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Experimental investigation into three-dimensional wavy liquid films under the influence of electrostatic forces


Three-dimensional interfacial waves that develop on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic forces applied to a falling film of dielectric liquid on its three-dimensional nonlinear wave dynamics. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were taken, and the complex wave topology was characterized through photography. The experiments show a complex interaction between the electric field and the hydrodynamics of the falling film, whereby electrostatic forces were found to both increase and decrease wave peak height in different regions of the wave. Additionally, an electrically induced breakup of the three-dimensional wave fronts, which leads to a locally doubled frequency in streamwise direction, is found. The ability to influence the wave topology demonstrated here opens the possibility to optimize heat transfer processes in falling liquid films.

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  1. Micro-Epsilon optoNCDT 2451 with an optical probe IFS 2401-3, allowing for a measurement range of 3 mm and an axial resolution of 0.12  μm

  2. Note, that all film thickness plots depict raw data, without interpolation or removing deviating signals. Therefore, some points deviate significantly from the wave shape. In most cases, the outliers give a too high value of the local film thickness as the confocal chromatic imaging system detects an earlier peak. In order to reduce the number of these outliers, the detection threshold of the device can be increased, but only at the expense of loosing parts of the wave profile, especially in the capillary wave region.


f s :

Electrically induced surface force

g :


n :

Coordinate normal to free surface

q :

Volumetric flow rate per unit width

t :

Coordinate tangential to free surface

t :


u :

Phase velocity

x, y, z :

Streamwise, crosswise and spanwise coordinates

y f y w :

CCI measuring distance to the fluid/wall

D :

Electric displacement

E :

Electric field strength

H :

Capacitor plate distance



δ g :

Thickness of the glass plate

δ f :

Film thickness


Electric permittivity


Optical wavelength


Kinematic viscosity


Electric potential




Surface tension


Wavelength of surface waves

\(Re=\frac{q}{\nu}\) :

Reynolds number of the liquid film


  • Adomeit P, Renz U (2000) Hydrodynamics of three-dimensional waves in laminar falling films. Int J Multiph Flow 26:1183–1208

    MATH  Article  Google Scholar 

  • Alekseenko S, Cherdantsev A, Cherdantsev M, Isaenkov S, Kharlamov S, Markovich D (2011) Application of a high-speed laser-induced fluorescence technique for studying the three-dimensional structure of annular gas-liquid flow. Exp Fluids 1–13

  • Alekseenko SV, Nakoryakov VE, Pokusaev BG (1994) Wave flow of liquid films. Begell House, Redding

    Google Scholar 

  • Alekseenko SV, Antipin VA, Guzanov VV, Kharlamov SM, Markovich DM (2005) Three-dimensional solitary waves on falling liquid film at low reynolds numbers. Phys Fluids 17:1–4

    Article  Google Scholar 

  • Allen PHG, Karayiannis TG (1995) Electrohydrodynamic enhancement of heat transfer and fluid flow. Heat Recovery Syst CHP 15(5):389–423

    Article  Google Scholar 

  • Chang HC, Cheng M, Demekhin EA, Kopelevic DI (1994) Secondary and tertiary excitation of three-dimensional patterns of a falling film. J Fluid Dyn 270:251–275

    MATH  Google Scholar 

  • Cohen-Sabban Joseph, Gaillard-Groleas Jerome, Pierre-Jean Crepin (2001) Quasi-confocal extended field surface sensing. Opt Metrol Roadmap Semicond Opt Data Storage Ind II 4449(1):178–183

    Google Scholar 

  • Darabi J, Ohadi MM, Desiatoun SV (2000) Falling film and spray evaporation enhancement using an applied electric field. J Heat Transf 122:741–748

    Article  Google Scholar 

  • Di Marco P, Grassi W (1994) Gas-liquid interface stability in presence of an imposed electric field. In: Proceedings of 12th UIT national conference, L’Aquila (I), pp 299–310

  • Dietze GF (2010) Flow separation in falling liquid films. PhD thesis, RWTH Aachen

  • Dietze GF, Kneer R (2011) Flow separation in falling liquid films. Frontiers Heat Mass Transf 2

  • Dietze GF, Leefken A, Kneer R (2008) Investigation of the backflow phenomenon in falling liquid films. JJ Fluid Mech 595:435–459

