College of Textiles, North Carolina State University, 2401 Research Drive, Raleigh, North Carolina 27695-8301, USA.
Langmuir. 2011 Oct 4;27(19):11867-72. doi: 10.1021/la202952e. Epub 2011 Sep 8.
Small drops can move spontaneously on conical fibers. As a drop moves along the cone, it must change shape to maintain a constant volume, and thus, it must change its surface energy. Simultaneously, the exposed surface area of the underlying cone must also change. The associated surface energies should balance each other, and the drop should stop moving when it reaches a location where the free energy is a minimum. In this paper, a minimum Gibbs free energy analysis has been performed to predict where a drop will stop on a conical fiber. To obtain the Gibbs free energies of a drop at different locations of a conical fiber, the theoretical expressions for the shape of a droplet on a conical fiber are derived by extending Carroll's equations for a drop on a cylindrical fiber. The predicted Gibbs free energy exhibits a minimum along the length of the cone. For a constant cone angle, as the contact angle between the liquid and the cone increases, the drop will move toward the apex of the cone. Likewise, for a constant contact angle, as the cone angle increases, the drop moves toward the apex. Experiments in which water and dodecane were placed on glass cones verify these dependencies. Thus, the final location of a drop on a conical fiber can be predicted on the basis of the geometry and surface energy of the cone, the surface tension and volume of the liquid, and the original location where the drop was deposited.
小液滴可以在锥形纤维上自发移动。当液滴沿着圆锥体移动时，它必须改变形状以保持恒定的体积，因此，它必须改变其表面能。同时，基底圆锥体的暴露表面积也必须改变。相关的表面能应该相互平衡，当液滴到达自由能最小的位置时，它应该停止移动。在本文中，进行了最小吉布斯自由能分析，以预测液滴在锥形纤维上的停止位置。为了获得锥形纤维上不同位置液滴的吉布斯自由能，通过扩展 Carroll 对圆柱纤维上液滴的方程，推导出了锥形纤维上液滴形状的理论表达式。预测的吉布斯自由能沿圆锥体的长度表现出最小值。对于恒定的锥角，随着液体与圆锥体之间的接触角增加，液滴将向圆锥体的顶点移动。同样，对于恒定的接触角，随着锥角的增加，液滴向顶点移动。在玻璃圆锥体上放置水和十二烷烃的实验验证了这些依赖性。因此，可以根据圆锥体的几何形状和表面能、液体的表面张力和体积以及液滴沉积的原始位置来预测液滴在锥形纤维上的最终位置。
