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Dynamics of a Reactive Thin Film

Published online by Cambridge University Press:  09 July 2012

P.M.J. Trevelyan ,
A. Pereira  and
S. Kalliadasis
P.M.J. Trevelyan
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales
A. Pereira
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
S. Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
*
∗ Corresponding author. E-mail: s.kalliadasis@imperial.ac.uk
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Abstract

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.

Keywords

thin filmsMarangoni effectchemical reactions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 99 - 145
Copyright
© EDP Sciences, 2012

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