部分浸入液池中的垂直旋转圆盘上的薄膜动力学
Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath
摘要：
本文研究了部分浸入液池中的垂直旋转圆盘的轴对称薄液膜流动问题。建立了旋转圆盘拖动薄膜的全三维自由边界问题的数学模型。由此，推导出包括弯月面区域的降维扩展润滑近似。这个问题构成了一个推广的经典拖出和拖入问题的情况下，轴对称流。由此产生的非线性四阶偏微分方程的膜轮廓数值求解使用有限元方案。对于一系列的参数稳定状态的发现和比较的渐近解。讨论了薄膜轮廓的模式，作为浸没深度和角速度的函数。
英文摘要：
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
