Math. Model. Nat. Phenom.
Volume 7, Number 4, 2012Modelling phenomena on micro- and nanoscale
|99 - 145
|09 July 2012
Dynamics of a Reactive Thin Film
Department of Chemical Engineering, Imperial College London, London
SW7 2AZ, United
2 Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales
∗ Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 76E17 / 76E30 / 76V05
Key words: thin films / Marangoni effect / chemical reactions
© EDP Sciences, 2012
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