- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Experimental investigations of liquid falling films flowing under an inclined planar substrate

Alexandros Charogiannis1, Fabian Denner2,3, Berend G. M. van Wachem3, Serafim Kalliadasis4, Benoit Scheid5, and Christos N. Markides1,*

  • 1Clean Energy Processes (CEP) Laboratory, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 2Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 3Chair of Mechanical Process Engineering, Otto-von-Guericke-Universitt Magdeburg Universittsplatz 2, 39106 Magdeburg, Germany
  • 4Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
  • 5TIPs, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50 1050 Bruxelles, Belgium

  • *Corresponding author: c.markides@imperial.ac.uk
PDF

Phys. Rev. Fluids 3, 114002 – Published 9 November, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.114002

Abstract

We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles (β=−15∘, −30∘, and −45∘, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of Ka=13.1 and 330), and flow Reynolds numbers covering the range Re=0.6–193. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about 40mm symmetrically on either side the centerline of the film span (80mm in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number Ka(=13.1) flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid Ka(=330) flows, rivulets were observed typically above Re≈30, depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with increasing Re, reaching a maximum that shifted to higher Re at larger inclinations. Furthermore, in flows that displayed pronounced rivulet formation [i.e., large (negative) β and higher Re], the local film-height standard deviation in regions corresponding to the rivulet crests and troughs was reduced compared to the film-height standard deviation calculated over the entire examined film region. The mean rivulet wavelength also increased at larger inclinations, peaking at 26 mm when Ka=330. Based on our experimental results and theoretical arguments, we hypothesize that the formation of rivulets can be attributed, at small β, to a secondary Rayleigh-Taylor instability mechanism that destabilizes the suspended two-dimensional wavefronts, and at larger β, to the primary Rayleigh-Taylor instability mechanism of a flat film coating the underside of the inclined plate.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (75)

