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Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

Ilyin, Daniil V. and Goddard, William A., III and Abarzhi, Snezhana I. (2020) Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities. Physics of Fluids, 32 (8). Art. No. 082105. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:20200803-085255665

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Abstract

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/5.0013165DOIArticle
https://arxiv.org/abs/2006.11064arXivDiscussion Paper
ORCID:
AuthorORCID
Ilyin, Daniil V.0000-0003-3534-771X
Goddard, William A., III0000-0003-0097-5716
Abarzhi, Snezhana I.0000-0002-8466-3084
Alternate Title:On interplay of surface tension and inertial stabilization mechanisms in the interface dynamics with interfacial mass flux
Additional Information:© 2020 Published under license by AIP Publishing. Submitted: 11 May 2020; Accepted: 26 June 2020; Published Online: 11 August 2020. This work is dedicated to the memory of Leo P. Kadanoff. The authors thank for support the University of Western Australia (Australia), Award/Contract Number 10101047 [S.I.A.]; the National Science Foundation (USA), Award/Contract Number 1404449 [S.I.A.]; the Japan Society for the Promotion of Science (Japan), Award/Contract Number S11140 [S.I.A.]; the Summer Undergraduate Research Fellowship Program at California Institute of Technology (USA), the Toni and Bob Perpall Fellowship [D.V.I.]; the Department of Energy (USA), Award/Contract Number DE-SC0017710 [W.A.G.]. S.I.A. expresses her gratitude to the late Professor Leo P. Kadanoff and the late Professor Sergei I. Anisimov for discussions on singularities and stabilization mechanisms and thanks Professor Yasuhide Fukumoto for discussions on fluid instabilities. The authors express their gratitude to Professor Sivashinsky for comments and for discussions of self-similar dynamics. Data Availability: The methods, the results, and the data presented in this work are freely available to the readers and on request from the authors.
Funders:
Funding AgencyGrant Number
University of Western Australia10101047
NSF140444
Japan Society for the Promotion of Science (JSPS)S11140
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Toni and Bob Perpall FellowshipUNSPECIFIED
Department of Energy (DOE)DE-SC0017710
Issue or Number:8
Record Number:CaltechAUTHORS:20200803-085255665
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200803-085255665
Official Citation:Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities. Daniil V. Ilyin, William A. Goddard III, and Snezhana I. Abarzhi. Physics of Fluids 32:8; doi: /10.1063/5.0013165
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104696
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Aug 2020 15:57
Last Modified:11 Aug 2020 17:51

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