Geodesic
Dynamics of a Reactive Thin Film
P.M.J. Trevelyan1, 2 ; A. Pereira1 ; S. Kalliadasis1
1 Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
2 Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 4, pp. 99-145

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Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler numbers. We analyze the steady state, its linear stability and nonlinear regime. In the latter case, long-wave models are compared with integral-boundary-layer ones and bifurcation diagrams for permanent solitary wave solutions of the different models are constructed. Time-dependent computations with the integral-boundary-layer models show that the system approaches a train of coherent structures that resemble the solitary pulses obtained in the bifurcation diagrams.
DOI : 10.1051/mmnp/20127408

P.M.J. Trevelyan 1, 2 ; A. Pereira 1 ; S. Kalliadasis 1

1 Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
2 Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales 
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P.M.J. Trevelyan; A. Pereira; S. Kalliadasis. Dynamics of a Reactive Thin Film. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 4, pp. 99-145. doi: 10.1051/mmnp/20127408

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