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.
Similar content being viewed by others
References
Bénard, H.: Les tourbillons cellulaires dans une nappe liquide. Rev. Gen. Sci. Pures Appl. 11, 1261 (1900)
Block, M.J.: Surface tension as the cause of Bénard cells and surface tension deformation in a liquid film. Nature 178, 650 (1956)
Burelbach, J.P., Bankoff, S.G., Davis, S.H.: Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463 (1988)
Colinet, P., Legros, J.C., Velarde, M.G.: Nonlinear Dynamics of Surface-Tension-Driven Instabilities. Wiley-VCH, Berlin (2001)
Fang, G., Ward, C.A.: Temperature measured close to the interface of an evaporating liquid. Phys. Rev. E 59, 417 (1999)
Kennard, E.K.: Kinetic Theory of Gases. McGraw-Hill, New York (1938)
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)
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)
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)
Nield, D.A.: Surface tension as the cause of Bénard cells and surface deformation in a liquid film. J. Fluid Mech. 19, 341 (1964)
Orzag, S.A.: Accurate solution of the Orr-Sommerfeld stabiltiy equation. J. Fluid Mech. 50, 689 (1971)
Ozen, O., Narayanan, R.: The physics of evaporative and convective instabilities in bilayer systems: linear theory. Phys. Fluids 16(12), 4644 (2004)
Palmer, H.J.: The hydrodynamic stability of rapidly evaporating liquids at reduced pressure. J. Fluid Mech. 75, 487 (1976)
Pearson, J.R.A.: On convection cells induced by surface tension. J. Fluid Mech. 4, 489 (1958)
Prosperetti, A., Plesset, M.S.: The stability of an evaporating liquid surface. Phys. Fluids 27(7), 1590 (1984)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12217-009-9126-8