Group members

Mark Blyth (UEA)

Dmitri Tseluiko (Imperial College)

Demetrius Papageorgiou (Imperial College)

Jean-Marc Vanden-Broeck (UCL)

Project summary

Supported by the EPSRC (grant number EP/D052289/1), we have been studying the effect of an electric field on the flow of a liquid film over topography. Experiments performed by Messe & Decre (2007), among others, revealed that a liquid film flowing over a substrate with a rectangular trench indentation exhibits a pronounced ridge ahead of the step down into the trench, and a depression ahead of the step back up out of the trench. The upstream capillary ridge and the downstream depression were both observed by Kalliadasis et al. (2000) in computations of two-dimensional film flow into a trench. The two features are visible in the graphs below.

The appearance of the capillary ridge (visible in the left hand figure above the step) is undesirable in coating applications, for example, where usually a smoothly coated surface is needed. With this in mind, our aim was to investigate how the character of the film surface is affected by an electric field. We imposed a normal electric field (for example by holding a flat electrode some distance from the film), and treated the film as a perfect conductor. Using the lubrication approximation, we derived a nonlinear partial differential equation which governs the shape of the film surface (see Tseluiko et al. (2008a) for details). The strength of the electric field is controlled through a parameter, We. As we increase the electric field, we find that the capillary ridge at the downward step is gradually ironed out. However, it is at the expense of the surface shape at the upward step, which develops a noticeable bulge as can be seen in the following figures.



There are some reservations over the validity of using the lubrication approximation at such a sharp topography. Nevertheless, boundary integral calculations for Stokes flow which are valid for any topography produce similar results (Tseluiko et al. 2008b).

As the intensity of the electric field is increased, through increased values of We, we can see waves upstream of the capillary ridge and downstream of the upward step. We are able to predict these waves through an asymptotic analysis based on the assumption of a downward or upward step of infinitesimal height. The same analysis produces formulae for the amplitude and period of the waves (Tseluiko et al. 2008c).

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References

2000 Kalliadasis, S., Bielarz, C. & Homsy, G. M., Steady free-surface thin film flows over topography, Phys. Fluids 12, 1889.

2007 Messe, S. & Decre, M. M. J., Experimental study of a gravity driven water film flowing down inclined plates with different patterns, Phillips Research Unclassified Report No. NL-UR 030/97.

2008a D. Tseluiko, M. G. Blyth, D. T. Papageorgiou & J.-M. Vanden-Broeck, Electrified viscous thin film flow over topography. Journal of Fluid Mechanics, 597, 449-475. DOI

2008b D. Tseluiko, M. G. Blyth, D. T. Papageorgiou & J.-M. Vanden-Broeck, Effect of an electric field on film flow down a corrugated wall at zero Reynolds number. Physics of Fluids, 20(4), 042103. DOI

2008c D. Tseluiko, M. G. Blyth, D. T. Papageorgiou & J.-M. Vanden-Broeck, Viscous electrified film flow over step topography. Submitted.

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