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Dynamics of ultra-thin two-layer films under the action of inclined temperature gradients

Published online by Cambridge University Press:  17 July 2009

ALEXANDER A. NEPOMNYASHCHY  and
ILYA B. SIMANOVSKII
ALEXANDER A. NEPOMNYASHCHY
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000, Haifa, Israel Minerva Centre for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, 32000, Haifa, Israel
ILYA B. SIMANOVSKII*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, 32000, Haifa, Israel Minerva Centre for Nonlinear Physics of Complex Systems, Technion – Israel Institute of Technology, 32000, Haifa, Israel
*
†Email address for correspondence: [email protected]
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Abstract

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film in the presence of an inclined temperature gradient is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. It has been found that for sufficiently large values of the ratio between the longitudinal and transverse Marangoni numbers, the real part of the linear growth rate does not depend on the direction of the wavenumber, except the case of nearly longitudinal disturbances. Numerous types of nonlinear evolution have been observed, among them are ordered systems of droplets, ‘splashes’, oblique waves, modulated transverse and longitudinal structures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 165 - 197
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Bandyopadhyay, D., Gulabani, R. & Sharma, A. 2005 Instability and dynamics of thin liquid bilayers. Ind. Engng Chem. Res. 44, 1259.Google Scholar
Bandyopadhyay, D. & Sharma, A. 2006 Nonlinear instabilities and pathways of rupture in thin liquid bilayers. J. Chem. Phys. 125, 054711.Google Scholar
Bandyopadhyay, D., Sharma, A. & Rastogi, C. 2008 Dewetting of the thin liquid bilayers on topologically patterned substrates: formation of microchannel and microdot arrays. Langmuir 24, 14048.CrossRefGoogle Scholar
Colinet, P., Joannes, L., Iorio, C. S., Haut, B., Bestehorn, M., Lebon, G. & Legros, J. C. 2003 Interfacial turbulence in evaporating liquids: theory and preliminary results of the ITEL-Master 9 sounding rocket experiment. Adv. Space Res. 32, 119.CrossRefGoogle Scholar
David, M. O., Reiter, G., Sitthai, T. & Schultz, J. 1998 Deformation of a glassy polymer film by long-range intermolecular forces. Langmuir 14, 5667.CrossRefGoogle Scholar
Davis, S. H. 1987 Thermocapillary instabilities. Ann. Rev. Fluid Mech. 19, 403.CrossRefGoogle Scholar
Demekhin, E. A., Kalliadasis, S. & Velarde, M. G. 2006 Suppressing falling film instabilities by Marangoni forces. Phys. Fluids 18, 042111.Google Scholar
Faldi, F., Composto, R. J. & Winey, K. I. 1995 Unstable polimer bilayers. 1. Morphology of dewetting. Langmuir 11, 4855.Google Scholar
Fisher, L. S. & Golovin, A. A. 2005 Nonlinear stability analysis of a two-layer thin liquid film: dewetting and autophobic behaviour. J. Coll. Interf. Sci. 291, 515.CrossRefGoogle Scholar
Golovin, A. A., Nepomnyashchy, A. A., Davis, S. H. & Zaks, M. A. 2001 Convective Cahn–Hilliard models: from coarsening to roughening. Phys. Rev. Lett. 85, 1550.CrossRefGoogle Scholar
Goussis, D. A. & Kelly, R. E. 1991 Surface wave and thermocapillary instabilities in a liquid film flow. J. Fluid Mech. 223, 25.Google Scholar
Haut, B. & Colinet, P. 2005 Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas. J. Colloid Interf. Sci. 285, 296.CrossRefGoogle ScholarPubMed
Indireshkumar, K. & Frenkel, A. L. 1997 Mutually penetrating motion of self-organized two-dimensional patterns of solitonlike structures. Phys. Rev. E 55, 1174.CrossRefGoogle Scholar
Israelachvili, J. N. 1992 Intermolecular and Surface Forces. Academic Press.Google Scholar
Joo, S. W. & Hsieh, K.-C. 2000 Interfacial instabilities in thin stratified viscous fluids under microgravity. Fluid Dyn. Res. 26, 203.CrossRefGoogle Scholar
Lambooy, P., Phelan, K. C., Haugg, O. & Krausch, G. 1996 Dewetting at the liquid-liquid interface. Phys. Rev. Lett. 76, 1110.CrossRefGoogle ScholarPubMed
Lenz, R. D. & Kumar, S. 2007 a Competitive displacement of thin liquid films on chemically patterned substrates. J. Fluid Mech. 571, 33.CrossRefGoogle Scholar
Lenz, R. D. & Kumar, S. 2007 b Instability of confined thin liquid film trilayers. J. Coll. Interf. Sci. 316, 660.CrossRefGoogle ScholarPubMed
Lifshitz, E. M. & Pitaevskii, L. P. 1980 Statistical Physics, Part 2. Pergamon.Google Scholar