  1. P. L. Kapitza, Wave flow of thin layers of a viscous fluid: I. Free flow, J. Exp. Theor. Phys. 18, 3 (1948).
  2. P. L. Kapitza and S. P. Kapitza, Wave flow of thin layers of a viscous fluid: III. Experimental study of undulatory flow conditions, J. Exp. Theor. Phys. 19, 105 (1949).
  3. A. Charogiannis, J. S. An, and C. N. Markides, A simultaneous planar laser-induced fluorescence, particle image velocimetry, and particle tracking velocimetry technique for the investigation of thin liquid-film flows, Exp. Therm. Fluid Sci. 68, 516 (2015).
  4. A. Charogiannis, F. Denner, B. G. M. van Wachem, S. Kalliadasis, and C. N. Markides, Detailed hydrodynamic characterization of harmonically excited falling-film flows: A combined experimental and computational study, Phys. Rev. Fluids 2, 014002 (2017).
  5. F. Denner, A. Charogiannis, M. Pradas, C. N. Markides, B. G. M. van Wachem, and S. Kalliadasis, Solitary waves on falling liquid films in the inertia-dominated regime, J. Fluid Mech. 837, 491 (2018).
  6. A. Charogiannis, F. Denner, B. G. M. van Wachem, S. Kalliadasis, and C. N. Markides, Statistical characteristics of falling-film flows: A synergistic approach at the crossroads of direct numerical simulations and experiments, Phys. Rev. Fluids 2, 124002 (2017).
  7. A. Cherdantsev, D. B. Hann, and B. J. Azzopardi, Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: Three-dimensional wavy structure and its relation to liquid entrainment, Int. J. Multiphase Flow 67, 52 (2014).
  8. I. Zadrazil, O. K. Matar, and C. N. Markides, An experimental characterization of downwards gas-liquid annular flow by laser-induced fluorescence: Flow regimes and film statistics, Int. J. Multiphase Flow 60, 87 (2014).
  9. I. Zadrazil and C. N. Markides, An experimental characterization of liquid films in downwards co-current gas-liquid annular flow by particle image and tracking velocimetry, Int. J. Multiphase Flow 67, 42 (2014).
  10. G. Karimi and M. Kawaji, Flow characteristics and circulatory motion in wavy falling films with and without counter-current gas flow, Int. J. Multiphase Flow 25, 1305 (1999).
  11. A. Charogiannis and C. N. Markides, Application of planar laser-induced fluorescence for the investigation of interfacial waves in liquid-films flowing under inverted substrates, Interfacial Phenom. Heat Transf. 4, 235 (2016).
  12. C. S. Yih, Stability of liquid flow down an inclined plane, Phys. Fluids 6, 321 (1963).
  13. E. J. Hinch, A note on the mechanism of the instability at the interface between two shearing fluids, J. Fluid Mech. 144, 463 (1984).
  14. R. E. Kelly, D. A. Goussis, S. P. Lin, and F. K. Hsu, The mechanism for surface wave instability in film flow down an inclined plane, Phys. Fluids 1, 819 (1989).
  15. M. K. Smith, The mechanism for the long-wave instability in thin liquid films, J. Fluid Mech. 217, 469 (1990).
  16. S. Kalliadasis, C. Ruyer-Quil, B. Scheid, and M. G. Velarde, Falling Liquid Films, Applied Mathematical Sciences Vol. 176 (Springer Verlag, Berlin, 2012).
  17. J. Liu, J. D. Paul, and J. P. Gollub, Measurements of the primary instabilities of film flows, J. Fluid Mech. 250, 69 (1993).
  18. J. Liu and J. P. Gollub, Onset of Spatially Chaotic Waves on Flowing Films, Phys. Rev. Lett. 70, 2289 (1993).
  19. J. Liu and J. P. Gollub, Solitary wave dynamics of film flows, Phys. Fluids 6, 1702 (1994).
  20. J. Liu, J. B. Schneder, and J. P. Gollub, Three-dimensional instabilities of film flows, Phys. Fluids 7, 55 (1995).
  21. T. Nosoko, P. N. Yoshimura, T. Nagata, and K. Oyakawa, Characteristics of two-dimensional waves on falling liquid films, Chem. Eng. Sci. 51, 725 (1996).
  22. T. Nosoko and A. Miyara, The evolution and subsequent dynamics of waves on a vertically falling liquid film, Phys. Fluids 16, 1118 (2004).
  23. B. Ramaswamy, S. Chippada, and S. W. Joo, A full-scale numerical study of interfacial instabilities in thin-film flows, J. Fluid Mech. 325, 163 (1996).
  24. K. Argyriadi, K. Serifi, and V. Bontozoglou, Nonlinear dynamics of inclined films under low-frequency forcing, Phys. Fluids 16, 2457 (2004).
  25. B. Scheid, C. Ruyer-Quil, and P. Manneville, Wave patterns in film flows: Modelling and three-dimensional waves, J. Fluid Mech. 562, 183 (2006).
