Title: Modeling film flows down a rotating slippery cylinder Show Chinese title

Title: 建模沿旋转滑腻圆柱体流动的薄膜

Abstract: This study investigates the nonlinear stability and dynamics of gravity-driven viscous films on a vertical rotating cylinder, considering both outer and inner surface flows with slip conditions at the cylinder wall. We develop an asymptotic model for the combined effects of rotation and wall slippage. Linear stability analysis indicates that wall slippage enhances instability on both surfaces, while rotation has differing impacts: it amplifies instability due to slip for outer surface flow but reduces it for inner surface flow. A weakly nonlinear stability analysis is then conducted to explore the combined impact of rotation and wall slip on flow stability beyond the linear regime, including the bifurcation of the nonlinear evolution equation for both surfaces. The traveling wave solution of the model is analyzed, showing how rotation affects nonlinear wave speed with a slippery wall. A stability analysis of the traveling wave solutions is also performed. Numerical simulations of the nonlinear evolution of the free surface reveal that increasing slip length enhances the choke phenomenon in inner surface flow, while rotation can delay this effect. Additionally, simulations show that for flow along the outer surface of a slippery rotating cylinder, the film tends to break up into droplets in the presence of rotation. Show Chinese abstract

Abstract: 本研究调查了在垂直旋转圆柱体上重力驱动的粘性薄膜的非线性稳定性和动力学，考虑了圆柱体壁面处具有滑移条件的外表面和内表面流动。 我们建立了一个渐近模型，用于研究旋转和壁面滑移的综合效应。 线性稳定性分析表明，壁面滑移会增强两个表面上的不稳定性，而旋转的影响不同：它会放大由于滑移引起的外表面流动的不稳定性，但会减少内表面流动的不稳定性。 随后进行了一项弱非线性稳定性分析，以探讨旋转和壁面滑移对流动稳定性在超出线性范围的影响，包括两个表面上非线性演化方程的分岔。 对模型的行波解进行了分析，展示了旋转如何影响具有滑动壁面的非线性波速。 还对行波解进行了稳定性分析。 自由表面非线性演化的数值模拟显示，增加滑移长度会增强内表面流动中的堵塞现象，而旋转可以延迟这种效应。 此外，模拟显示，在旋转滑动圆柱体外表面流动时，膜在旋转存在的情况下倾向于破裂成液滴。