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Improved approximations for flows of thin films.

机译：改进的薄膜流动近似值。

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摘要

Film flow equations are simplified equations for modeling the flow of thin liquid films. They are ordinary differential equations in terms of the film thickness. Typically, the boundary-layer approximation to the Navier-Stokes equation is employed, a velocity profile is assumed, and conservation of momentum then yields a film equation. Surface tension is usually important in which case the film equations are third order. Existing film equations are adequate when the substrate is not moving and when the substrate is moving in the absence of inertial effects. These equations are deficient in the important case of a moving substrate when inertia is included and the film connects with a reservoir of liquid that is substantially hydrostatic. In that case, the inertial terms of the film equations do not die off as the film thickens, unlike the viscous terms or the inertial terms when the wall is stationary, and so a hydrostatic reservoir is not described. The main goals of this thesis are to explore the cause of the deficiency and, if possible, propose a remedy.;To test the starting hypothesis that the assumption of a parabolic velocity profile is the cause of the deficiency, three studies were conducted. First, the full set of boundary-layer equations was solved exactly, without assuming a velocity profile, for the linearized case where the film thickness is close to its value far downstream. The velocity profile was found to be either parabolic, when inertia was neglected, or very close to parabolic when inertia was included. Second, two model problems with fixed boundaries were solved using the commercial code Fluent. Parabolic or near parabolic velocity profiles were also found. Third, complete free boundary calculations were obtained from collaborators having their own CFD codes for the flow called slot coating. These results again supported the use of a parabolic velocity profile as a good approximation. Furthermore, film profiles based on the parabolic film equation matched the CFD profiles well when inertial terms were small to moderate.;With a parabolic velocity profile established as appropriate, an approach other than introducing a non-parabolic velocity profile was indicated. It was recognized that evaluating the inertial terms using average velocity, as traditionally done for flow in conduits, while continuing to evaluate the viscous terms using the parabolic velocity profile, gives rise to a film equation where the inertial terms die off as the film thickness increases as desired. The downstream asymptotic behavior of this plug-parabolic film equation was shown to be identical to that of the parabolic film equation. An unexpected but additionally desired behavior was exhibited: film profiles could be computed when inertial terms were dominant. As inertia increased, the profiles exhibited curvature relaxation, unlike the parabolic and other known film equations. Curvature relaxation due to inertia is an important phenomenon in coating, resulting in the ability to coat thinner as speed is increased and the disappearance of the instability called ribbing.;Predictions of coating thickness for the dip coating process, where a film is withdrawn from a pool of liquid, were made using the plug-parabola film equation. Comparisons with experimental and CFD data were limited because of a lack of results when inertia is important. Comparisons with experimental and computational data for slot coating show the correct qualitative behavior but indicate an early onset of meniscus relaxation. It may be necessary to modify the plug-parabola film equation, perhaps by blending it with the parabolic film equation, to delay the onset of curvature relaxation.
机译：膜流方程是简化的薄膜液流模型。它们是关于膜厚度的常微分方程。典型地，采用对Navier-Stokes方程的边界层近似，假设速度分布，然后动量守恒产生薄膜方程。在这种情况下，薄膜方程是三阶的，表面张力通常很重要。当基材不移动时以及基材在没有惯性作用的情况下移动时，现有的薄膜方程式就足够了。当包括惯性并且薄膜与基本为流体静压的液体容器连接时，在移动的衬底的重要情况下，这些方程式是不足的。在那种情况下，膜方程式的惯性项不会随着膜的增厚而消失，这与壁固定时的粘性项或惯性项不同，因此没有描述静水容器。本论文的主要目的是探讨缺陷的原因，并在可能的情况下提出补救措施。为了检验假设抛物线速度分布是缺陷的起因，进行了三项研究。首先，在膜厚度接近其下游值的线性化情况下，无需假设速度分布，即可精确求解整个边界层方程组。当忽略惯性时，发现速度分布要么是抛物线的，要么包括惯性时，速度分布非常接近抛物线。其次，使用商业代码Fluent解决了两个具有固定边界的模型问题。还发现了抛物线速度或接近抛物线速度。第三，从协作者获得了完整的自由边界计算，这些协作者具有自己的CFD代码（称为缝隙涂层）。这些结果再次支持抛物线速度曲线的良好近似。此外，当惯性项小到中等时，基于抛物线薄膜方程的薄膜轮廓与CFD轮廓匹配良好。通过适当地建立抛物线速度轮廓，表明了一种引入非抛物线速度轮廓的方法。人们已经认识到，像传统上对导管中的流量所做的那样，使用平均速度来评估惯性项，同时继续使用抛物线速度曲线来评估粘性项，会产生一个薄膜方程，其中随着薄膜厚度的增加，惯性项消失如预期的。该插塞-抛物线方程的下游渐近行为被证明与抛物线膜方程的下游渐近行为相同。出现了意想不到但又令人满意的行为：当惯性项占主导地位时，可以计算出薄膜轮廓。随着惯性的增加，轮廓显示出曲率松弛，这与抛物线方程和其他已知的膜方程不同。惯性引起的曲率松弛是涂层中的一个重要现象，随着速度的增加，涂层的能力变得更薄，不稳定性的消失称为肋纹。浸涂工艺中涂层厚度的预测，即浸涂过程使用塞-抛物线膜方程式来计算液体池。由于惯性很重要时缺乏结果，因此与实验数据和CFD数据的比较受到限制。与缝隙涂层的实验数据和计算数据进行比较，显示出正确的定性行为，但表明弯液面松弛的早期发作。可能有必要修改插值-抛物线薄膜方程，也许将其与抛物线薄膜方程混合，以延迟曲率松弛的开始。

著录项

  • 作者

    Lowry, Christine Elizabeth.;

  • 作者单位

    Rochester Institute of Technology.;

  • 授予单位 Rochester Institute of Technology.;
  • 学科 Engineering Chemical.;Engineering Mechanical.
  • 学位 M.S.
  • 年度 2010
  • 页码 105 p.
  • 总页数 105
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 公共建筑;
  • 关键词

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