McHale G
School of Biomedical & Natural Sciences, Nottingham Trent University, Clifton Lane, Nottingham, UK.
Langmuir. 2007 Jul 17;23(15):8200-5. doi: 10.1021/la7011167. Epub 2007 Jun 20.
The properties of superhydrophobic surfaces are often understood by reference to the Cassie-Baxter and Wenzel equations. Recently, in a paper deliberately entitled to be provocative, it has been suggested that these equations are wrong; a suggestion said to be justified using experimental data. In this paper, we review the theoretical basis of the equations. We argue that these models are not so much wrong as have assumptions that define the limitations on their applicability and that with suitable generalization they can be used with surfaces possessing some types of spatially varying defect distributions. We discuss the relationship of the models to the previously published experiments and using minimum energy considerations review the derivations of the equations for surfaces with defect distributions. We argue that this means the roughness parameter and surface area fractions are quantities local to the droplet perimeter and that the published data can be interpreted within the models. We derive versions of the Cassie-Baxter and Wenzel equations involving roughness and Cassie-Baxter solid fraction functions local to the three-phase contact line on the assumption that the droplet retains an average axisymmetry shape. Moreover, we indicate that, for superhydrophobic surfaces, the definition of droplet perimeter does not necessarily coincide with the three-phase contact line. As a consequence, the three-phase contact lines within the contact perimeter beneath the droplet can be important in determining the observed contact angle on superhydrophobic surfaces.
超疏水表面的特性通常通过参考卡西 - 巴克斯特(Cassie - Baxter)方程和温泽尔(Wenzel)方程来理解。最近,在一篇故意取了挑衅性标题的论文中,有人提出这些方程是错误的;据称这一观点有实验数据作为支撑。在本文中,我们回顾了这些方程的理论基础。我们认为这些模型并非错误,而是其假设限定了它们的适用范围,并且通过适当的推广,它们可用于具有某些类型空间变化缺陷分布的表面。我们讨论了这些模型与先前已发表实验的关系,并利用最小能量考虑因素回顾了具有缺陷分布表面方程的推导过程。我们认为这意味着粗糙度参数和表面积分数是液滴周边局部的量,并且已发表的数据可以在这些模型内得到解释。在液滴保持平均轴对称形状的假设下,我们推导了涉及粗糙度和三相接触线局部卡西 - 巴克斯特固体分数函数的卡西 - 巴克斯特方程和温泽尔方程的版本。此外,我们指出,对于超疏水表面,液滴周边的定义不一定与三相接触线重合。因此,液滴下方接触周边内的三相接触线在确定超疏水表面上观察到的接触角时可能很重要。