國立清華大學 數學系

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-wave solutions on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model derived on the basis of thin-film theory and second using the Stokes equations for zero Reynolds number flow. 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 which incorporates long-range effects is developed to analyse attractions and repulsions and the formation of bound states of pulses. The infinite sequence of bound-state solutions found for non- electrified flow is shown to reduce to a finite set for electrified flow due to the algebraic decay of the tails. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. The electric field is shown to regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.