奇黏度对基底上热毛细自润湿薄膜流动不稳定性的影响

Effect of Odd Viscosity on Instability of Thermocapillary Self-Rewetting Thin Film Flows on a Substrate

摘要: 本研究探讨了奇黏度对倾斜加热基底上自润湿薄膜流动不稳定性的影响。采用包含偶黏度和奇黏度的广义牛顿流体模型，在润滑近似条件下推导出Benney型非线性演化方程。通过线性稳定性理论分析薄膜稳定性，结果表明：当加热基底时，热毛细效应可稳定薄膜；而在冷却条件下，则会促进不稳定性。奇黏度能够降低扰动增长速率，在两种热条件下均具有稳定薄膜的作用，并降低临界Marangoni数。数值模拟进一步验证了这些结果，显示奇黏度能够抑制界面波的振幅和频率。此外，基底倾角、雷诺数和毛细数的变化对不稳定性有显著影响，而缩短基底长度则有助于减轻不稳定性。本研究为利用奇黏度控制自润湿薄膜流动的稳定性提供了理论基础，并为奇黏度与热毛细效应相互作用提供了新的研究视角。

Abstract: This study investigates the effect of odd viscosity on the stability of self-rewetting thin-film flows on an inclined heated substrate. A generalized Newtonian model incorporating both even and odd viscosities is employed to derive a Benney-type nonlinear evolution equation under the lubrication approximation. The stability of the thin film is analyzed using linear stability theory, revealing that thermocapillary effects stabilize the film when heating the substrate, while promoting instability under cooling. Odd viscosity, which reduces disturbance growth rates, stabilizes the film in both thermal conditions, and lowers the critical Marangoni number. Numerical simulations support these findings, showing that odd viscosity suppresses the amplitude and frequency of interfacial waves. Additionally, variations in the substrate inclination, Reynolds number, and capillary number significantly influence the instability, while reducing the substrate length mitigates instability. This study lays the theoretical foundation for using odd viscosity to control the stability of self-rewetting thin-film flows and presents new perspectives on the interaction between odd viscosity and thermocapillary effects.