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Experimental evidence for a short-wave global mode in film flow along periodic corrugations

Published online by Cambridge University Press:  08 February 2013

Z. Cao ,
M. Vlachogiannis  and
V. Bontozoglou
Z. Cao
Affiliation:
Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece
M. Vlachogiannis
Affiliation:
Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece Technological Educational Institute of Larissa, GR-41110 Larissa, Greece
V. Bontozoglou*
Affiliation:
Department of Mechanical Engineering, University of Thessaly, GR-38334 Volos, Greece
*
†Email address for correspondence: [email protected]
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Abstract

The primary instability of liquid film flow along periodically corrugated substrates is studied experimentally. Two different wall shapes, of the same wavelength and height, are tested for a wide range of inclinations. It is found that, beyond a specific inclination, a new instability mode occurs before the classical, convective, long-wave one. This is a short, travelling wave, which is highly regular and persistently two-dimensional, and appears to be a global mode. The exact shape of the corrugations has a leading-order effect on the inclination at which the new mode appears and on its wavelength at inception. Compared with the behaviour of film flow on a flat substrate, the presently tested periodic walls are found to delay very significantly, but each one to a different extent, the onset of the primary instability. This delay increases with inclination, and presents a distinct discontinuity when transition from the long- to the short-wave mode takes place.

JFM classification

Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 718 , 10 March 2013 , pp. 304 - 320
Copyright
©2013 Cambridge University Press

