# 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

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topTrevelyan, 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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