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Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

Published online by Cambridge University Press:  14 September 2018

M. G. Blyth Open the ORCID record for M. G. Blyth [Opens in a new window] ,
D. Tseluiko ,
T.-S. Lin  and
S. Kalliadasis
M. G. Blyth*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
D. Tseluiko
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
T.-S. Lin
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan
S. Kalliadasis
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 210 - 235
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Copyright
© 2018 Cambridge University Press 

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