Dynamics of a Reactive Thin Film

P.M.J. Trevelyan; A. Pereira; S. Kalliadasis

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 4, page 99-145
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Trevelyan, P.M.J., Pereira, A., and Kalliadasis, S.. "Dynamics of a Reactive Thin Film." Mathematical Modelling of Natural Phenomena 7.4 (2012): 99-145. <http://eudml.org/doc/222330>.

@article{Trevelyan2012,
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.},
author = {Trevelyan, P.M.J., Pereira, A., Kalliadasis, S.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {thin films; Marangoni effect; chemical reactions},
language = {eng},
month = {7},
number = {4},
pages = {99-145},
publisher = {EDP Sciences},
title = {Dynamics of a Reactive Thin Film},
url = {http://eudml.org/doc/222330},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Trevelyan, P.M.J.
AU - Pereira, A.
AU - Kalliadasis, S.
TI - Dynamics of a Reactive Thin Film
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/7//
PB - EDP Sciences
VL - 7
IS - 4
SP - 99
EP - 145
AB - 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.
LA - eng
KW - thin films; Marangoni effect; chemical reactions
UR - http://eudml.org/doc/222330
ER -

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