Thermocapillary instability in self-rewetting liquid films flowing down a heated soft vertical fibre

In this article, we examine the stability of self-rewetting films (SRF) flowing along a soft vertical cylinder where the flow is driven by the combined action of gravity and thermocapillarity. A long-wave model is formulated to capture the evolution of the liquid layer thickness and the substrate deformation where the film flow interacts with the soft structure through gravity, thermocapillary forces, and the elasticity of the soft fibre with the Winkler-based framework. Using the model, we explore the impact of quadratic thermocapillarity of SRF films including elasticity of the soft fibre and film thickness on the temporal stability. The conventional thermocapillarity (when T_i < T_m) along with elasticity of soft fibre augments the instability whereas the anomalous thermocapillarity (when T_i > T_m) suppresses the instability with T_i and T_m denoting the interface temperature and minimum surface tension temperature respectively. The time-dependent computations of the coupled nonlinear partial differential equation (PDE) of the interface reveal soft-layer deformation which may also lead to localized bulging in the interface due to conventional thermocapillarity and elasticity of the soft fibre. The results of numerical simulations are consistent with our linear theory.