Absolute and convective instabilities in non-local active-dissipative equations arising in the modelling of thin liquid films
conference contributionposted on 10.07.2015 by Dmitri Tseluiko, Mark G. Blyth, Demetrios T. Papageorgiou
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Absolute and convective instabilities in a non-local model that arises in the analysis of thin-film flows over flat or corrugated walls in the presence of an applied electric field are discussed. Electrified liquid films arise, for example, in coating processes where liquid films are deposited onto a target surfaces with a view to producing an evenly coating layer. In practice, the target surface, or substrate, may be irregular in shape and feature corrugations or indentations. This may lead to non-uniformities in the thickness of the coating layer. Attempts to mitigate film-surface irregularities can be made using, for example, electric fields. We analyse the stability of such thin-film flows and show that if the amplitude of the wall corrugations and/or the strength of the applied electric field is increased the convectively unstable flow undergoes a transition to an absolutely unstable flow
Financial support from the EPSRC under grant EP/K041134/1. The work of DT and MGB was partly supported by the London Mathematical Society under the grant 41114. The work of DT was additionally supported by the EPSRC under grant EP/J001740/1.
- Mathematical Sciences