Dynamics of a Reactive Thin Film

¹ Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom
² Division of Mathematics & Statistics, University of Glamorgan, Pontypridd, CF37 1DL, Wales

^∗ Corresponding author. E-mail: s.kalliadasis@imperial.ac.uk

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.