  26. N. Kofman, S. Mergui, and C. Ruyer-Quil, Three-dimensional instabilities of quasi-solitary waves in falling liquid films, J. Fluid Mech. 757, 854 (2014).
  27. M. Rietz, R. Rohlfs, W. adn Kneer, and B. Scheid, Experimental investigation of thermal structures in regular three-dimensional falling films, Eur. Phys. J.-Spec. Top. 224, 355 (2015).
  28. S. V. Alekseenko, V. A. Antipin, V. V. Guzanov, S. M. Kharlamov, and D. M. Markovich, Three-dimensional solitary waves on falling liquid film at low Reynolds numbers, Phys. Fluids 17, 121704 (2005).
  29. E. A. Demekhin, E. N. Kalaidin, S. Kalliadasis, and S. Yu. Vlaskin, Three-dimensional localized coherent structures of surface turbulence. I. Scenarios of two-dimensional–three-dimensional transition, Phys. Fluids 19, 114103 (2007).
  30. E. A. Demekhin, E. N. Kalaidin, S. Kalliadasis, and S. Y. Vlaskin, Three-dimensional localized coherent structures of surface turbulence. II. Λ solitons, Phys. Fluids 19, 114104 (2007).
  31. E. A. Demekhin, E. N. Kalaidin, and A. S. Selin, Three-dimensional localized coherent structures of surface turbulence. III. Experiment and model validation, Phys. Fluids 22, 092103 (2010).
  32. E. A. Demekhin, E. N. Kalaidin, S. Kalliadasis, and S. Y. Vlaskin, Three-dimensional localized coherent structures of surface turbulence: Model validation with experiments and further computations, Phys. Rev. E 82, 036322 (2010).
  33. P. N. Yoshimura, T. Nosoko, and T. Nagata, Enhancement of mass transfer into a falling laminar liquid film by two-dimensional surface waves: Some experimental observations and modelling, Chem. Eng. Sci. 51, 1231 (1996).
  34. C. D. Park and T. Nosoko, Three-dimensional wave dynamics on a falling film and associated mass transfer, AIChE 49, 2715 (2003).
  35. P. Adomeit and U. Renz, Hydrodynamics of three-dimensional waves in laminar falling films, Int. J. Multiphase Flow 26, 1183 (2000).
  36. S. V. Alekseenko, V. V. Guzanov, D. M. Markovich, and S. M. Kharlamov, Specific features of a transition from the regular two-dimensional to three-dimensional waves on falling liquid films, Tech. Phys. Lett. 38, 739 (2012).
  37. S. V. Alekseenko, A. V. Bobylev, V. V. Guzanov, D. M. Markovich, and S. M. Kharlamov, Formation of rivulets in isothermal liquid film flow during transition to a three-dimensional wave regime, Tech. Phys. Lett. 40, 1031 (2014).
  38. S. M. Kharlamov, V. V. Guzanov, A. V. Bobylev, S. V. Alekseenko, and D. M. Markovich, The transition from two-dimensional to three-dimensional waves in falling liquid films: Wave patterns and transverse redistribution of local flow rates, Phys. Fluids 27, 114106 (2015).
  39. E. A. Chinnov and O. A. Kabov, Marangoni effect on wave structure in liquid films, Microgravity Sci. Technol. 19, 18 (2007).
  40. V. V. Lel, A. Kellerman, G. Dietze, R. Kneer, and A. N. Pavlenko, Investigations of the Marangoni effect on the regular structures in heated wavy liquid films, Exp. Fluids 44, 341 (2008).
  41. E. A. Chinnov and S. S. Abdurakipov, Thermal entry length in falling liquid films at high Reynolds numbers, Int. J. Heat Mass Transfer 56, 775 (2013).
  42. C. N. Markides, R. Mathie, and A. Charogiannis, An experimental characterization of spatiotemporally resolved heat transfer in thin liquid-film flows falling over an inclined heated foil, Int. J. Heat Mass Transfer 93, 872 (2016).
  43. S. W. Joo, S. H. Davis, and S. G. Bankoff, A mechanism for rivulet formation in heated falling films, J. Fluid Mech. 321, 279 (1996).
  44. B. Scheid, S. Kalliadasis, C. Ruyer-Quil, and P. Colinet, Spontaneous channeling of solitary pulses in heated-film flows, Europhys. Lett. 84, 64002 (2008).
  45. B. Scheid, S. Kalliadasis, C. Ruyer-Quil, and P. Colinet, Interaction of three-dimensional hydrodynamic and thermocapillary instabilities in film flows, Phys. Rev. E 78, 066311 (2008).
  46. D. A. Rothrock, Study of flows down the underside of an inclined plane, Ph.D. thesis, University of Cambridge, Cambridge, UK, 1968 (unpublished).
  47. F. Zhang, Z. Zhang, and J. Geng, Study on shrinkage characteristics of heated falling films, AIChE 51, 2899 (2005).
  48. F. Zhang, X. Zhao, J. Geng, Y.-T. Wu, and Z. Zhang, A new insight into Marangoni effect in non-isothermal falling liquid films, Exp. Therm Fluid Sci. 31, 361 (2007).
