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Effect of surfactants on the inertialess instability of a two-layer film flow

Published online by Cambridge University Press:  30 October 2007

PENG GAO  and
XI-YUN LU
PENG GAO
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
XI-YUN LU*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Author to whom correspondence should be addressed: xlu@ustc.edu.cn
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Abstract

The effect of insoluble surface and interfacial surfactants on the inertialess instability of a two-fluid film flow down an inclined plane is investigated based on a normal mode analysis. The results reveal that the inertialess instability of relatively long waves can be predominantly weakened by a surface surfactant and enhanced by an interfacial surfactant. For sufficiently large viscosity ratio of the upper layer to the lower one, a destabilizing influence of the surface surfactant is also detected; this is thus a rare example demonstrating the possible destabilizing effect of the surfactant on the flow with a free surface. When the upper layer is less viscous and hence the instability due to the viscosity stratification disappears, a new instability can be triggered by the presence of an interfacial surfactant. Both the surfactants on the surface and the interface can stabilize or destabilize the short-wave instabilities, which occur for negligible surface and interfacial tensions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007 , pp. 495 - 507
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2, 554–574.CrossRefGoogle Scholar
Blyth, M. G. & Pozrikidis, C. 2004 a Effect of surfactant on the stability of film flow down an inclined plane. J. Fluid Mech. 521, 241–250.CrossRefGoogle Scholar
Blyth, M. G. & Pozrikidis, C. 2004 b Effect of surfactants on the stability of two-layer channel flow. J. Fluid Mech. 505, 59–86.CrossRefGoogle Scholar
Chen, K. P. 1993 Wave formation in the gravity-driven low-Reynolds number flow of two fluid films down an inclined plane. Phys. Fluids A 5, 3038–3048.CrossRefGoogle Scholar
Frenkel, A. L. & Halpern, D. 2002 Stokes-flow instability due to interfacial surfactant. Phys. Fluids 14, L45–L48.CrossRefGoogle Scholar
Gao, P. & Lu, X.-Y. 2006 Effect of surfactants on the long-wave stability of oscillatory film flow. J. Fluid Mech. 562, 345–354.CrossRefGoogle Scholar
Halpern, D. & Frenkel, A. L. 2003 Destabilization of a creeping flow by interfacial surfactant: linear theory extended to all wavenumbers. J. Fluid Mech. 485, 191–220.CrossRefGoogle Scholar
Hu, J., Millet, S., Botton, V., Hadid, H. B. & Henry, D. 2006 Inertialess temporal and spatio-temporal stability analysis of the two-layer film flow with density stratification. Phys. Fluids 18, 104101.CrossRefGoogle Scholar
Jiang, W. Y., Helenbrook, B. & Lin, S. P. 2004 Inertialess instability of a two-layer liquid film flow. Phys. Fluids 16, 652–663.CrossRefGoogle Scholar
Jiang, W. Y., Helenbrook, B. T., Lin, S. P. & Weinstein, S. J. 2005 Low-Reynolds-number instabilities in three-layer flow down an inclined wall. J. Fluid Mech. 539, 387–416.CrossRefGoogle Scholar
Kao, T. W. 1968 Role of viscosity stratification in the stability of two-layer flow down an incline. J. Fluid Mech. 33, 561–572.CrossRefGoogle Scholar
Kliakhandler, I. L. 1999 Long interfacial waves in multilayer thin films and coupled Kuramoto–Sivashinsky equations. J. Fluid Mech. 391, 45–65.CrossRefGoogle Scholar
Kliakhandler, I. L. & Sivashinsky, G. I. 1997 Viscous damping and instabilities in stratified liquid film flowing down a slightly inclined plane. Phys. Fluids 9, 23–30.CrossRefGoogle Scholar
Lin, S. P. 1970 Stabilizing effects of surface-active agents on a film flow. AIChE J. 16, 375–379.CrossRefGoogle Scholar
Loewenherz, D. S. & Lawrence, C. J. 1989 The effect of viscosity stratification on the stability of a free surface flow at low Reynolds number. Phys. Fluids A 1, 1686–1693.CrossRefGoogle Scholar
Pozrikidis, C. 2004 Instability of multi-layer channel and film flows. Adv. Appl. Mech. 40, 179–239.CrossRefGoogle Scholar
Wang, C. K., Seaborg, J. J. & Lin, S. P. 1978 Instability of multi-layered liquid films. Phys. Fluids 21, 1669–1673.CrossRefGoogle Scholar
Wei, H.-H. 2005 a Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane. Phys. Fluids 17, 012103.CrossRefGoogle Scholar
Wei, H.-H. 2005 b On the flow-induced Marangoni instability due to the presence of surfactant. J. Fluid Mech. 544, 173–200.CrossRefGoogle Scholar
Wei, H.-H. 2007 Role of base flows on surfactant-driven interfacial instabilities. Phys. Rev. E 75, 036306.Google ScholarPubMed
Wei, H.-H., Halpern, D. & Grotberg, J. B. 2005 Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary. J. Colloid Interface Sci. 285, 769–780.CrossRefGoogle Scholar
Weinstein, S. J. & Chen, K. P. 1999 Large growth rate instabilities in three-layer flow down an incline in the limit of zero Reynolds number. Phys. Fluids 11, 3270–3282.CrossRefGoogle Scholar
Weinstein, S. J. & Kurz, M. R. 1991 Long-wavelength instabilities in three-layer flow down an incline. Phys. Fluids A 3, 2680–2687.CrossRefGoogle Scholar
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 29–53.CrossRefGoogle Scholar
Whitaker, S. & Jones, L. O. 1966 Stability of falling liquid films. Effect of interface and interfacial mass transport. AIChE J. 12, 421–431.CrossRefGoogle Scholar
Yih, C. S. 1963 Stability of liquid flow down an inclined plane. Phys. Fluids 6, 321–334.CrossRefGoogle Scholar
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