    MATH  Article  Google Scholar 

  • Dietze GF, Al-Sibai F, Kneer R (2009) Experimental study of flow separation in laminar falling liquid films. J Fluid Mech 637:73–104

    MATH  Article  Google Scholar 

  • Eames IW, Sabir HM (1997) Potential benefits of electrohydrodynamic enhancement of two-phase heat transfer in the design of refrigeration systems. Appl Therm Eng 17(1):79–92

    Article  Google Scholar 

  • Griffing EM, Bankoff SG, Miksis MJ, Schluter RA (2006) Electrohydrodynamics of thin flowing films. J Fluids Eng 128(2):276–283

    Article  Google Scholar 

  • Griffiths DJ (2006) Introduction to electrodynamics, 3rd edn. Pearson Education, Delhi

    Google Scholar 

  • Landau LD, Lifshitz EM (1975) Electrodynamics of continuous media, 2nd edn. Pergamon, Oxford

    Google Scholar 

  • Laohalertdecha S, Naphon P, Wongwises S (2007) A review of electrohydrodynamic enhancement of heat transfer. Renew Sustain Energy Rev 11(5):858–876

    Article  Google Scholar 

  • Lel VV, Al-Sibai F, Kneer R (2005) Local thickness and wave velocity measurement of wavy falling liquid films with chromatic confocal imaging method and a fluorescence intensity technique. Exp Fluids 39:856–864

    Article  Google Scholar 

  • Liu J, Schneider JB, Gollub JP (1994) Three-dimensional instabilities of film flows. Phys Fluids 7:55–67

    MathSciNet  Article  Google Scholar 

  • Nosoko P, Yoshimura PN, Nagata T, Oyakawa K (1996) Characteristics of two-dimensional waves on a falling liquid film. Chem Eng Sci 51(5):725–732

    Article  Google Scholar 

  • Park CD, Nosoko T (2003) Three-dimensional wave dynamics on a falling film and associated mass transfer. AIChE J 49(11):2715–2727

    Article  Google Scholar 

  • Scheid B, Ruyer-Quil C, Manneville P (2006) Wave patterns in film flows: modelling and three-dimensional waves. J Fluid Mech 562:183–222

    MathSciNet  MATH  Article  Google Scholar 

  • Tailby SR, Portalski S (1962) The determination of the wavelength on a vertical film of liquid flowing down a hydrodynamically smooth plate. Chem Eng Res Des 40:114–122

    Google Scholar 

  • Tomar G, Gerlach D, Biswas G, Alleborn N, Sharma A, Durst F, Welch SWJ, Delgado A (2007) Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. J Comput Phys 227:1267–1285

    MathSciNet  MATH  Article  Google Scholar 

  • Tsvelodub O, Samatov S (2010) Effect of the electric field on the wave flow regimes of a thin film of a viscous dielectric fluid. J Appl Mech Tech Phys 51:359–368

    MathSciNet  Article  Google Scholar 

  • Whitham GB (1974) Linear and nonlinear waves. Wiley, New York

    MATH  Google Scholar 

  • Yamashita K, Yabe A (1997) Electrohydrodynamic enhancement of falling film evaporation heat transfer and its long-term effect on heat exchangers. J Heat Transf 119:339–347

    Article  Google Scholar 

  • Zhou DW, Gambaryan-Roisman T, Stephan P (2009) Flow visualization and local measurement of forced convection heat transfer in a microtube. J Heat Transf 33(2):273–283

    Google Scholar 

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The authors thank Anne Mettner and Norman Lahann for their contribution to the development of the three-dimensional excitation mechanism employed to obtain the experimental results. Additionally, we would like to thank the reviewers for their constructive comments and ideas on this manuscript, in particular with respect to Fig. 6. This work was financially supported by the Deutsche Forschungsgemeinschaft (grant number DFG KN 764/3-1).

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Correspondence to Wilko Rohlfs.

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Rohlfs, W., Dietze, G.F., Haustein, H.D. et al. Experimental investigation into three-dimensional wavy liquid films under the influence of electrostatic forces. Exp Fluids 53, 1045–1056 (2012).

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  • Particle Image Velocimetry
  • Wave Front
  • Liquid Film
  • Spanwise Direction
  • Wave Crest