Absolute instability induced by Marangoni effect in thin liquid film flows on vertical cylindrical surfaces

Abstract

This paper investigates a thin liquid film flowing down the interior or exterior surface of a vertical uniformly heated cylinder under the influence of gravity. A thin liquid film model, which is applicable to both cases, is derived to examine the Marangoni effect on the spatial-temporal dynamics. Linear stability analysis predicts that an absolutely unstable mode could be initiated by the Marangoni effect even if the film thickness is very thin compared to the cylinder’s radius. The linear stability analysis shows that the instability is always absolute for arbitrary capillary number if a composite Marangoni number M=3MaBi2(1+Bi)2 exceeds a critical value M=-17+773≈0.71 (Ma is the Marangoni number, and Bi is the Biot number). Direct numerical simulations of the linearized and the full thin film model demonstrated the linear analysis. Results of the direct numerical simulations also show that the film has a strong tendency to break up into more droplets or rupture in the absolute instability regime. Nonlinear study also shows that the coalescence of droplets/ring waves and bound state are weakly dependent on the absolute or convective instability.