Dynamics of a Reactive Thin Film

Philip Michael Joseph Trevelyan, A. Pereira, Serafim Kalliadasis

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)99-145
JournalMathematical Modelling of Natural Phenomena
Issue number4
Publication statusPublished - 9 Jul 2012


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