惯性与滑移对包覆在纤维上的液膜不稳定性的影响
Inertia and slip effects on the instability of a liquid film coated on a fibre
AI总结：
本研究针对纤维表面液膜的不稳定性问题，建立了基于轴对称Navier-Stokes方程的线性不稳定性分析框架，揭示了惯性与滑移对失稳模式、扰动增长的作用规律，并通过直接数值模拟验证了理论结果，还发现弱惯性下滑移使卫星液滴体积呈幂律减小。
摘要：
为探究惯性和滑移对纤维表面液膜不稳定性的影响，本文通过线性不稳定性分析，提出了一个基于轴对称Navier-Stokes方程的理论框架。该模型表明，滑移会显著增强黏性膜流动中的扰动增长，而对以惯性为主导的流动影响极小。此外，在无滑移边界条件下，薄膜的主导失稳模式不受惯性影响，与无滑移润滑模型的预测高度吻合。反之，当引入滑移时，随着惯性减小，主导波数会出现明显下降，这一趋势可通过本文提出的大滑移润滑模型得到刻画。随后，本文对Navier-Stokes方程开展了直接数值模拟，进一步验证了线性阶段的理论结论。在非线性动力学方面，无滑移模拟显示，液膜内部存在由表面附近的流体惯性驱动的复杂涡结构。此外，在弱惯性场景下，滑移会导致卫星液滴体积减小，且二者符合幂律关系。
英文摘要：
To investigate the influence of inertia and slip on the instability of a liquid film on a fibre, a theoretical framework based on the axisymmetric Navier-Stokes equations is proposed via linear instability analysis. The model reveals that slip significantly enhances perturbation growth in viscous film flows, whereas it exerts minimal influence on flows dominated by inertia. Moreover, under no-slip boundary conditions, the dominant instability mode of thin films remains unaltered by inertia, closely aligning with predictions from a no-slip lubrication model. Conversely, when slip is introduced, the dominant wavenumber experiences a noticeable reduction as inertia decreases. This trend is captured by an introduced lubrication model with giant slip. Direct numerical simulations of the Navier-Stokes equations are then performed to further confirm the theoretical findings at the linear stage. For the nonlinear dynamics, no-slip simulations show complex vortical structures within films, driven by fluid inertia near surfaces. Additionally, in scenarios with weak inertia, a reduction in the volume of satellite droplets is observed due to slip, following a power-law relationship.
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