Thin-liquid-film flow on three-dimensional topographically patterned rotating cylinders
Thin-liquid-film flow on three-dimensional topographically patterned rotating cylinders
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三维地形图案旋转圆柱体上的薄膜液流
DOI：
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发表时间：
2021
影响因子：
3.7
通讯作者：
Satish Kumar
中科院分区：
文献类型：
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作者：
Chance Parrish;Lucas Pham;Satish Kumar
具有表面形貌的旋转离散物体的涂覆是制造过程中经常遇到的问题。表面形貌可能在涂层中引起不期望的干扰，导致不均匀厚度的涂层。为了研究这个问题，我们在三维地形图案的圆柱体，围绕其水平轴旋转的薄液体涂层的流动模型。描述涂层厚度的变化作为轴向坐标，角坐标和时间的函数的演化方程数值求解使用可变时间步长有限差分格式。在快速旋转圆柱的极限下，我们忽略重力的影响，并发现液体在图案波峰或图案波谷处积聚。使用长波分析，我们推导出一个表达式的临界韦伯数，这些制度分开。如果重力再结合，在波峰或波谷处的液体积聚可能导致涂层在其重量下下垂，导致形成液滴或环，其在大旋转速率下的间距由离心力和表面张力之间的平衡控制。在较低的旋转速率，其中重力占主导地位，模拟结果表明，圆柱地形往往会改变液滴形成的速度，但不一定系统地影响液滴之间的间距。流动可视化实验产生的结果，同意定量模拟和长波分析的预测。我们观察到最均匀的涂层在实验中，在中等转速下，在涂层厚度的扰动发展缓慢。这表明，为了在实践中获得几乎均匀的涂层，涂层的固化速度必须快于扰动的发展。
Abstract The coating of rotating discrete objects with surface topography is a problem commonly encountered in manufacturing processes. Surface topography may induce undesired disturbances in the coating, leading to coatings of non-uniform thickness. To study this problem, we model the flow of thin liquid coatings in three dimensions on topographically patterned cylinders that rotate about their horizontal axes. An evolution equation describing variations in the coating thickness as a function of the axial coordinate, the angular coordinate, and time is solved numerically using a variable time-step finite-difference scheme. In the limit of a rapidly rotating cylinder, we neglect the effects of gravity and find that liquid accumulates at either pattern crests or pattern troughs. Using a long-wave analysis, we derive an expression for the critical Weber number that separates these regimes. If gravity is reincorporated, the accumulation of liquid at crests or troughs may cause the coating to sag under its weight, leading to the formation of droplets or rings whose spacing at large rotation rates is controlled by the balance between centrifugal and surface-tension forces. At lower rotation rates, where gravitational forces dominate, simulation results indicate that cylinder topography tends to alter the rate at which droplets form, but does not necessarily systematically affect the spacing between droplets. Flow visualization experiments yield results that agree quantitatively with predictions of the simulations and long-wave analysis. We observe the most uniform coatings in experiments at moderate rotation rates, where disturbances in the coating thickness develop slowly. This indicates that to obtain nearly uniform coatings in practice, the coating must be solidified faster than disturbances can develop.