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Critical Evolution of Finite Perturbations of a Water Evaporation Surface in Porous Media

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Abstract—

It is shown that the approximate steady-state solutions, which satisfy the model dissipative equation that describes the process of water evaporation in the neighborhood of the instability threshold of a phase transition interface, determine localized damped finite-amplitude perturbations when a certain condition is fulfilled. These steady-state solutions can be used for forecasting the scenario of the development of a perturbation with sufficient accuracy if this perturbation has no common points with any steady-state solution. If the initial position of the phase transition front is located between the spectrally stable solution and any of the steady-state solutions, this front damps. If the initial position of the front is located above at least one of the spectrally unstable steady-state solutions, then the solution is catastrophically restructured.

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Funding

The work was carried out with financial support from the Russian Science Foundation under the grant no. 16-11-10195.

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Authors and Affiliations

  1. Ishlinskii Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    S. V. Gorkunov & V. A. Shargatov

  2. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia

    S. V. Gorkunov & V. A. Shargatov

  3. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    A. T. Il’ichev

  4. Bauman Moscow State Technical University, Moscow, Russia

    A. T. Il’ichev

Authors
  1. S. V. Gorkunov
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  2. A. T. Il’ichev
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  3. V. A. Shargatov
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Corresponding authors

Correspondence to A. T. Il’ichev or V. A. Shargatov.

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Translated by E.A. Pushkar

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Gorkunov, S.V., Il’ichev, A.T. & Shargatov, V.A. Critical Evolution of Finite Perturbations of a Water Evaporation Surface in Porous Media. Fluid Dyn 55, 204–212 (2020). https://doi.org/10.1134/S0015462820020044

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  • DOI: https://doi.org/10.1134/S0015462820020044

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