College of Textiles, North Carolina State University, 2401 Research Drive, Raleigh, North Carolina 27695-8301, USA.
Langmuir. 2010 Oct 19;26(20):16000-4. doi: 10.1021/la1031448.
In 1976, B. J. Carroll derived the equation to show that a symmetric liquid droplet sitting on a thin cylindrical fiber would acquire a bell shape at equilibrium. We have extended his derivation to describe a drop located at the top end of a vertical, cylindrical fiber. By minimizing the Gibbs free energy of the drop at the fiber tip, it was found that the drop consists of two portions, a spherical cap on the fiber tip and a full, symmetrical bell located on the fiber body adjacent to the fiber tip. The experimental verification of the predicted shapes was performed using water, ethylene glycol, and Kaydol drops on nylon cylindrical fibers. Only four parameters are required to obtain agreement between the theoretical shape and the observed shape: the drop volume, the fiber radius, the surface tension of the liquid, and the Young contact angle of the liquid on a flat surface of the same composition as the fiber.
1976 年，B.J.卡罗尔推导出一个方程，表明对称的液滴置于细圆柱纤维上时将在平衡状态下呈现钟形。我们已经扩展了他的推导，以描述位于垂直圆柱纤维顶端的液滴。通过最小化纤维尖端处液滴的吉布斯自由能，发现液滴由两部分组成，一部分是纤维尖端上的球形帽，另一部分是位于纤维尖端相邻的纤维主体上的完整对称钟形。使用水、乙二醇和 Kaydol 液滴在尼龙圆柱纤维上进行了预测形状的实验验证。仅需四个参数即可在理论形状和观察到的形状之间获得一致：液滴体积、纤维半径、液体的表面张力以及与纤维相同组成的平面上液体的杨接触角。
