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, singlehump solitary pulses and their interactions. The flow structures are analysed first using a longwave 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 nonuniform solutions exist only beyond a critical value of the electric field strength; moreover, solitarypulse solutions are present only at sufficiently high supercritical electricfield strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the farfield decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weakinteraction theory predicts an infinite sequence of boundstate solutions for nonelectrified flow, and a finite set for electrified flow. The existence of singlehump pulse solutions and twopulse bound states is confirmed for the Stokes equations via boundaryelement 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 timedependent simulations of the longwave model.
Original language  English 

Pages (fromto)  210235 
Number of pages  26 
Journal  Journal of Fluid Mechanics 
Volume  855 
Early online date  14 Sep 2018 
DOIs  
Publication status  Published  25 Nov 2018 
Profiles

Mark Blyth
 School of Mathematics  Professor of Applied Mathematics
 Fluid and Solid Mechanics  Member
Person: Research Group Member, Academic, Teaching & Research