Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T08:55:10.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional dynamics of falling films in the presence of insoluble surfactants

Published online by Cambridge University Press:  13 November 2020

Assen Batchvarov ,
Lyes Kahouadji Open the ORCID record for Lyes Kahouadji [Opens in a new window] ,
Cristian R. Constante-Amores ,
Gabriel Farah Norões Gonçalves ,
Seungwon Shin Open the ORCID record for Seungwon Shin [Opens in a new window] ,
Jalel Chergui Open the ORCID record for Jalel Chergui [Opens in a new window] ,
Damir Juric Open the ORCID record for Damir Juric [Opens in a new window] ,
Richard V. Craster Open the ORCID record for Richard V. Craster [Opens in a new window]  and
Omar K. Matar Open the ORCID record for Omar K. Matar [Opens in a new window]
Assen Batchvarov
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
Lyes Kahouadji*
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
Cristian R. Constante-Amores
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
Gabriel Farah Norões Gonçalves
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
Seungwon Shin
Affiliation:
Department of Mechanical and System Design Engineering, Hongik University, Seoul121-791, Republic of Korea
Jalel Chergui
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), CNRS, Université Paris Saclay, Bât. 507, Rue du Belvédère, Campus Universitaire, 91405Orsay, France
Damir Juric
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), CNRS, Université Paris Saclay, Bât. 507, Rue du Belvédère, Campus Universitaire, 91405Orsay, France
Richard V. Craster
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
Omar K. Matar
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, LondonSW7 2AZ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the effect of insoluble surfactants on the wave dynamics of vertically falling liquid films. We use three-dimensional numerical simulations and employ a hybrid interface-tracking/level-set method, taking into account Marangoni stresses induced by gradients of interfacial surfactant concentration. Our numerical predictions for the evolution of the surfactant-free, three-dimensional wave topology are validated against the experimental work of Park & Nosoko (AIChE J., vol. 49, 2003, pp. 2715–2727). The addition of surfactants is found to influence significantly the development of horseshoe-shaped waves. At low Marangoni numbers, we show that the wave fronts exhibit spanwise oscillations before eventually acquiring a quasi-two-dimensional shape. In addition, the presence of Marangoni stresses is found to suppress the peaks of the travelling waves and preceding capillary wave structures. At high Marangoni numbers, a near-complete rigidification of the interface is observed.

JFM classification

Waves/Free-surface Flows: Capillary waves Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A16
Check for updates
Copyright
© The Author(s), 2020. Published by 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

