Thus far studies on dip coating focus on the asymptotic layer thickness which is reached only in the lower part of the layer when the withdrawal time is sufficiently long. This work attempts to offer a complete description of the evolution of layer thickness profile with withdrawal time for vertical withdrawal of Newtonian fluids using simulation and the Buckingham π theorem. The results show that over time, the withdrawal process successively undergoes two regimes: (I) an unsteady film region and an unsteady meniscus region and (II) an unsteady film region connected to a steady meniscus region through an unsteady meniscus region. The controlling factors for the two regimes are identified at different values of capillary number and Reynolds number. Models are proposed to predict the heights of the demarcations between different regions. The models agree well with experimental results when the controlling forces are viscous force and gravity.

中文翻译：

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牛顿流体垂直提取浸涂过程中不稳定区域和稳定区域之间以及薄膜和弯月面之间分界的时间演变

迄今为止，浸涂的研究集中在渐进层厚度上，当撤回时间足够长时，该厚度仅在层的下部达到。这项工作试图使用模拟和白金汉 π 定理来完整描述牛顿流体垂直抽取的层厚度剖面随抽取时间的演变。结果表明，随着时间的推移，退出过程连续经历两种状态：（I）非稳态薄膜区域和非稳态弯月面区域以及（II）非稳态薄膜区域通过非稳态弯月面区域连接到稳定弯月面区域。两种状态的控制因素在不同的毛细管数和雷诺数值下被确定。提出了模型来预测不同区域之间分界线的高度。当控制力为粘性力和重力时，模型与实验结果非常吻合。