Bottiglione F, Carbone G
Politecnico di Bari, Department of Mechanics, Mathematics and Management DMMM and Viale Japigia, 182-70126 Bari, Italy.
J Phys Condens Matter. 2015 Jan 14;27(1):015009. doi: 10.1088/0953-8984/27/1/015009. Epub 2014 Dec 3.
The apparent contact angle of large 2D drops with randomly rough self-affine profiles is numerically investigated. The numerical approach is based upon the assumption of large separation of length scales, i.e. it is assumed that the roughness length scales are much smaller than the drop size, thus making it possible to treat the problem through a mean-field like approach relying on the large-separation of scales. The apparent contact angle at equilibrium is calculated in all wetting regimes from full wetting (Wenzel state) to partial wetting (Cassie state). It was found that for very large values of the roughness Wenzel parameter (r(W) > -1/ cos θ(Y), where θ(Y) is the Young's contact angle), the interface approaches the perfect non-wetting condition and the apparent contact angle is almost equal to 180°. The results are compared with the case of roughness on one single scale (sinusoidal surface) and it is found that, given the same value of the Wenzel roughness parameter rW, the apparent contact angle is much larger for the case of a randomly rough surface, proving that the multi-scale character of randomly rough surfaces is a key factor to enhance superhydrophobicity. Moreover, it is shown that for millimetre-sized drops, the actual drop pressure at static equilibrium weakly affects the wetting regime, which instead seems to be dominated by the roughness parameter. For this reason a methodology to estimate the apparent contact angle is proposed, which relies only upon the micro-scale properties of the rough surface.
对具有随机粗糙自仿射轮廓的二维大液滴的表观接触角进行了数值研究。数值方法基于长度尺度大分离的假设，即假设粗糙度长度尺度远小于液滴尺寸，从而可以通过依赖尺度大分离的类似平均场方法来处理该问题。在从完全润湿（文策尔状态）到部分润湿（卡西状态）的所有润湿状态下计算平衡时的表观接触角。结果发现，对于非常大的粗糙度文策尔参数值（r(W) > -1/ cos θ(Y)，其中θ(Y)是杨氏接触角），界面接近完美的非润湿条件，表观接触角几乎等于180°。将结果与单一尺度粗糙度（正弦表面）的情况进行了比较，发现在相同的文策尔粗糙度参数rW值下，随机粗糙表面情况下的表观接触角要大得多，这证明了随机粗糙表面的多尺度特性是增强超疏水性的关键因素。此外，研究表明，对于毫米级液滴，静态平衡时的实际液滴压力对润湿状态的影响较弱，而润湿状态似乎主要由粗糙度参数决定。因此，提出了一种仅依赖粗糙表面微观尺度特性来估计表观接触角的方法。
