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

Abstract

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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Notes

  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.

Abbreviations

f s :

Electrically induced surface force

g :

Gravity

n :

Coordinate normal to free surface

q :

Volumetric flow rate per unit width

t :

Coordinate tangential to free surface

t :

Time

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

α:

Angle

δ g :

Thickness of the glass plate

δ f :

Film thickness

∈:

Electric permittivity

λ:

Optical wavelength

ν:

Kinematic viscosity

ψ:

Electric potential

ρ:

Density

σ:

Surface tension

Λ:

Wavelength of surface waves

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

Reynolds number of the liquid film

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Acknowledgments

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). https://doi.org/10.1007/s00348-012-1342-0

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  • DOI: https://doi.org/10.1007/s00348-012-1342-0

Keywords

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