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The flow of an electrified liquid film down an inclined plane wall isinvestigated with the focus on coherent structures in the form of travellingwaves on the film surface, in particular, single-hump solitary pulses and theirinteractions. The flow structures are analysed first using a long-wave model,which is valid in the presence of weak inertia, and second using the Stokesequations. For obtuse angles, gravity is destablising and solitary pulses existeven in the absence of an electric field. For acute angles, spatiallynon-uniform solutions exist only beyond a critical value of the electric fieldstrength; moreover, solitary-pulse solutions are present only at sufficientlyhigh supercritical elec- tric field strengths. The electric field increases theamplitude of the pulses, can generate recirculation zones in the humps, andalters the far-field decay of the pulse tails from ex- ponential to algebraicwith a significant impact on pulse interactions. A weak-interaction theorypredicts an infinite sequence of bound-state solutions for non-electrifiedflow, and a finite set for electrified flow. The existence of single-hump pulsesolutions and two-pulse bound states is confirmed for the Stokes equations viaboundary-element computations. In addition, the electric field is shown totrigger a switch from absolute instability to convective instability, therebyregularising the dynamics, and this is confirmed by time- dependent simulationsof the long-wave model.

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