Theoretical and numerical analyses of the effect of cross-diffusion on the gravitational instability in ternary mixtures

Min Chan Kim, Kwang Ho Song

Research output: Contribution to journalArticle

Abstract

To understand the effect of cross diffusion on the onset and the growth of the gravitational instabilities in a ternary solution more rigorously, theoretical and numerical analyses are conducted by considering all cross diffusion coefficients. We clearly showed that the stable concentration field is possible even for the complex-eigenvalues systems, such as acetone(1)-benzene(2)-CCl4(common solvent) ternary mixture. By employing Faddeeva functions, we extended the previous asymptotic analysis into the complex eigenvalue systems. In addition, by considering all possible cross diffusion coefficients, i.e., complex conjugate, and real and distinct eigenvalues system, we derive the linear stability equations in the uncoupled form, solve them, and conduct nonlinear numerical simulations employing the linear stability result as an initial condition. Through the present asymptotic, linear and nonlinear analyses, the instability motions in the double-diffusive (DD), diffusive-layer convection (DLC) and extended double diffusive (EDD) regimes are clearly identified. The present asymptotic, linear and nonlinear analyses support each other and are in good agreement with the previous theoretical, numerical and experimental work.

Original languageEnglish
Article number118511
JournalInternational Journal of Heat and Mass Transfer
Volume143
DOIs
Publication statusPublished - 2019 Nov 1

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gravitational instability
eigenvalues
diffusion coefficient
acetone
Asymptotic analysis
convection
Acetone
Benzene
benzene
Computer simulation
simulation

Keywords

  • Complex eigenvalue
  • Cross diffusion
  • Gravitational instability
  • Numerical simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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title = "Theoretical and numerical analyses of the effect of cross-diffusion on the gravitational instability in ternary mixtures",
abstract = "To understand the effect of cross diffusion on the onset and the growth of the gravitational instabilities in a ternary solution more rigorously, theoretical and numerical analyses are conducted by considering all cross diffusion coefficients. We clearly showed that the stable concentration field is possible even for the complex-eigenvalues systems, such as acetone(1)-benzene(2)-CCl4(common solvent) ternary mixture. By employing Faddeeva functions, we extended the previous asymptotic analysis into the complex eigenvalue systems. In addition, by considering all possible cross diffusion coefficients, i.e., complex conjugate, and real and distinct eigenvalues system, we derive the linear stability equations in the uncoupled form, solve them, and conduct nonlinear numerical simulations employing the linear stability result as an initial condition. Through the present asymptotic, linear and nonlinear analyses, the instability motions in the double-diffusive (DD), diffusive-layer convection (DLC) and extended double diffusive (EDD) regimes are clearly identified. The present asymptotic, linear and nonlinear analyses support each other and are in good agreement with the previous theoretical, numerical and experimental work.",
keywords = "Complex eigenvalue, Cross diffusion, Gravitational instability, Numerical simulation",
author = "Kim, {Min Chan} and Song, {Kwang Ho}",
year = "2019",
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language = "English",
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T1 - Theoretical and numerical analyses of the effect of cross-diffusion on the gravitational instability in ternary mixtures

AU - Kim, Min Chan

AU - Song, Kwang Ho

PY - 2019/11/1

Y1 - 2019/11/1

N2 - To understand the effect of cross diffusion on the onset and the growth of the gravitational instabilities in a ternary solution more rigorously, theoretical and numerical analyses are conducted by considering all cross diffusion coefficients. We clearly showed that the stable concentration field is possible even for the complex-eigenvalues systems, such as acetone(1)-benzene(2)-CCl4(common solvent) ternary mixture. By employing Faddeeva functions, we extended the previous asymptotic analysis into the complex eigenvalue systems. In addition, by considering all possible cross diffusion coefficients, i.e., complex conjugate, and real and distinct eigenvalues system, we derive the linear stability equations in the uncoupled form, solve them, and conduct nonlinear numerical simulations employing the linear stability result as an initial condition. Through the present asymptotic, linear and nonlinear analyses, the instability motions in the double-diffusive (DD), diffusive-layer convection (DLC) and extended double diffusive (EDD) regimes are clearly identified. The present asymptotic, linear and nonlinear analyses support each other and are in good agreement with the previous theoretical, numerical and experimental work.

AB - To understand the effect of cross diffusion on the onset and the growth of the gravitational instabilities in a ternary solution more rigorously, theoretical and numerical analyses are conducted by considering all cross diffusion coefficients. We clearly showed that the stable concentration field is possible even for the complex-eigenvalues systems, such as acetone(1)-benzene(2)-CCl4(common solvent) ternary mixture. By employing Faddeeva functions, we extended the previous asymptotic analysis into the complex eigenvalue systems. In addition, by considering all possible cross diffusion coefficients, i.e., complex conjugate, and real and distinct eigenvalues system, we derive the linear stability equations in the uncoupled form, solve them, and conduct nonlinear numerical simulations employing the linear stability result as an initial condition. Through the present asymptotic, linear and nonlinear analyses, the instability motions in the double-diffusive (DD), diffusive-layer convection (DLC) and extended double diffusive (EDD) regimes are clearly identified. The present asymptotic, linear and nonlinear analyses support each other and are in good agreement with the previous theoretical, numerical and experimental work.

KW - Complex eigenvalue

KW - Cross diffusion

KW - Gravitational instability

KW - Numerical simulation

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