Skip to main content

Phase diagram for the onset of circulating waves and flow reversal in inclined falling films

  • Wilko Rohlfs (a1) and Benoit Scheid (a2)

The onset of circulating waves, i.e. waves with a circulating eddy in the main wave hump, and the onset of flow reversal, i.e. a vortex in the first capillary minimum, in inclined falling films is investigated as a function of the Reynolds number and inclination number using the weighted integral boundary layer (WIBL) model and direct numerical simulations (DNS). Analytical criteria for the onset of circulating waves and flow reversal based on the wave celerity, the average film thickness and the maximum and minimum film thickness have been approximated using self-similar parabolic velocity profiles. This approximation has been validated by second-order WIBL and DNS simulations. It is shown that the onset of circulating waves in the phase diagram for homoclinic solutions (waves of infinite wavelength) is strongly dependent on the inclination, but independent of the streamwise viscous dissipation effect. On the contrary, the onset of flow reversal shows a clear dependence on the viscous dissipation. Furthermore, simulation results for limit cycles (finite wavelength) reveal a strong increase of the corresponding critical Reynolds number with the excitation frequency. Additionally, a critical ratio between the maximum and substrate film thickness (value of approximately 2.5) was found for the onset of circulating waves, which is independent of wavelength, inclination, viscous dissipation and Reynolds number.

Corresponding author
Email address for correspondence:
Hide All
Albert, C., Marschall, H. & Bothe, D. 2014 Direct numerical simulation of interfacial mass transfer into falling films. Intl J. Heat Mass Transfer 69, 343357.
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 (2–3), 197207.
Alekseenko, S. V., Nakoryakov, V. E. & Pokusaev, B. G. 1994 Wave Flow of Liquid Films. Begell House.
Binz, M., Rohlfs, W. & Kneer, R. 2014 Direct numerical simulations of a thin liquid film coating an axially oscillating cylindrical surface. Fluid Dyn. Res. 46, 041402.
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335354.
Brauner, N. & Maron, D. M. 1983 Modeling of wavy flow in inclined thin films. Chem. Engng Sci. 38 (5), 775788.
Chakraborty, S., Nguyen, P.-K., Ruyer-Quil, C. & Bontozoglou, V. 2014 Extreme solitary waves on falling liquid films. J. Fluid Mech. 745, 564591.
Chang, H.-C. & Demekhin, E. A. 2002 Complex Wave Dynamics on Thin Films (ed. Möbius, D. & Miller, R.). Elsevier.
Davies, J. T. 1960 The importance of surfaces in chemical engineering. Trans. Inst. Chem. Engrs 38, 289293.
Dietze, G. F.2010 Flow separation in falling liquid films. PhD thesis, RWTH Aachen.
Dietze, G. F., Al-Sibai, F. & Kneer, R. 2009 Experimental study of flow separation in laminar falling liquid films. J. Fluid Mech. 637, 73104.
Dietze, G. F., Leefken, A. & Kneer, R. 2008 Investigation of the backflow phenomenon in falling liquid films. J. Fluid Mech. 595, 435459.
Dietze, G. F., Rohlfs, W., Nährich, K., Kneer, R. & Scheid, B. 2014 Three-dimensional flow structures in laminar falling films. J. Fluid Mech. 743, 75123.
Doedel, E. J.2008 AUTO07P continuation and bifurcation software for ordinary differential equations. Montreal Concordia University.
Doro, E. O. & Aidun, C. K. 2013 Interfacial waves and the dynamics of back flow in falling liquid films. J. Fluid Mech. 726, 261284.
Gao, D., Morley, N. B. & Dhir, V. 2003 Numerical simulation of wavy falling film flow using VOF method. J. Comput. Phys. 192, 624642.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201225.
Hu, J., Yang, X., Yu, J. & Dai, G. 2014 Numerical simulation of carbon dioxide ( ) absorption and interfacial mass transfer across vertically wavy falling film. Chem. Engng Sci. 116, 243253.
Islam, M. A.2009 Wave dynamics and simultaneous heat and mass transfer of falling liquid film. PhD thesis, Graduate School of Science and Engineering, Saga University, Japan.
Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College, University of London.
Kalliadasis, S., Ruyer-Quil, C., Scheid, B. & Velarde, M. G. 2013 Falling Liquid Films. Springer.
Kouhikamali, R., Abadi, S. M. A. N. R. & Hassani, M. 2014 Numerical investigation of falling film evaporation of multi-effect desalination plant. Appl. Therm. Engng 70 (1), 477485.
Liu, J. & Gollub, J. P. 1994 Solitary wave dynamics of film flows. Phys. Fluids 6 (5), 17021712.
Malamataris, N. A. & Balakotaiah, V. 2008 Flow structure underneath the large amplitude waves of a vertically falling film. AIChE J. 54 (7), 17251740.
Malamataris, N. A., Vlachogiannis, M. & Bontozoglou, V. 2002 Solitary waves on inclined films: flow structure and binary interactions. Phys. Fluids 14 (3), 10821094.
Maron, D. M., Brauner, N. & Hewitt, G. F. 1989 Flow patterns in wavy thin films: numerical simulation. Intl Commun. Heat Mass Transfer 16 (5), 655666.
Miyara, A. 2000 Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall. Intl J. Therm. Sci. 39 (9–11), 10151027.
Ooshida, T. 1999 Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Phys. Fluids 11 (11), 32473269.
Portalski, S. 1964 Eddy formation in film flow down a vertical plate. Ind. Engng Chem. Fundam. 3 (1), 4953.
Roberts, R. M. & Chang, H.-C. 2000 Wave-enhanced interfacial transfer. Chem. Engng Sci. 55 (6), 11271141.
Rohlfs, W., Binz, M. & Kneer, R. 2014 On the stabilizing effect of a liquid film on a cylindrical core by oscillatory motions. Phys. Fluids 26, 022101.
Rusche, H.2002 Computational fluid dynamics of dispersed two-phase flows at high phase fractions. PhD thesis, Imperial Collage, University of London.
Ruyer-Quil, C. & Manneville, P. 2000 Improved modeling of flows down inclined planes. Eur. Phys. J. B 15, 357369.
Ruyer-Quil, C. & Manneville, P. 2005 On the speed of solitary waves running down a vertical wall. J. Fluid Mech. 531, 181190.
Scheid, B., Ruyer-Quil, C., Thiele, U., Kabov, P. A., Legros, J. C. & Colinet, P. 2005 Validity domain of the Benney equation including the Marangoni effect for closed and open flows. J. Fluid Mech. 562, 183222.
Ubbink, O.1997 Numerical prediction of two fluid systems with sharp interfaces. PhD thesis, Imperial College, University of London.
Wasden, F. K. & Dukler, A. E. 1989 Insights into the hydrodynamics of free falling wavy films. AIChE J. 35 (2), 187195.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed