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The Convective Instabilities in a Liquid–Vapor System with a Non-equilibrium Evaporation Interface

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Abstract

Rayleigh–Marangoni–Bénard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz–Knudsen’s relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.

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References

  • Bénard, H.: Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. Pures Appl. 11, 1261 (1900)

    Google Scholar 

  • Block, M.J.: Surface tension as the cause of Bénard cells and surface tension deformation in a liquid film. Nature 178, 650 (1956)

    Article  Google Scholar 

  • Burelbach, J.P., Bankoff, S.G., Davis, S.H.: Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463 (1988)

    Article  MATH  Google Scholar 

  • Colinet, P., Legros, J.C., Velarde, M.G.: Nonlinear Dynamics of Surface-Tension-Driven Instabilities. Wiley-VCH, Berlin (2001)

    Book  MATH  Google Scholar 

  • Fang, G., Ward, C.A.: Temperature measured close to the interface of an evaporating liquid. Phys. Rev. E 59, 417 (1999)

    Article  Google Scholar 

  • Kennard, E.K.: Kinetic Theory of Gases. McGraw-Hill, New York (1938)

    Google Scholar 

  • Liu, R., Liu, Q.S.: Linear stability analyses of convection in two-layer system with an evaporating vapor-liquid interface. Acta Mech. Sin. 22, 109 (2006)

    Article  MathSciNet  Google Scholar 

  • Margerit, J., Colinet, P., Lebon, G., Iorio, C.S., Legros, J.C.: Interfacial nonequilibrium and Bénard-Marangoni instability of a liquid–vapor system. Phys. Rev. E 68, 041601 (2003)

    Article  Google Scholar 

  • Miller, C.A.: Stability of moving surface in fluid systems with heat and mass transport. Part II-Combined effects of transport and density difference between phases. AIChE 19, 909 (1973)

    Article  Google Scholar 

  • Nield, D.A.: Surface tension as the cause of Bénard cells and surface deformation in a liquid film. J. Fluid Mech. 19, 341 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  • Orzag, S.A.: Accurate solution of the Orr-Sommerfeld stabiltiy equation. J. Fluid Mech. 50, 689 (1971)

    Article  Google Scholar 

  • Ozen, O., Narayanan, R.: The physics of evaporative and convective instabilities in bilayer systems: linear theory. Phys. Fluids 16(12), 4644 (2004)

    Article  Google Scholar 

  • Palmer, H.J.: The hydrodynamic stability of rapidly evaporating liquids at reduced pressure. J. Fluid Mech. 75, 487 (1976)

    Article  MATH  Google Scholar 

  • Pearson, J.R.A.: On convection cells induced by surface tension. J. Fluid Mech. 4, 489 (1958)

    Article  MATH  Google Scholar 

  • Prosperetti, A., Plesset, M.S.: The stability of an evaporating liquid surface. Phys. Fluids 27(7), 1590 (1984)

    Article  MATH  Google Scholar 

  • Rayleigh, L.: On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag. 32(6), 529 (1916)

    Google Scholar 

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Correspondence to Qiusheng Liu.

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Liu, R., Liu, Q. The Convective Instabilities in a Liquid–Vapor System with a Non-equilibrium Evaporation Interface. Microgravity Sci. Technol. 21 (Suppl 1), 233–240 (2009). https://doi.org/10.1007/s12217-009-9126-8

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  • DOI: https://doi.org/10.1007/s12217-009-9126-8

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