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We model two ways to couple chemistry and hydrodynamics. One represents a
reactive mixture of surfactants on a thin liquid film [1] and the other
describes
droplets that react chemically with the substrate [2]. The coupling is due
to
concentration-dependent Marangoni forces and a
substrate-coverage-dependent
wettability, respectively.
Both are modelled by coupled reaction-diffusion and thin film equations
derived
via long-wave or lubrication approximation from the general transport
equations.
For the reactive droplets the solution structure is analysed explaining different experimentally observed regimes of running droplets [2-4]. A special focus lies on the discussion of existence regions of running and sitting droplets and the related drift-pitchfork bifurcation. We conclude this part with a comparison of simulations and experiments for different modes of periodic drop movement. Finally, for the reactive surfactants we analyse the behaviour of pulse and front solutions of the underlying reaction-diffusion system in dependence of the coupling to the supporting liquid film. [1] A. Pereira, P. M. J. Trevelyan, U. Thiele, and S. Kalliadasis, preprint (2005) [2] U. Thiele, K. John and M. B{\"a}r, {\it Phys. Rev. Lett.}, \textbf{93}, 027802 (2004); K. John, M. B{\"a}r and U. Thiele, {\it Eur. Phys. J. E}, \textbf{18} 183--199 (2005); [3] F. Domingues~Dos~Santos and T.~Ondarcuhu, {\it Phys. Rev. Lett.} \textbf{75}, 2972 (1995); [4] S.~W. Lee, D.~Y. Kwok, and P.~E. Laibinis, {\it Phys. Rev. E} \textbf{65}, 051602 (2002); [5] Y. Sumino {\it et al.}, {\it Phys. Rev. Lett.} \textbf{94}, 068301 (2005). |
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