Thermocapillary ultrathin self-rewetting film flows down a rotating fibre

Abstract

This study investigates the influence of thermocapillarity on the dynamics and nonlinear stability of an ultrathin self-rewetting film flowing down a uniformly heated rotating vertical fibre. To capture the combined effects of intermolecular forces (van der Waals attraction) and centrifugal forces (due to rotation), a thin-film evolution equation is derived, assuming the film thickness is much smaller than the fibre radius. Linear stability analysis shows that the van der Waals attraction and rotation always enhance instability, whether acting alone or together. The impact of thermocapillarity in the presence of both van der Waals attraction and rotation on absolute/convective instability is also discussed. When $T^i<T_0$, where $T^i$ is the interfacial temperature and $T_0$ is the temperature at which surface tension is minimum, absolute instability occurs at a lower Marangoni number compared to the case where van der Waals attraction and rotation are absent. When $T^i>T_0$, the convective instability region expands with a higher Marangoni number, even when van der Waals attraction and rotation are present. A weakly nonlinear analysis using the method of multiple scales is conducted to study the bifurcation behavior of the nonlinear evolution equation. The results indicate the existence of both subcritical and supercritical regimes and demonstrate how thermocapillarity, combined with rotation and van der Waals forces, influences the shift of the bifurcation point. Finally, numerical simulations of the nonlinear evolution equation are performed for various flow parameters. These results explain how rotation, thermal effects, and intermolecular forces influence the flow dynamics.