2134/15489
Dmitri Tseluiko
Dmitri
Tseluiko
Mark G. Blyth
Mark G.
Blyth
Demetrios T. Papageorgiou
Demetrios T.
Papageorgiou
Jean-Marc Vanden-Broeck
Jean-Marc
Vanden-Broeck
Electrified viscous thin film flow over topography
Loughborough University
2014
Fluid mechanics
Bounded states
Electric fields
Topography
Viscous flow
Films
Mathematical Sciences not elsewhere classified
2014-08-11 11:43:57
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Electrified_viscous_thin_film_flow_over_topography/9388376
The 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.