Math. Model. Nat. Phenom.
Volume 7, Number 4, 2012Modelling phenomena on micro- and nanoscale
|Page(s)||99 - 145|
|Published online||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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.