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References

Argyriadi, K., Vlachogiannis, M. & Bontozoglou, V. 2006 Experimental study of inclined film flow along periodic corrugations: the effect of wall steepness. Phys. Fluids 18, 012102.CrossRefGoogle Scholar
Balmforth, N. J. & Liu, J. J. 2004 Roll waves in mud. J. Fluid Mech. 519, 33–54.Google Scholar
Bontozoglou, V. & Papapolymerou, G. 1997 Laminar film flow down a wavy incline. Intl J. Multiphase Flow 23, 69–79.Google Scholar
Bontozoglou, V. & Serifi, K. 2008 Falling film flow along steep two-dimensional topography: the effect of inertia. Intl J. Multiphase Flow 34, 734–747.Google Scholar
Brevdo, L., Laure, P., Dias, F. & Bridges, T. J. 1999 Linear pulse structure and signalling in a film flow on an inclined plane. J. Fluid Mech. 396, 37–71.CrossRefGoogle Scholar
Bull, J. L. & Grotberg, J. B. 2003 Surfactant spreading on thin viscous films: Film thickness evolution and periodic wall stretch. Exp. Fluids 34, 1–15.Google Scholar
Chang, H. C. & Demekhin, E. A. 2002 Complex Wave Dynamics on Thin Films. Elsevier.Google Scholar
Choudhari, M. 1993 Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature. Theor. Comput. Fluid Dyn. 4, 101–117.Google Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81, 1131–1198.CrossRefGoogle Scholar
D’Alessio, S. J. D., Pascal, J. P. & Jasmine, H. A. 2009 Instability in gravity-driven flow over uneven surfaces. Phys. Fluids 21, 062105.Google Scholar
Dávalos-Orozco, L. A. 2007 Nonlinear instability of a thin film flowing down a smoothly deformed surface. Phys. Fluids 19, 074103.Google Scholar
Davies, A. G. & Heathershaw, A. D. 1984 Surface-wave propagation over sinusoidally varying topography. J. Fluid Mech. 144, 419–443.Google Scholar
Duprat, C., Ruyer-Quil, C., Kalliadasis, S. & Giorgiutti-Dauphiné, F. 2007 Absolute and convective instabilities of a viscous film flowing down a vertical fibre. Phys. Rev. Lett. 98, 244502.Google Scholar
Gaskell, P. H., Jimack, P. K., Sellier, M., Thompson, H. M. & Wilson, M. C. T. 2004 Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography. J. Fluid Mech. 509, 253–280.CrossRefGoogle Scholar
Georgantaki, A., Vatteville, J., Vlachogiannis, M. & Bontozoglou, V. 2011 Measurements of liquid film flow as a function of fluid properties and channel width: evidence for surface-tension-induced long-range transverse coherence. Phys. Rev. E 84, 026325.Google Scholar
Häcker, T. & Uecker, H. 2009 An integral boundary layer equation for film flow over inclined wavy bottoms. Phys. Fluids 21, 092105.Google Scholar
Heining, C. & Aksel, N. 2009 Bottom reconstruction in thin-film flow over topography: steady solution and linear stability. Phys. Fluids 21, 083605.Google Scholar
Helbig, K., Nasarek, R., Gambaryan-Roisman, T. & Stephan, P. 2009 Effect of longitudinal minigrooves on flow stability and wave characteristics of falling liquid films. J. Heat Transfer 131, 011601.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.Google Scholar
Kalliadasis, S. & Homsy, G. M. 2001 Stability of free-surface thin-film flows over topography. J. Fluid Mech. 448, 387–410.Google Scholar
Liu, J., Paul, J. D. & Gollub, J. P. 1993 Measurements of the primary instabilities of film flows. J. Fluid Mech. 250, 69–101.Google Scholar
Luo, H. & Pozrikidis, C. 2006 Effect of inertia on film flow over oblique and three-dimensional corrugations. Phys. Fluids 18, 078107.Google Scholar
Nguyen, P.-K. & Bontozoglou, V. 2011 Steady solutions of inertial film flow along strongly undulated substrates. Phys. Fluids 23, 052103.Google Scholar
Nguyen, C. C. & Plourde, F. 2011 Wavy wall influence on the hydrodynamic instability of a liquid film flowing along an inclined plane. Intl J. Heat Fluid Flow 32, 698–707.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980.Google Scholar
Oron, A. & Heining, C. 2008 Weighted-residual integral boundary-layer model for the nonlinear dynamics of thin liquid films falling on an undulating vertical wall. Phys. Fluids 20, 082102.Google Scholar
Pollak, T., Haas, A. & Aksel, N. 2011 Side wall effects on the instability of thin gravity-driven films – from long-wave to short-wave instability. Phys. Fluids 23, 094110.Google Scholar
Pozrikidis, C. 1988 The flow of a liquid film along a periodic wall. J. Fluid Mech. 188, 275–300.Google Scholar
Pozrikidis, C. 2003 Effect of surfactants on film flow down a periodic wall. J. Fluid Mech. 496, 105–127.CrossRefGoogle Scholar
Quéré, D. 1999 Fluid coating on a fibre. Annu. Rev. Fluid Mech. 31, 347–384.Google Scholar
Ruban, A. I. 1984 On the generation of Tollmien-Schlichting waves by sound. Fluid Dyn 19, 709–717.Google Scholar
Ruyer-Quil, C. & Manneville, P. 2000 Improved modelling of flows down inclined planes. Eur. Phys. J. B 15, 357–369.Google Scholar
de Santos, J. M., Melli, T. R. & Scriven, L. E. 1991 Mechanics of gas–liquid flow in packed-bed contactors. Annu. Rev. Fluid Mech. 23, 233–260.Google Scholar
Shetty, S. & Cerro, R. L. 1993 Flow of a thin film over a periodic surface. Intl J. Multiphase Flow 19, 1013–1027.Google Scholar
Trifonov, Y. Y. 1998 Viscous liquid film flow over a vertical corrugated surface and waves formation on the film free surface. In Third Intl Conf. on Multiphase Flow. Lyon..Google Scholar
Trifonov, Y. Y. 1999 Viscous liquid film flows over a periodic surface. Intl J. Multiphase Flow 24, 1139–1161.Google Scholar
Trifonov, Y. Y. 2007 Stability of a viscous liquid film flowing down a periodic surface. Intl J. Multiphase Flow 33, 1186–1204.Google Scholar
Tseluiko, D., Blyth, M. G., Papageorgiou, D. T. & Vanden-Broeck, J.-M. 2008 Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Phys. Fluids 20, 042103.Google Scholar
Tseluiko, D. & Blyth, M. 2009 Effect of inertia on electrified film flow over a wavy wall. J. Engng Maths 65, 229–242.CrossRefGoogle Scholar
Valluri, P., Matar, O. K., Hewitt, G. F. & Mendes, M. A. 2005 Thin film flow over structured packings at moderate reynolds numbers. Chem. Engng Sci. 60, 1965–1975.Google Scholar
Vlachogiannis, M. & Bontozoglou, V. 2002 Experiments on laminar film flow along a periodic wall. J. Fluid Mech. 457, 133–156.Google Scholar
Vlachogiannis, M., Samandas, A., Leontidis, V. & Bontozoglou, V. 2010 Effect of channel width on the primary instability of inclined film flow. Phys. Fluids 22, 012106.Google Scholar
Wang, C.-Y. 1981 Liquid film flowing slowly down a wavy incline. AIChE J. 27, 207–212.Google Scholar
Weinstein, S. J. & Ruschak, K. J. 2004 Coating flows. Annu. Rev. Fluid Mech. 36, 29–53.Google Scholar
Wierschem, A. & Aksel, N. 2004 Influence of inertia on eddies created in films creeping over strongly undulated substrates. Phys. Fluids 16, 4566–4574.Google Scholar
Wierschem, A., Bontozoglou, V., Heining, C., Uecker, H. & Aksel, N. 2008 Linear resonance in viscous films on inclined wavy planes. Intl J. Multiphase Flow 34, 580–589.Google Scholar
Wierschem, A., Lepski, C. & Aksel, N. 2005 Effect of long undulated bottoms on thin gravity-driven films. Acta Mech. 179, 41–66.Google Scholar