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Title: Two-dimensional pulse dynamics and the formation of bound states on electrified falling films
Authors: Blyth, Mark G.
Tseluiko, Dmitri
Lin, Te-Sheng
Kalliadasis, Serafim
Keywords: Low-Reynolds-number flows
MHD and electrohydrodynamics
Thin films
Issue Date: 2018
Publisher: © Cambridge University Press (CUP)
Citation: BLYTH, M.G. ... et al, 2018. Two-dimensional pulse dynamics and the formation of bound states on electrified falling films. Journal of Fluid Mechanics, 855, pp.210-235.
Abstract: The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.
Description: This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2018.592. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge University Press .
Version: Accepted for publication
DOI: 10.1017/jfm.2018.592
URI: https://dspace.lboro.ac.uk/2134/34881
Publisher Link: https://doi.org/10.1017/jfm.2018.592
ISSN: 0022-1120
Appears in Collections:Published Articles (Maths)

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