Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-21T11:29:18.978Z Has data issue: false hasContentIssue false
  • English
  • Français

Rayleigh–Taylor stability in an evaporating binary mixture

Published online by Cambridge University Press:  04 June 2018

Dipin S. Pillai Open the ORCID record for Dipin S. Pillai [Opens in a new window]  and
R. Narayanan
Dipin S. Pillai*
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
R. Narayanan
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Phase change: Condensation/evaporation Convection: Marangoni convection Interfacial Flows (free surface): Thin films
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 848 , 10 August 2018 , R1
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbassi, A. & Winterton, R. H. S. 1989 The non-boiling vapour film. Intl J. Heat Mass Transfer 32, 1649–1655.CrossRefGoogle Scholar
Adham-Khodaparast, K., Kawaji, M. & Antar, B. N. 1995 The Rayleigh–Taylor and Kelvin–Helmholtz stability of a viscous liquid-vapor. Phys. Fluids 7, 359–364.CrossRefGoogle Scholar
Bestehorn, M. & Merkt, D. 2006 Regular surface patterns on Rayleigh–Taylor unstable evaporating films heated from below. Phys. Rev. Lett. 97, 127802.CrossRefGoogle ScholarPubMed
Dietze, G. F. & Ruyer-Quil, C. 2013 Wavy liquid films in interaction with a confined laminar gas flow. J. Fluid Mech. 722, 348–393.CrossRefGoogle Scholar
Hsieh, D. Y. 1972 Effects of heat and mass transfer on Rayleigh–Taylor instability. Trans. ASME J. Basic Engng 156–160.CrossRefGoogle Scholar
Huang, A. & Joseph, D. D. 1992 Instability of the equilibrium of a liquid below its vapor between horizontal heated plates. J. Fluid Mech. 242, 235–247.CrossRefGoogle Scholar
Kanatani, K. & Oron, A. 2011 Nonlinear dynamics of confined thin liquid–vapor bilayer systems with phase change. Phys. Fluids 23, 032102.CrossRefGoogle Scholar
Kim, B. J. & Kim, K. D. 2016 Rayleigh–Taylor instability of viscous fluids with phase change. Phys. Rev. E 93, 043123.Google ScholarPubMed
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.CrossRefGoogle Scholar
Labrosse, G. 2011 Méthodes numriques: Méthodes spectrale: Méthodes locales globales, méthodes globales, problèmes d’Helmotz et de Stokes, équations de Navier–Stokes. Ellipses Marketing.Google Scholar
Li, Y. & Yoda, M. 2016 An experimental study of buoyancy-Marangoni convection in confined and volatile binary fluids. Intl J. Heat Mass Transfer 102, 369–380.CrossRefGoogle Scholar
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, 239–264.CrossRefGoogle Scholar
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.Google ScholarPubMed
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, 909–915.CrossRefGoogle Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.CrossRefGoogle Scholar
Ozen, O. & Narayanan, R. 2004 The physics of evaporative and convective instabilities in bilayer systems: Linear theory. Phys. Fluids 16, 4644.CrossRefGoogle Scholar
Panzarella, C. H., Davis, S. H. & Bankoff, G. 2000 Nonlinear dynamics in horizontal film boiling. J. Fluid Mech. 402, 163–194.CrossRefGoogle Scholar
Rajabi, A. A. A. & Winterton, R. H. S. 1987 Heat transfer across vapour film without ebullition. Intl J. Heat Mass Transfer 30, 1703–1708.CrossRefGoogle Scholar
Rayleigh, Lord 1882 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. s1‐14, 170–177.CrossRefGoogle Scholar
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, 170–183.CrossRefGoogle Scholar
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, 380–388.Google Scholar
Savino, R. & Paterna, D. 2006 Marangoni effect and heat pipe dry-out. Phys. Fluids 18, 118103.CrossRefGoogle Scholar
Sharp, D. H. 1984 An overview of Rayleigh–Taylor instability. Physica D 12, 3–18.Google Scholar
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, 775–792.CrossRefGoogle Scholar
Uguz, K. E. & Narayanan, R. 2012 Instability in evaporative mixtures. I. The effect of solutal Marangoni convection. Phys. Fluids 24, 094101.Google Scholar
Yiantsios, S. G. & Higgins, B. G. 1989 Rayleigh–Taylor instability in thin viscous films. Phys. Fluids A 1, 1484–1501.CrossRefGoogle Scholar
Zhang, N. 2006 Surface tension-driven convection flow in evaporating liquid layers. In Surface Tension-Driven Flows and Applications (ed. Savino, R.), pp. 147–170. Research Signpost.Google Scholar

Pillai and Narayanan supplementary movie 1

The spatio-temporal evolution of the R-T unstable interface in the absence of phase change for pure ethanol bilayer. The interface approaches rupture.

Download Pillai and Narayanan supplementary movie 1(Video)
Video 1.1 MB

Pillai and Narayanan supplementary movie 2

Saturation of R-T unstable interface to a steady configuration in the presence of phase change for pure ethanol bilayer, ΔT=5°C.

Download Pillai and Narayanan supplementary movie 2(Video)
Video 1 MB

Pillai and Narayanan supplementary movie 3

Velocity profile in each phase for the binary mixture, showing "flow reversal" in the liquid phase as the interface approaches the heated bottom wall.

Download Pillai and Narayanan supplementary movie 3(Video)
Video 3.4 MB