Skip to main content Accessibility help
×
Home

Rayleigh–Taylor stability in an evaporating binary mixture

  • Dipin S. Pillai (a1) and R. Narayanan (a1)

Abstract

A heavy-over-light configuration of a fluid bilayer may be stabilized in the presence of a phase change if the system consists of a single component. However, if the fluid is composed of a binary mixture with the more volatile component having the lower surface tension, it is known that a Marangoni instability occurs. This instability owes its origin to concentration gradients created by the phase change, even though the phase change otherwise has a stabilizing effect. In this study, it is shown via a nonlinear model under a long-wavelength approximation, that this Marangoni destabilization is insufficient to cause a rupture of the interface under practical operating conditions. Computations reveal that the stabilizing effect of the phase change dominates as the film becomes thin by reversing the direction of the Marangoni flow, thereby halting the instability and any hope of rupture.

Copyright

Corresponding author

Email address for correspondence: dipinsp@ufl.edu

References

Hide All
Abbassi, A. & Winterton, R. H. S. 1989 The non-boiling vapour film. Intl J. Heat Mass Transfer 32, 16491655.
Adham-Khodaparast, K., Kawaji, M. & Antar, B. N. 1995 The Rayleigh–Taylor and Kelvin–Helmholtz stability of a viscous liquid-vapor. Phys. Fluids 7, 359364.
Bestehorn, M. & Merkt, D. 2006 Regular surface patterns on Rayleigh–Taylor unstable evaporating films heated from below. Phys. Rev. Lett. 97, 127802.
Dietze, G. F. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348393.
Hsieh, D. Y. 1972 Effects of heat and mass transfer on Rayleigh–Taylor instability. Trans. ASME J. Basic Engng 156160.
Huang, A. & Joseph, D. D. 1992 Instability of the equilibrium of a liquid below its vapor between horizontal heated plates. J. Fluid Mech. 242, 235247.
Kanatani, K. & Oron, A. 2011 Nonlinear dynamics of confined thin liquid–vapor bilayer systems with phase change. Phys. Fluids 23, 032102.
Kim, B. J. & Kim, K. D. 2016 Rayleigh–Taylor instability of viscous fluids with phase change. Phys. Rev. E 93, 043123.
Konovalov, V. V., Lyubimov, D. V. & Lyubimova, T. P. 2017 Influence of phase transition on the instability of a liquid–vapor interface in a gravitational field. Phys. Rev. Fluids 2, 063902.
Labrosse, G. 2011 Méthodes numriques: Méthodes spectrale: Méthodes locales globales, méthodes globales, problèmes d’Helmotz et de Stokes, équations de Navier–Stokes. Ellipses Marketing.
Li, Y. & Yoda, M. 2016 An experimental study of buoyancy-Marangoni convection in confined and volatile binary fluids. Intl J. Heat Mass Transfer 102, 369380.
Lister, J. R., Rallison, J. M. & Rees, S. J. 2010 The nonlinear dynamics of pendent drops on a thin film coating the underside of a ceiling. J. Fluid Mech. 647, 239264.
Margerit, J., Colinet, P., Lebon, G., Iorio, C. S. & Legros, J. C. 2003 Interfacial nonequilibrium and Benard–Marangoni instability of a liquid–vapor system. Phys. Rev. E 68, 041601.
Miller, C. A. 1973 Stability of moving surfaces in fluid systems with heat and mass transport II. Combined effects of transport and density difference between phases. AIChE J. 19, 909915.
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.
Ozen, O. & Narayanan, R. 2004 The physics of evaporative and convective instabilities in bilayer systems: Linear theory. Phys. Fluids 16, 4644.
Panzarella, C. H., Davis, S. H. & Bankoff, G. 2000 Nonlinear dynamics in horizontal film boiling. J. Fluid Mech. 402, 163194.
Rajabi, A. A. A. & Winterton, R. H. S. 1987 Heat transfer across vapour film without ebullition. Intl J. Heat Mass Transfer 30, 17031708.
Rayleigh, Lord 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. s1‐14, 170177.
Ruyer-Quil, C. & Manneville, P. 2002 Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations. Phys. Fluids 14, 170183.
Savino, R., Cecere, A. & Paola, R. D. 2009 Surface tension-driven flow in wickless heat pipes with self-rewetting fluids. Intl J. Heat Mass Transfer 30, 380388.
Savino, R. & Paterna, D. 2006 Marangoni effect and heat pipe dry-out. Phys. Fluids 18, 118103.
Sharp, D. H. 1984 An overview of Rayleigh–Taylor instability. Physica D 12, 318.
Theofanous, T. G., Tu, J. P., Dinh, A. T. & Dinh, T. N. 2002 The boiling crisis phenomenon Part I: Nucleation and nucleate boiling heat transfer. Exp. Therm. Fluid Sci. 26, 775792.
Uguz, K. E. & Narayanan, R. 2012 Instability in evaporative mixtures. I. The effect of solutal Marangoni convection. Phys. Fluids 24, 094101.
Yiantsios, S. G. & Higgins, B. G. 1989 Rayleigh–Taylor instability in thin viscous films. Phys. Fluids A 1, 14841501.
Zhang, N. 2006 Surface tension-driven convection flow in evaporating liquid layers. In Surface Tension-Driven Flows and Applications (ed. Savino, R.), pp. 147170. Research Signpost.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Rayleigh–Taylor stability in an evaporating binary mixture

  • Dipin S. Pillai (a1) and R. Narayanan (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed