and G. D. Salvucci, “Evaporation from porous media in the presence of a water table,” Vadose Zone J. 10 (4), 1309–1318 (2011).CrossRefGoogle Scholar
  8. 8.
    G. G. Tsypkin, “Stability of the evaporation and condensation surfaces in a porous medium,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 70–76 (2017) [Fluid Dyn. 52, 777–785 (2017)].zbMATHGoogle Scholar
  9. 9.
    M. Tuller, D. Or, and L. M. Dudley, “Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores,” Water Resour. Res. 35 (7), 1949–1964 (1999).CrossRefGoogle Scholar
  10. 10.
    M. P. Vukalovitch, Thermodynamic Properties of Water and Steam (Mashgiz, Moscow, 1955, 1958).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.Ishlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia

Personalised recommendations