Abstract
It is shown that when steady states of a multistable kinetic system are attained at the extreme ends on the free surface of a thin liquid film, a simultaneous chemical and hydrodynamic wave can propagate with a constant velocity in the direction of the preferable concentration plateau. By using a systematic long-wave analysis, it is demonstrated that the surface deformation can cause thinning of the film when the wave propagates in the direction of the higher concentration region, while the film can swell when the wave moves in the opposite direction. The analysis, based on the presence of a long lateral diffusional scale compared with the film thickness, fails when the reaction scheme and the induced fluid motion act as to arrest the wave and reduce its velocity almost to a complete halt. Under such conditions, the separation of the scales is invalidated by developing shocks with steep local gradients which can result in a forward-breaking wave or film rupture.
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