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Interfacial hydrodynamic waves driven by chemical reactions

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Abstract

Consider the interaction between a horizontal thin liquid film and a reaction–diffusion process on the surface of the film. The reaction–diffusion process is modeled by the bistable/excitable FitzHugh–Nagumo prototype, a system of two equations for the evolution in time and space of two species, the activator and inhibitor. It is assumed that one of the species, the inhibitor, acts as a surfactant and the coupling between hydrodynamics and chemistry occurs through the solutocapillary Marangoni effect induced by spatial changes of the inhibitor’s concentration. The coupled system is analyzed with a long-wave expansion of the hydrodynamic equations of motion, transport equations for the two species and wall/free-surface boundary conditions. Depending on the values of the pertinent parameters, the bistable/excitable medium can induce both periodic stationary patterns and solitary waves on the free surface.

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Correspondence to Serafim Kalliadasis.

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Pereira, A., Trevelyan, P.M.J., Thiele, U. et al. Interfacial hydrodynamic waves driven by chemical reactions. J Eng Math 59, 207–220 (2007). https://doi.org/10.1007/s10665-007-9143-9

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  • DOI: https://doi.org/10.1007/s10665-007-9143-9

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