Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario M5S 3G8, Canada.
Adv Colloid Interface Sci. 2014 Feb;204:1-14. doi: 10.1016/j.cis.2013.12.001. Epub 2013 Dec 14.
Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.
滴形技术广泛用于表面张力测量。已有大量文献表明，随着液滴/气泡形状逐渐接近球形，所有滴形技术的性能都会恶化。人们已经通过研究拉普拉斯滴偏离球形的程度来努力量化滴形技术的适用范围。文献中引入了一个形状参数，并多次进行修改以适应不同的滴状组合。然而，每当考虑到一个新的配置时，就会出现新的问题。因此，需要有一种通用的形状参数，适用于悬滴、固着液滴、液桥以及被捕获的气泡。在这项工作中，为了达到这个目的，使用总高斯曲率作为形状参数的统一方法。总高斯曲率是微分几何和表面热力学中常用的无量纲量，可用于计算不同拉普拉斯滴的形状。这里将使用总高斯曲率定义的新形状参数应用于悬滴和约束固着液滴，作为说明。分析表明，与之前的定义相比，新的定义更优越，能更好地反映实验结果，特别是在邦数的极值处。
