论文标题
倾斜表面上有圆形足迹的液滴的身份
Identities for Droplets with Circular Footprint on Tilted Surfaces
论文作者
论文摘要
确切的数学身份是在基于平坦倾斜表面的圆形接触边界的液滴的相关参数之间介绍的。其中两个身份来自力平衡，一个来自扭矩平衡。倾斜表面覆盖了无柄或吊坠滴的全部倾斜度，包括壁上液滴的中间情况（垂直表面）。通过在较小的键号上的线性响应近似的可用解决方案以及从数值解决方案获得的，使用表面Evolver软件，都可以通过线性响应近似的可用解决方案进行测试。详细讨论了通过数值解决方案以身份出现的某些角度大暴力的微妙之处。有人争论着身份如何在两个方面有用。首先是通过从身份获得的表达式替换一些年轻拉普拉斯方程中的一些未知值。其次是使用身份估算近似分析或数值解决方案的误差，而无需提及精确解决方案。
Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young-Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.
