Porcheron F, Monson P A
Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-9303, USA.
Langmuir. 2006 Feb 14;22(4):1595-601. doi: 10.1021/la051946v.
We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.
我们给出了在平均场近似下求解的晶格气体模型中，粗糙固体表面上液滴的密度分布和接触角的计算结果。对于光滑表面的情况，这种方法得到的接触角可以由杨氏方程很好地描述。我们考虑通过在表面放置有序排列的柱状物来创建粗糙表面，以此模拟所谓的超疏水表面，并针对一系列柱状物高度进行了计算。随着柱状物高度增加，表观接触角呈现出两种状态。在第一种状态下，液体渗透到柱间体积中，接触角在达到恒定值之前随柱状物高度增加。这种行为类似于温泽尔方程所描述的粗糙表面上的接触角情况，尽管接触角被低估了。在第二种状态下，液体基本上不渗透到柱间体积中，接触角与柱状物高度无关。这种情况类似于卡西 - 巴克斯特方程所设想的异质表面上的接触角情况，但该方程高估了接触角。对于更大的柱状物高度，可以观察到液滴的两种状态，一种类似温泽尔状态，另一种类似卡西状态。
