Lobaton E J, Salamon T R
Mathematical and Algorithmic Sciences Research Center, Bell Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
J Colloid Interface Sci. 2007 Oct 1;314(1):184-98. doi: 10.1016/j.jcis.2007.05.059. Epub 2007 May 25.
The interface shape separating a gas layer within a superhydrophobic surface consisting of a square lattice of posts from a pressurized liquid above the surface is computed numerically. The interface shape is described by a constant mean curvature surface that satisfies the Young-Laplace equation with the three-phase gas-liquid-solid contact line assumed pinned at the post outer edge. The numerical method predicts the existence of constant mean curvature solutions from the planar, zero curvature solution up to a maximum curvature that is dependent on the post shape, size and pitch. An overall force balance between surface tension and pressure forces acting on the interface yields predictions for the maximum curvature that agree with the numerical simulations to within one percent for convex shapes such as circular and square posts, but significantly over predicts the maximum curvature for non-convex shapes such as a circular post with a sinusoidal surface perturbation. Changing the post shape to increase the contact line length, while maintaining constant post area, results in increases of 2 to 12% in the maximum computable curvature for contact line length increases of 11 to 77%. Comparisons are made to several experimental studies for interface shape and pressure stability.
对由方形柱阵列构成的超疏水表面内的气体层与表面上方的加压液体之间的界面形状进行了数值计算。界面形状由常平均曲率曲面描述，该曲面满足杨氏-拉普拉斯方程，且假设三相气-液-固接触线固定在柱体的外边缘。数值方法预测了从平面零曲率解到最大曲率的常平均曲率解的存在，最大曲率取决于柱体的形状、尺寸和间距。作用在界面上的表面张力和压力之间的整体力平衡得出了最大曲率的预测结果，对于圆形和方形柱体等凸形形状，该预测结果与数值模拟结果的误差在1%以内，但对于具有正弦表面扰动的圆形柱体等非凸形形状，却显著高估了最大曲率。在保持柱体面积不变的情况下，改变柱体形状以增加接触线长度，会使接触线长度增加11%至77%时，最大可计算曲率增加2%至12%。并与几项关于界面形状和压力稳定性的实验研究进行了比较。