REFERENCES

Alekseenko, S. V., Nokariakov, V. E., Pokusaev, B. G. & Fukano, T. 1994 Wave Flow of Liquid Films. Begell House.Google Scholar
Benjamin, T. B. 1964 Effects of surface contamination on wave formation in falling liquid films (stabilizing effect of surface active agents on wave formation in contaminated falling liquid film). Arch. Mech. 16 (3), 615–626.Google Scholar
Bhat, F. A. & Samanta, A. 2018 Linear stability of a contaminated fluid flow down a slippery inclined plane. Phys. Rev. E 98 (3), 1–19.CrossRefGoogle Scholar
Blyth, M. G. & Pozrikidis, C. 2004 Effect of surfactant on the stability of film flow down an inclined plane. J. Fluid Mech. 521, 241–250.CrossRefGoogle Scholar
Bobylev, A. V., Guzanov, V. V., Kvon, A. Z. & Kharlamov, S. M. 2019 Influence of soluble surfactant on wave evolution on falling liquid films. J. Phys.: Conf. Ser. 1382, 012073.Google Scholar
Chang, H. C. 1994 Wave evolution on a falling film. Annu. Rev. Fluid. Mech. 26 (1), 103–136.CrossRefGoogle Scholar
Chang, H. C., Cheng, M., Demekhin, E. A. & Kopelevich, D. I. 1994 Secondary and tertiary excitation of three-dimensional patterns on a falling film. J. Fluid Mech. 270, 251–276.CrossRefGoogle Scholar
Chang, H. C., Demekhin, E. A., Kalaidin, E. & Ye, Y. 1996 Coarsening dynamics of falling-film solitary waves. Phys. Rev. E 54 (2), 1467–1477.CrossRefGoogle ScholarPubMed
Cheng, M. & Chang, H. C. 1995 Competition between subharmonic and sideband secondary instabilities on a falling film. Phys. Fluids 7 (1), 34–54.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22 (104), 745–745.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131–1198.CrossRefGoogle Scholar
Dietze, G. F., Rohlfs, W., Nährich, K., Kneer, R. & Scheid, B. 2014 Three-dimensional flow structures in laminar falling liquid films. J. Fluid Mech. 743, 75–123.CrossRefGoogle Scholar
Fallest, D. W., Lichtenberger, A. M., Fox, C. J. & Daniels, K. E. 2010 Fluorescent visualization of a spreading surfactant. New J. Phys. 12 (7), 073029.CrossRefGoogle Scholar
Georgantaki, A., Vlachogiannis, M. & Bontozoglou, V. 2012 The effect of soluble surfactants on liquid film flow. J. Phys.: Conf. Ser. 395, 012165.Google Scholar
Georgantaki, A., Vlachogiannis, M. & Bontozoglou, V. 2016 Measurements of the stabilisation of liquid film flow by the soluble surfactant sodium dodecyl sulfate (SDS). Intl J. Multiphase Flow 86, 28–34.CrossRefGoogle Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (12), 2182–2189.CrossRefGoogle Scholar
Hu, T., Fu, Q. & Yang, L. 2020 Falling film with insoluble surfactants: effects of surface elasticity and surface viscosities. J. Fluid Mech. 889, 1–19.CrossRefGoogle Scholar
Joo, S. W. & Davis, S. H. 1992 Instabilities of three-dimensional viscous falling films. J. Fluid Mech. 242 (529), 529–547.CrossRefGoogle Scholar
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2012 Falling Liquid Films. Springer.CrossRefGoogle Scholar
Kapitza, P. L. 1948 Wave flow of thin layers of viscous liquids. II. Flow in a contact with a gase flux and heat transfer. Zh. Eksp. Teor. Fiz. 18, 3–28.Google Scholar
Karapetsas, G. & Bontozoglou, V. 2013 The primary instability of falling films in the presence of soluble surfactants. J. Fluid Mech. 729, 123–150.CrossRefGoogle Scholar
Karapetsas, G. & Bontozoglou, V. 2014 The role of surfactants on the mechanism of the long-wave instability in liquid film flows. J. Fluid Mech. 741, 139–155.CrossRefGoogle Scholar
Liu, J., Paul, J. D. & Gollub, J. P. 1993 Measurements of the primary instabilities of film flows. J. Fluid Mech. 250, 69–101.CrossRefGoogle Scholar
Liu, J., Schneider, J. B. & Gollub, J. P. 1995 Three-dimensional instabilities of film flows. Phys. Fluids 7 (1), 55–67.CrossRefGoogle Scholar
Nusselt, W. 1923 Der Wärmeaustausch am Berieselungskühler. Z. Ver. Dtsch. Ing. 67, 206–210.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931–980.CrossRefGoogle Scholar
Park, C. D. & Nosoko, T. 2003 Three-dimensional wave dynamics on a falling film and associated mass transfer. AIChE J. 49 (11), 2715–2727.CrossRefGoogle Scholar
Pereira, A. & Kalliadasis, S. 2008 Dynamics of a falling film with solutal Marangoni effect. Phys. Rev. E 78 (3), 1–19.CrossRefGoogle ScholarPubMed
Scheid, B., Ruyer-Quil, C. & Manneville, P. 2006 Wave patterns in film flows: modelling and three-dimensional waves. J. Fluid Mech. 562, 183–222.CrossRefGoogle Scholar
Shin, S., Chergui, J. & Juric, D. 2017 A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. J. Mech. Sci. Technol. 31 (4), 1739–1751.CrossRefGoogle Scholar
Shin, S., Chergui, J., Juric, D., Kahouadji, L., Matar, O. K. & Craster, R. V. 2018 A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant. J. Comput. Phys. 359, 409–435.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2002 Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity. J. Comput. Phys. 180 (2), 427–470.CrossRefGoogle Scholar
Shin, S. & Juric, D. 2009 A hybrid interface method for three-dimensional multiphase flows based on front tracking and level set techniques. Intl J. Numer. Meth. Fluids 60, 753–778.CrossRefGoogle Scholar
Shkadov, V. Ya., Velarde, M. G. & Shkadova, V. P. 2004 Falling films and the Marangoni effect. Phys. Rev. E 69 (5), 15.CrossRefGoogle ScholarPubMed
Shu, C. W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (2), 439–471.CrossRefGoogle Scholar
Strickland, S. L., Shearer, M. & Daniels, K. E. 2015 Spatiotemporal measurement of surfactant distribution on gravity–capillary waves. J. Fluid Mech. 777, 523–543.CrossRefGoogle Scholar
Tailby, S. R. & Portalski, S. 1962 The determination of the wavelength on a vertical film of liquid flowing down a hydrodynamically smooth plate. Trans. Inst. Chem. Engrs 40, 114–122.Google Scholar
Wang, Y. X. & Wen, J. M. 2006 Gear method for solving differential equations of Gear systems. J. Phys.: Conf. Ser. 48, 143–148.Google Scholar
Wei, H.-H. 2005 On the flow-induced Marangoni instability due to the presence of surfactant. J. Fluid Mech. 544, 173.CrossRefGoogle Scholar
Whitaker, S. 1964 Effect of surface active agents on the stability of falling liquid films. Ind. Engng Chem. Fundam. 3 (2), 132–142.CrossRefGoogle Scholar