Dynamics of a Reactive Thin Film

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 th...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2012-01, Vol.7 (4), p.99-145
Main Authors: Trevelyan, P.M.J., Pereira, A., Kalliadasis, S.
Format: Article
Language:English
Subjects:
76E17
76E30
76V05
Boundary layer
chemical reactions
Gravity
Marangoni effect
Mathematical models
Thin films
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Summary: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.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/20127408