Abstract Rayleigh-Taylor (RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability, while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled. Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 1226 2026), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2021 MS01007), and the Inner Mongolia Grassland Talent, China (Grant No. 12000-12102013).
Siyi An(安思亦) and Yongjun Jian(菅永军) Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate 2023 Chin. Phys. B 32 064701
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