Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

doi:10.1088/1674-1056/acc78b

中国物理B ›› 2023, Vol. 32 ›› Issue (6): 64701-064701.doi: 10.1088/1674-1056/acc78b

Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Siyi An(安思亦) and Yongjun Jian(菅永军)^†

School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China

收稿日期:2022-10-30 修回日期:2023-02-19 接受日期:2023-03-25 出版日期:2023-05-17 发布日期:2023-06-07
通讯作者: Yongjun Jian E-mail:jianyj@imu.edu.cn
基金资助:
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).

Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Siyi An(安思亦) and Yongjun Jian(菅永军)^†

School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China

Received:2022-10-30 Revised:2023-02-19 Accepted:2023-03-25 Online:2023-05-17 Published:2023-06-07
Contact: Yongjun Jian E-mail:jianyj@imu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Rayleigh-Taylor instability, self-rewetting film, viscoelastic liquid

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.

Key words: Rayleigh-Taylor instability, self-rewetting film, viscoelastic liquid

中图分类号: (Interfacial instabilities (e.g., Rayleigh-Taylor))

47.20.Ma

47.15.gm (Thin film flows) 47.50.-d (Non-Newtonian fluid flows)

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[J]. 中国物理B, 2023, 32(6): 64701-064701.

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[J]. Chin. Phys. B, 2023, 32(6): 64701-064701.

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Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Rayleigh-Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

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