Merkt, D., Pototsky, A., Bestehorn, M. & Thiele, U. 2005 Long-wave theory of bounded two-layer films with a free liquid-liquid interface: short- and long-time evolution. Phys. Fluids 17, 064104.CrossRefGoogle Scholar
Miladinova, S., Slavtchev, S., Lebon, G. & Legros, J.-C. 2002 Long-wave instabilities of non-uniformly heated falling films. J. Fluid Mech. 453, 153.CrossRefGoogle Scholar
Morariu, M. D., Schaffer, E. & Steiner, U. 2003 Capillary instabilities by fluctuation induced forces. Europ. Phys. J. E 12, 375.Google Scholar
Nepomnyashchy, A. A. & Simanovskii, I. B. 2006 Decomposition of a two-layer thin liquid film flowing under the action of Marangoni stresses. Phys. Fluids 18, 112101.CrossRefGoogle Scholar
Nepomnyashchy, A. A. & Simanovskii, I. B. 2007 Marangoni instability in ultrathin two-layer films. Phys. Fluids 19, 122103.CrossRefGoogle Scholar
Nepomnyashchy, A. A. & Simanovskii, I. B. 2008 Dynamics of non-isothermic ultra-thin two-layer films. In Proceedings of the Third International Topical Team Workshop on Two-Phase Systems for Ground and Space Applications, Bruxelles, Belgium; Microgravity Sci. Technol. 20 (3–4), 149–154.CrossRefGoogle Scholar
Nepomnyashchy, A. A, Simanovskii, I. B. & Braverman, L. M. 2001 Stability of thermocapillary flows with inclined temperature gradient. J. Fluid Mech. 442, 141.Google Scholar
Nepomnyashchy, A. A., Simanovskii, I. B. & Legros, J. C. 2006 Interfacial Convection in Multilayer Systems. Springer.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931.Google Scholar
Ospennikov, N. A. & Schwabe, D. 2004 Thermocapillary flow without return flow–linear flow. Exp. Fluids 36, 938.Google Scholar
Pan, Q., Winey, K. I., Hu, H. H. & Composto, R. J. 1997 Unstable polimer bilayers. 2. The effect of film thickness. Langmuir 13, 1758.Google Scholar
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2004 Alternative pathways of dewetting for a thin liquid two-layer film. Phys. Rev. E 70, 025201.Google ScholarPubMed
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2005 Morphology changes in the evolution of liquid two-layer films. J. Chem. Phys. 122, 224711.Google Scholar
Pototsky, A., Bestehorn, M., Merkt, D. & Thiele, U. 2006 Evolution of interface patterns of three-dimensional two-layer liquid films. Europhys. Lett. 74, 665.CrossRefGoogle Scholar
Renger, C., Muller-Buschbaum, P., Stamm, M. & Hinrichsen, G. 2000 Investigation and retardation of the dewetting on top of highly viscous amorphous substrates. Macromolecules 33, 8388.CrossRefGoogle Scholar
Saprykin, S., Demekhin, E. & Kalliadasis, S. 2005 a Self-organization of two-dimensional waves in an active dispersive-dissipative nonlinear medium. Phys. Rev. Let. 94, 224101.CrossRefGoogle Scholar
Saprykin, S., Demekhin, E. & Kalliadasis, S. 2005 b Two-dimensional wave dynamics in thin films. II. Formation of lattices of interacting stationary solitary pulses. Phys. Fluids 17, 117106.CrossRefGoogle Scholar
Scriven, L. E. & Sternling, C. V. 1964 On cellular convection driven by surface-tension gradients: effect of mean surface tension and surface viscosity. J. Fluid Mech. 19, 321.CrossRefGoogle Scholar
Sferrazza, M., Heppenstall-Butler, M., Cubitt, R., Bucknall, D., Webster, J. & Jones, R. A. L. 1998 Interfacial instability driven by dispersive forces: the early stages of spinodal dewetting of a thin polymer film on a polymer substrate. Phys. Rev. Let. 81, 5173.Google Scholar
Sferrazza, M., Xiao, C., Jones, R. A. L., Bucknall, D. G., Webster, J. & Penfold, J. 1997 Evidence for capillary waves at immiscible polymer/polymer interfaces. Phys. Rev. Let. 78, 3693.CrossRefGoogle Scholar
Shklyaev, O. E. & Nepomnyashchy, A. A. 2004 Thermocapillary flows under an inclined temperature gradient. J. Fluid Mech. 504, 99.Google Scholar
Simanovskii, I. B. & Nepomnyashchy, A. A. 1993 Convective Instabilities in Systems with Interface. Gordon and Breach.Google Scholar
Simanovskii, I., Nepomnyashchy, A., Shevtsova, V., Colinet, P. & Legros, J. C. 2006 Nonlinear Marangoni convection with the inclined temperature gradient in multilayer systems. Phys. Rev. E 73, 066310.Google Scholar
Smith, K. A. 1966 On convective instability induced by surface-tension gradients J. Fluid Mech. 24, 401.Google Scholar
Thiele, U. & Knobloch, E. 2004 Thin liquid films on a slightly inclined heated plate Physica D 190, 213.Google Scholar
Ueno, I., Kurosawa, T. & Kawamura, H. 2002 Thermocapillary convection in thin liquid layer with temperature gradient inclined to free surface, Heat Transfer 2002. In Proceedings of the Twelfth International Heat Transfer Conference, Grenoble, France, pp. 129–134.Google Scholar