Abstract
The stability of vertical flows through a horizontally extended two-dimensional region of a porous medium is considered in the case of presence of a phase transition front. It is shown that the plane steady-state phase transition front may have several steady-state positions in the wettable porous medium and the necessary condition of their existence is obtained. The spectral stability of the plane phase transition interface is investigated. It is found that in the presence of capillary forces exerted on the phase transition front in the wettable medium the plane front can be destabilized on the mode with both infinite and zero wavenumbers (short- and long-wave instabilities); the short-wave instability can then exist even in the case of the sole steady-state position of the front.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.T. Il’ichev and G.G. Tsypkin, “Instabilities of Uniform Filtration Flows with Phase Transition,” JETP 107, No. 4, 699–711 (2008).
A.T. Il’ichev and G.G. Tsypkin, “Catastrophic Transition to Instability of Evaporation Front in a Porous Medium,” Europ. J. Mech B Fluids 27, No. 6, 665–677 (2008).
G.G. Tsypkin and A.T. Il’ichev, “Gravitational Stability of the Interface in Water over Steam Geothermal Reservoirs,” Transp. Porous Media 55, No. 2, 183–199 (2004).
A.T. Ilichev and V.A. Shargatov, “Dynamics ofWater Evaporation Fronts,” ComputationalMathematics and Mathematical Physics 53, No. 9, 1350–1370 (2013).
V.A. Shargatov, A.T. Il’Ichev, and G.G. Tsypkin, “Dynamics and Stability of Moving Fronts ofWater Evaporation in a Porous Medium,” Int. J. Heat and Mass Transfer 83, 552–561 (2015).
S.A. Gibun, A.V. Krivosheev, and V.A. Shargatov, “Existence of a Steady-State Water Evaporation Front in a Horizontally Extended Low-Permeability Region,” Fluid Dynamics 50 (2), 240–249 (2015).
Z.H. Khan and D. Pritchard, “LiquidVapour Fronts in Porous Media: Multiplicity and Stability of Front Positions,” Int. J. of Heat Mass Transfer. 2013. V. 61. P. 1–17.
M.P. Vukalovich, Thermodynamic Properties of Water and Steam (Mashgiz, Moscow, 1955) [in Russian].
A.A. Afanas’ev, A.A. Barmin, and O.E. Melnik, “Hydrodynamic Stability of Evaporation Fronts in Porous Media,” Fluid Dynamics 42 (5), 773–783 (2007).
A.A. Afanas’ev and A.A. Barmin, “Unsteady One-DimensionalWater and Steam Flows through a Porous Medium with Allowance for Phase Transitions,” Fluid Dynamics 42 (4), 627–636 (2007).
A.A. Afanas’ev, “A Representation of the Equations of Multicomponent Multiphase Seepage,” PMM Journal of Applied Mathematics and Mechanics 76, No. 2, 192–198 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Shargatov, 2017, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2017, Vol. 52, No. 1, pp. 148–159.
Rights and permissions
About this article
Cite this article
Shargatov, V.A. Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media. Fluid Dyn 52, 146–157 (2017). https://doi.org/10.1134/S0015462817010148
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462817010148