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Download fileElectrified viscous thin film flow over topography
journal contribution
posted on 2014-08-11, 11:43 authored by Dmitri TseluikoDmitri Tseluiko, Mark G. Blyth, Demetrios T. Papageorgiou, Jean-Marc Vanden-BroeckThe gravity-driven flow of a liquid film down an inclined wall with periodic
indentations in the presence of a normal electric field is investigated. The film is
assumed to be a perfect conductor, and the bounding region of air above the film is
taken to be a perfect dielectric. In particular, the interaction between the electric field
and the topography is examined by predicting the shape of the film surface under
steady conditions. A nonlinear, non-local evolution equation for the thickness of the
liquid film is derived using a long-wave asymptotic analysis. Steady solutions are
computed for flow into a rectangular trench and over a rectangular mound, whose
shapes are approximated with smooth functions. The limiting behaviour of the film
profile as the steepness of the wall geometry is increased is discussed. Using substantial
numerical evidence, it is established that as the topography steepness increases towards
rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the
film does not touch the wall. In the absence of an electric field, the film develops a
capillary ridge above a downward step and a slight depression in front of an upward
step. It is demonstrated how an electric field may be used to completely eliminate the
capillary ridge at a downward step. In contrast, imposing an electric field leads to the
creation of a free-surface ridge at an upward step. The effect of the electric field on
film flow into relatively narrow trenches, over relatively narrow mounds, and down
slightly inclined substrates is also considered.
Funding
This research was supported by the EPSRC under grant EP/D052289/1. The work of DTP was supported in part by the National Science Foundation grant DMS-0405639.
History
School
- Science
Department
- Mathematical Sciences
Published in
JOURNAL OF FLUID MECHANICSVolume
597Pages
449 - 475 (27)Citation
TSELUIKO, D. ... (et al.), 2008. Electrified viscous thin film flow over topography. Journal of Fluid Mechanics, 597, pp. 449-475.Publisher
© Cambridge University PressVersion
- VoR (Version of Record)
Publication date
2008ISSN
0022-1120eISSN
1469-7645Publisher version
Language
- en