  49. F. Zhang, J. Peng, J. Geng, Z.-X. Wang, and Z.-B. Zhang, Thermal imaging study on the surface wave of heated falling liquid films, Exp. Therm Fluid Sci. 33, 424 (2009).
  50. A. Indeikina, I. Veretennikov, and H.-C. Chang, Drop fall-off from pendant rivulets, J. Fluid Mech. 338, 173 (1997).
  51. S. V. Alekseenko and S. I. Markovich, D. M. Shtork, Wave flow of rivulets on the outer surface of an inclined cylinder, Phys. Fluids 8, 3288 (1996).
  52. S. V. Alekseenko, V. A. Antipin, A. V. Bobylev, and D. M. Markovich, Application of PIV to velocity measurements in a liquid film flowing down an inclined cylinder, Exp. Fluids 43, 197 (2007).
  53. P.-T. Brun, A. Damiano, P. Rieu, G. Balestra, and F. Gallaire, Rayleigh-Taylor instability under an inclined plane, Phys. Fluids 27, 084107 (2015).
  54. B. Scheid, N. Kofman, and W. Rohlfs, Critical inclination for absolute/convective instability transition in inverted falling films, Phys. Fluids 28, 044107 (2016).
  55. N. Kofman, W. Rohlfs, F. Gallaire, B. Scheid, and C. Ruyer-Quil, Prediction of two-dimensional dripping onset of a liquid film under inclined plane, Int. J. Multiphase Flow 104, 286 (2018).
  56. W. Rohlfs, P. Pischke, and B. Scheid, Hydrodynamic waves in films flowing under an inclined plane, Phys. Rev. Fluids 2, 044003 (2017).
  57. W. Rohlfs and B. Scheid, Phase diagram for the onset of circulating waves and flow reversal in inclined falling films, J. Fluid Mech. 763, 322 (2015).
  58. T.-S. Lin and L. Kondic, Thin films flowing down inverted substrates: Two dimensional flow, Phys. Fluids 22, 052105 (2010).
  59. T.-S. Lin, L. Kondic, and A. Filippov, Thin films flowing down inverted substrates: Three dimensional flow, Phys. Fluids 24, 022105 (2012).
  60. H. E. Huppert, Flow and instability of a viscous current down a slope, Nature (London) 300, 427 (1982).
  61. S. M. Troian, E. Herbolzheimer, S. A. Safran, and J. F. Joanny, Fingering instabilities of driven spreading films, Europhys. Lett. 10, 25 (1989).
  62. M. A. Spaid and G. M. Homsy, Stability of Newtonian and viscoelastic dynamic contact lines, Phys. Fluids 8, 460 (1996).
  63. S. Kalliadasis, Nonlinear instability of a contact line driven by gravity, J. Fluid Mech. 413, 355 (2000).
  64. M. Rietz, B. Scheid, F. Gallaire, N. Kofman, R. Kneer, and W. Rohlfs, Dynamics of falling films on the outside of a vertical rotating cylinder: Waves, rivulets and dripping transitions, J. Fluid Mech. 832, 189 (2017).
  65. R. Mathie, H. Nakamura, and C. N Markides, Heat transfer augmentation in unsteady conjugate thermal systems, part II: Applications, Int. J. Heat Mass Transfer 56, 819 (2013).
  66. W. Nusselt, Die Oberflächenkondensation des wasserdampfes, Zetrschr. Ver. Deutch. Ing. 60, 541 (1916).
  67. M. Pradas, D. Tseluiko, and S. Kalliadasis, Rigorous coherent-structure theory for falling liquid films: Viscous dispersion effects on bound-state formation and self-organization, Phys. Fluids 23, 044104 (2011).
  68. G. Balestra, N. Kofman, P.-T. Brun, B. Scheid, and F. Gallaire, Three-dimensional Rayleigh-Taylor instability under a unidirectional curved substrate, J. Fluid Mech. 837, 19 (2018).
  69. A. Georgantaki, J. Vatteville, M. Vlachogiannis, and V. Bontozoglou, 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 (2011).
  70. V. Pollak, A. Haas, and N. Aksel, Side wall effects on the instability of thin gravity-driven films: From long-wave to short-wave instability, Phys. Fluids 23, 094110 (2011).
  71. T. D. Karapantsios, S. V. Paras, and A. J. Karabelas, Statistical characteristics of free falling films at high Reynolds numbers, Int. J. Multiphase Flow 15, 1 (1989).
  72. K. Moran, J. Inumaru, and M. Kawaji, Instantaneous hydrodynamics of a laminar wavy liquid film, Int. J. Multiph. Flow 28, 731 (2002).
  73. D. H. Sharp, An overview of Rayleigh-Taylor instability, Phys. D. (Amsterdam, Neth.) 12, 3 (1984).
  74. M. Fermigier, L. Limat, J. E. Wesfreid, P. Boudinet, and C. Quilliet, Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer, J. Fluid Mech. 236, 349 (1992).
  75. J. R. Lister, R. C. Kerr, N. J. Russell, and A. Crosby, Rayleigh-Taylor instability of an inclined buoyant viscous cylinder, J. Fluid Mech. 671, 313 (2011).

Outline

Information

Phys. Rev. Fluids 3, 114002– Published 9 November, 2018
  • Received 26 February 2018
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation