Mathematical Sciences: Computational Two-Phase Viscous Drop Spreading

数学科学：计算两相粘性液滴扩散

• 批准号: 9623092
• 负责人: Richard Braun
• 金额: $ 6万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623092&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Computational; Two; Phase

9623092 Braun Motivated by the complex transport associated with spreading process such as the spreading of solder droplets and coating processes, a research program is proposed on the spreading of a droplet that is covered by a film. Often in soldering and other processes involving spreading, the drop may become very thin which indicates the presence of multiple length scales. Based on the author's previous research, the first approach proposed is a multi-scale asymptotic analysis (lubrication theory) to derive nonlinear diffusion equations for the free surfaces; those nonlinear diffusion equations will be solved using a spectrally-accurate implementation of the method of lines. All quantities of interest may be computed in this approximation once the required free surfaces have been found. A second approach is also proposed, via boundary integral equations, under the approximation of Stokes flow in the drop and film. This approach relaxes the requirement that the drop and film be thin, but still requires that the flow be slow. We propose making a direct comparison between the two approaches in order to evaluate the utility of each in various situations. The work proposed will develop models only for the fluid dynamics, and inclusion of reactive effects will be proposed in a subsequent project. Important processes in manufacturing involve the spreading of a fluid droplet in the presence of another fluid; one example is soldering, where, in many instances, the presence of a thin layer of a second fluid, the flux, is required for the process to work at all. Because the use of lead-based solder is no longer allowed, understanding of this droplet spreading process for other kind of solder materials would be very helpful in understanding alternative solder materials. The work proposed in the project is developing some preliminary models necessary for the development of a complete model for a spreading solder drop. The proposed program is to develop theory for the spreading of a droplet on a flat plate that is covered by a thin film of a different fluid. Computer codes will be developed that predict how fast the drop spreads, and the shapes of the drop and the film that covers the drop. In summary, sophisticated mathematical techniques will be applied to a problem of technological importance. The computer codes resulting from this project are expected to be applicable to related wetting problems in different technological areas (e.g. coating processes) subsequent to the completion of this project.

受焊锡液滴扩散和镀膜过程等扩散过程相关的复杂输运的启发，提出了一种研究被薄膜覆盖的液滴扩散的方案。通常在焊接和其他涉及扩散的过程中，液滴可能变得非常薄，这表明存在多个长度尺度。在前人研究的基础上，提出了一种多尺度渐近分析方法（润滑理论）来推导自由表面的非线性扩散方程；这些非线性扩散方程将用谱线法的精确实现来求解。一旦找到所需的自由曲面，所有感兴趣的量都可以用这个近似来计算。第二种方法是利用边界积分方程，在液滴和膜中的斯托克斯流近似下提出的。这种方法放宽了对液滴和薄膜薄的要求，但仍然要求流动缓慢。我们建议在这两种方法之间进行直接比较，以便评估每种方法在各种情况下的效用。拟议的工作将仅为流体动力学建立模型，并将在随后的项目中提议纳入反应效应。制造中的重要过程涉及在存在另一种流体的情况下液滴的扩散；一个例子是焊接，其中，在许多情况下，第二流体，助焊剂的薄层的存在是整个过程工作所必需的。由于不再允许使用铅基焊料，因此了解其他焊料材料的这种液滴扩散过程将对了解替代焊料材料非常有帮助。该项目提出的工作是开发一些必要的初步模型，以开发一个完整的扩展焊点模型。这个计划是为液滴在被不同流体薄膜覆盖的平板上的扩散发展理论。计算机代码将被开发出来，以预测液滴扩散的速度、液滴的形状和覆盖液滴的薄膜。总之，复杂的数学技术将被应用于一个重要的技术问题。本项目产生的计算机代码预计将适用于本项目完成后不同技术领域（如涂层工艺）的相关润湿问题。