Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T07:34:33.507Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear forced waves in a vertical rivulet flow

Published online by Cambridge University Press:  01 April 2015

S. V. Alekseenko ,
S. P. Aktershev ,
A. V. Bobylev ,
S. M. Kharlamov  and
D. M. Markovich
S. V. Alekseenko
Affiliation:
Kutateladze Institute of Thermophysics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
S. P. Aktershev*
Affiliation:
Kutateladze Institute of Thermophysics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
A. V. Bobylev
Affiliation:
Kutateladze Institute of Thermophysics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
S. M. Kharlamov
Affiliation:
Kutateladze Institute of Thermophysics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
D. M. Markovich
Affiliation:
Kutateladze Institute of Thermophysics, Novosibirsk, 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This article presents the results of numerical simulations of three-dimensional waves on the surface of a rivulet flowing down a vertical plate. The Kapitza–Shkadov approach is used to describe the wave flow of the rivulet. Various characteristics of linear and nonlinear regular waves in the rivulet are obtained through numerical calculations as a function of the forcing frequency at different Reynolds numbers and contact wetting angles. The results of the simulations are compared with the authors’ previous experimental data. The comparison shows that the applied model adequately describes the shape of the wave surface of a rivulet, although the wave propagation velocity and wavelength are underestimated.

JFM classification

Interfacial Flows (free surface): Contact lines Waves/Free-surface Flows: Solitary waves Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , pp. 350 - 373
Check for updates
Copyright
© 2015 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

