On reactive thin liquid films falling down a vertical cylinder

Abstract

Chemical reactions in thin liquid films falling down vertical cylinders are widely present in various industrial settings, such as in combustion chambers of internal combustion engines. However, the effect of chemical reactions, especially the non-isothermal reactions, on the dynamics of thin films remains poorly understood. Therefore, in this paper, we systematically study the dynamics of a thin liquid film flowing down vertical cylinders in the presence of an exothermic or endothermic chemical reaction. A reduced model based on the assumption that the film thickness is much smaller than the cylinder radius is firstly derived. We then examine the effect of chemical reactions on the linear stability of the evolution equation as well as its nonlinear behaviors, including the profile and propagation speed of steady traveling waves. We find that the size and propagation speed of sliding beads on the cylinder are suppressed for an exothermic chemical reaction and promoted for an endothermic chemical reaction, respectively. In the end, we perform direct numerical simulations of the full nonlinear evolution equation, which are consistent with the predications from linear stability analysis and nonlinear traveling wave solutions. Our results provide new insight into the influence of chemical reactions on the dynamics of thin films falling down the cylindrical substrate.