Interfacial hydrodynamic waves driven by chemical reactions

A. Pereira, Philip Trevelyan, U. Thiele, S. Kalliadasis

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)207-220
Number of pages13
JournalJournal of Engineering Mathematics
Early online date21 Apr 2007
Publication statusE-pub ahead of print - 21 Apr 2007


  • Hydrodynamic effects induced by chemical-wave propagation
  • Reaction–diffusion processes
  • Surfactants
  • Thin-film flows


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