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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Pages 1531–1553 (Mi zvmmf9919)  

This article is cited in 8 scientific papers (total in 8 papers)

Dynamics of water evaporation fronts

A. T. Il'icheva, V. A. Shargatovb

a Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
b National Research Nuclear University УMEPhIФ, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: 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.

Key words: porous medium diffusion humidity water evaporation front, phase transition, stability, bifurcation, Kolmogorov–Petrovskii–Piskunov equation, numerical method.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-12051-офи-м

DOI: https://doi.org/10.7868/S0044466913090081

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1350–1370

Bibliographic databases:

UDC: 519.634
Received: 07.02.2013

Citation: A. T. Il'ichev, V. A. Shargatov, “Dynamics of water evaporation fronts”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1531–1553; Comput. Math. Math. Phys., 53:9 (2013), 1350–1370

Citation in format AMSBIB
\by A.~T.~Il'ichev, V.~A.~Shargatov
\paper Dynamics of water evaporation fronts
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 9
\pages 1531--1553
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 9
\pages 1350--1370

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    This publication is cited in the following articles:
    1. V. A. Shargatov, A. T. Il'ichev, G. G. Tsypkin, “Dynamics and stability of moving fronts of water evaporation in a porous medium”, Int. J. Heat Mass Transf., 83 (2015), 552–561  crossref  isi  elib  scopus
    2. S. A. Gubin, V. A. Krivosheev, A. V. Shargatov, “Existence of a steady-statewater evaporation front in a horizontally extended low-permeability region”, Fluid Dyn., 50:2 (2015), 240–249  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. A. Shargatov, “Instability of a liquid-vapor phase transition front in inhomogeneous wettable porous media”, Fluid Dyn., 52:1 (2017), 146–157  crossref  mathscinet  zmath  isi  scopus
    4. G. G. Tsypkin, V. A. Shargatov, “Influence of capillary pressure gradient on connectivity of flow through a porous medium”, Int. J. Heat Mass Transf., 127:C (2018), 1053–1063  crossref  isi  scopus
    5. V. A. Shargatov, “Dynamics and stability of air bubbles in a porous medium”, Comput. Math. Math. Phys., 58:7 (2018), 1172–1187  mathnet  crossref  crossref  isi  elib
    6. Shargatov V.A., Gorkunov V S., Il'chev A.T., “Dynamics of Front-Like Water Evaporation Phase Transition Interfaces”, Commun. Nonlinear Sci. Numer. Simul., 67 (2019), 223–236  crossref  mathscinet  isi  scopus
    7. Lippoth F., Prokert G., “Well-Posedness For a Moving Boundary Model of An Evaporation Front in a Porous Medium”, J. Math. Fluid Mech., 21:3 (2019), UNSP 40  crossref  isi
    8. V. A. Shargatov, A. T. Il'ichev, “Dynamics of Perturbations under Diffusion in a Porous Medium”, Proc. Steklov Inst. Math., 310 (2020), 291–303  mathnet  crossref  crossref  isi  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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