Dynamics of front-like water evaporation phase transition interfaces

•We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor.•Properties of traveling fronts are analyzed analytically and numerically.•The asymptotic behavior of perturbation...

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Published in:	Communications in nonlinear science & numerical simulation Vol. 67; pp. 223 - 236
Main Authors:	Shargatov, V.A., Gorkunov, S.V., Il’ichev, A.T.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01-02-2019 Elsevier Science Ltd
Subjects:	Asymptotic properties Differential equations Domains Evaporation Fingering Front stability Interface KPP equation Mathematical models Phase transitions Porous materials Porous medium Surface stability Turning point bifurcation Porous medium Evaporation Turning point bifurcation Front stability Interface Fingering KPP equation
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Abstract	•We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor.•Properties of traveling fronts are analyzed analytically and numerically.•The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation.•The expression for a speed of the traveling front was obtained.•The comparison was made of the known results of front dynamics for the model diffusion equation and their dynamics in general situation. We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other.
AbstractList	•We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor.•Properties of traveling fronts are analyzed analytically and numerically.•The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation.•The expression for a speed of the traveling front was obtained.•The comparison was made of the known results of front dynamics for the model diffusion equation and their dynamics in general situation. We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other. We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other.
Author	Gorkunov, S.V. Shargatov, V.A. Il’ichev, A.T.
Author_xml	– sequence: 1 givenname: V.A. surname: Shargatov fullname: Shargatov, V.A. email: shargatov@mail.ru organization: Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo pr., 101, Moscow 119526, Russia – sequence: 2 givenname: S.V. surname: Gorkunov fullname: Gorkunov, S.V. email: gorkunov.ser@mail.ru organization: Ishlinsky Institute for Problems in Mechanics RAS, Vernadskogo pr., 101, Moscow 119526, Russia – sequence: 3 givenname: A.T. surname: Il’ichev fullname: Il’ichev, A.T. email: ilichev@mi.ras.ru organization: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, Moscow 119991, Russia
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Cites_doi	10.1016/0001-8708(76)90098-0 10.1016/0167-2789(93)90197-9 10.1209/0295-5075/122/10001 10.1016/j.ijheatmasstransfer.2014.12.027 10.1016/S0092-8240(79)80020-8 10.1017/S0308210500024525 10.1007/BF01019332 10.1016/j.euromechflu.2007.11.006 10.1134/S0965542513090078 10.1007/BF02101705 10.1134/S106377610810018X 10.1098/rspa.2002.1087 10.1016/0022-0396(92)90153-E
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Keywords	Porous medium Evaporation Turning point bifurcation Front stability Interface Fingering KPP equation
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SubjectTerms	Asymptotic properties Differential equations Domains Evaporation Fingering Front stability Interface KPP equation Mathematical models Phase transitions Porous materials Porous medium Surface stability Turning point bifurcation
Title	Dynamics of front-like water evaporation phase transition interfaces
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