Alekseenko, S. V., Antipin, V. A., Bobylev, A. V. & Markovich, D. M. 2007 Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder. Exp. Fluids 43, 197–207.CrossRefGoogle Scholar
Alekseenko, S. V., Antipin, V. A., Guzanov, V. V., Kharlamov, S. M. & Markovich, D. M. 2005 Three-dimensional solitary waves on falling liquid film at low Reynolds numbers. Phys. Fluids 17, 121704.CrossRefGoogle Scholar
Alekseenko, S. V., Bobylev, A. V., Guzanov, V. V., Markovich, D. M. & Kharlamov, S. M. 2010 Regular waves on a vertically flowing rivulets at different wetting angles. Thermophys. Aeromech. 17, 371–384.Google Scholar
Alekseenko, S. V., Markovich, D. M. & Shtork, S. I. 1996 Wave flow of rivulets on the outer surface of an inclined cylinder. Phys. Fluids 8, 3288–3299.CrossRefGoogle Scholar
Alekseenko, S. V., Nakoryakov, V. Ye. & Pokusaev, B. G. 1985 Wave formation on a vertical falling liquid film. AIChE J. 31, 1446–1460.CrossRefGoogle Scholar
Allen, R. F. & Biggin, C. M. 1974 Longitudinal flow of a lenticular liquid filament down an incline plane. Phys. Fluids 17, 287–291.Google Scholar
Argyriadi, K., Serifi, K. & Bontozoglou, V. 2004 Nonlinear dynamics of inclined films under low-frequency forcing. Phys. Fluids 16, 2457–2468.CrossRefGoogle Scholar
Benilov, E. S. 2009 On the stability of shallow rivulets. J. Fluid Mech. 636, 455–474.Google Scholar
Birnir, B., Mertens, K., Putkaradze, V. & Vorobieff, P. 2008 Meandering fluid streams in the presence of flowrate fluctuations. Phys. Rev. Lett. 101, 114501.Google Scholar
Chang, H.-C. & Demekhin, E. A. 2002 Complex Wave Dynamics on Thin Films. Elsevier.Google Scholar
Davis, S. H. 1980 Moving contact lines and rivulet instabilities. Part 1. The static rivulet. J. Fluid Mech. 98, 225–242.CrossRefGoogle Scholar
Demekhin, E. A., Kalaidin, E. N. & Selin, A. S. 2010 Three-dimensional localized coherent structures of surface turbulence. 3. Experiment and model validation. Phys. Fluids 22, 092103.CrossRefGoogle Scholar
Demekhin, E. A. & Shkadov, V. Ya. 1984 Three-dimensional waves in a liquid flowing down a wall. Fluid Dyn. 19, 689–695.Google Scholar
Diez, J., Gonzalez, A. & Kondic, L. 2009 On the breakup of fluid rivulets. Phys. Fluids 21, 082105.Google Scholar
Diez, J., Gonzalez, A. & Kondic, L. 2012 Instability of a transverse liquid rivulet on an inclined plane. Phys. Fluids 24, 032104.Google Scholar
Duffy, B. R. & Moffatt, H. K. 1995 Flow of a viscous trickle on a slowly varying incline. Chem. Engng J. 60, 141–146.Google Scholar
Dussan, E. B. & Davis, S. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 71–95.Google Scholar
Fedotkin, I. M., Mel’nichuk, G. A., Koval’, F. F. & Klimkin, E. V. 1984 Hydrodynamics of rivulet flow on a vertical surface. J. Engng Phys. 46, 9–14.CrossRefGoogle Scholar
Geshev, P. I. & Kuibin, P. A. 1995 Waves on rivulet flow along incline cylinder. In Ninth International Conference on Numerical Methods in Laminar and Turbulent Flow (ed. Taylor, C. & Durbetaki, P.), vol. 9, pp. 996–1006. Pineridge.Google Scholar
Johnson, M. F. G., Schluter, R. A., Miksis, M. J. & Bankoff, S. G. 1999 Experimental study of rivulet formation on an inclined plate by fluorescent imaging. J. Fluid Mech. 394, 339–354.CrossRefGoogle Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. Springer.Google Scholar
Kim, H., Kim, J. & Kang, B. H. 2004 Meandering instability of a rivulet. J. Fluid Mech. 498, 245–256.CrossRefGoogle Scholar
Kondic, L. & Diez, J. 2001 Pattern formation in the flow of thin films down an incline: constant flux configuration. Phys. Fluids 13, 3168–3184.Google Scholar
Kuibin, P. A. 1996 An asymptotic description of the rivulet flow along an inclined cylinder. J. Engng Thermophys. 6, 33–45.Google Scholar
Le Grand-Piteira, N., Daerr, A. & Limat, L. 2006 Meandering rivulets on a plane: a simple balance between inertia and capillarity. Phys. Rev. Lett. 96, 254–503.Google Scholar
Lemaitre, C., de Langre, E. & Hémon, P. 2010 Rainwater rivulets running on a stay cable subject to wind. Eur. J. Mech. (B/Fluids) 29, 251–258.CrossRefGoogle Scholar
Myers, T. G., Liang, H. X. & Wetton, B. 2004 The stability and flow of a rivulet driven by interfa-cial shear and gravity. Intl J. Non-Linear Mech. 39, 1239–1249.Google Scholar
Nakagawa, T. & Scott, J. C. 1984 Stream meanders on a smooth hydrophobic surface. J. Fluid Mech. 149, 89–99.CrossRefGoogle Scholar
Paterson, C., Wilson, S. K. & Duffy, B. R. 2013 Pinning, de-pinning and re-pinning of a slowly varying rivulet. Eur. J. Mech. (B/Fluids) 41, 94–108.CrossRefGoogle Scholar
Perazzo, C. A. & Gratton, J. 2004 Navier–Stokes solutions for parallel flow in rivulets on an in-clined plane. J. Fluid Mech. 507, 367–379.Google Scholar
Purvis, J. A., Mistry, R. D., Markides, C. N. & Matar, O. K. 2013 An experimental investigation of fingering instabilities and growth dynamics in inclined counter-current gas–liquid channel flow. Phys. Fluids 25, 122104.CrossRefGoogle Scholar
Rayleigh, L. 1878 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Robertson, A. C., Taylor, I. J., Wilson, S. K., Duffy, B. R. & Sullivan, J. M. 2010 Numerical simulation of rivulet evolution on a horizontal cable subject to an external aerodynamic field. J. Fluids Struct. 26, 50–73.CrossRefGoogle Scholar
Saber, H. H. & El-Genk, M. S. 2004 On the breakup of a thin liquid film subject to interfacial shear. J. Fluid Mech. 500, 113–133.CrossRefGoogle Scholar
Schmuki, P. & Laso, M. 1990 On the stability of rivulet flow. J. Fluid Mech. 215, 125–143.Google Scholar
Sullivan, J. M., Paterson, C., Wilson, S. K. & Duffy, B. R. 2012 A thin rivulet or ridge subject to a uniform transverse shear stress at its free surface due to an external airflow. Phys. Fluids 24, 082109.Google Scholar
Tanasijczuk, A. J., Perazzo, C. A. & Gratton, J. 2010 Navier–Stokes solutions for steady parallel-sided pendent rivulets. Eur. J. Mech. (B/Fluids) 29, 465–471.CrossRefGoogle Scholar
Towell, G. D. & Rothfeld, L. B. 1966 Hydrodynamics of rivulet flow. AIChE J. 12, 972–980.CrossRefGoogle Scholar
Weiland, R. H. & Davis, S. H. 1981 Moving contact lines and rivulet instabilities. Part 2. Long waves on flat rivulets. J. Fluid Mech. 107, 261–280.Google Scholar
Wilson, S. K. & Duffy, B. R. 1998 On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow. Phys. Fluids 10, 13–22.CrossRefGoogle Scholar
Wilson, S. K. & Duffy, B. R. 2005 Unidirectional flow of a thin rivulet on a vertical substrate subject to a prescribed uniform shear stress. At its free surface. Phys. Fluids 17, 108105.CrossRefGoogle Scholar
Wilson, S. K., Sullivan, J. M. & Duffy, B. R. 2011 The energetics of the breakup of a sheet and of a rivulet on a vertical substrate in the presence of a uniform surface shear stress. J. Fluid Mech. 674, 281–306.CrossRefGoogle Scholar
Ye, Y. & Chang, H.-C. 1999 A spectral theory for fingering on a prewetted plane. Phys. Fluids 11, 2494–2515.CrossRefGoogle Scholar
Young, G. W. & Davis, S. H. 1987 Rivulet instabilities. J. Fluid Mech. 176, 1–31.CrossRefGoogle Scholar