Effect of Thermocapillary on Absolute and Convective Instability of Film Flow of Self-Rewetting Fluid

Abstract

The dynamics of a self-rewetting film falling along a vertical fiber under the influence of gravity are considered. The evolution equation of the interface of the self-rewetting film is established in the framework of a long-wave approximation theory. The effect of thermocapillarity (Marangoni effect) on the absolute/convective instability (AI/CI) is investigated for self-rewetting fluids of which the surface tension is a quadratic function of the temperature at the surface. The effect of thermocapillarity on the Rayleigh-Plateau instability is investigated by examining the dispersion relation. The characteristics of self-rewetting fluids are considered for different Marangoni numbers (Ma) in different regions of absolute/convective instability using a spatio-temporal stability analysis. Numerical simulations of the nonlinear evolution in various regions of absolute/convective instability are also performed. The results of numerical simulations are in excellent agreement with the spatio-temporal stability analysis. The effect of thermocapillarity on absolute and convective instability depends on the difference between the temperature at the interface $\bar {\varTheta }_{i}$ , and the temperature corresponding the minimum surface tension Θ0. The results indicate that the thermocapillarity suppresses the absolute instability and enhances the convective instability as Ma increases when $\bar {\varTheta }_{i}-{\varTheta }_{0}> 0$ , and enhances the absolute instability as Ma increases when $\bar {\varTheta }_{i}-{\varTheta }_{0}< 0$ .