Advanced Materials and Technologies Laboratory, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University , Blacksburg, Virginia 24061-0238, United States.
Langmuir. 2017 Jul 18;33(28):7181-7190. doi: 10.1021/acs.langmuir.7b01524. Epub 2017 Jul 6.
This paper presents a fractal model to describe wettability on multiscale randomly rough surfaces. Hydrophobic or superhydrophobic surfaces, produced by processes such as electrodeposition and etching, lead to the creation of random roughness at multiple length scales on the surface. This paper considers the description of such surfaces with a fractal asperity model based on the Weierstrass-Mandelbrot (W-M) function, where the fractal parameters are uniquely determined from a power spectrum of the surface. By use of this description, a model is presented to evaluate the apparent contact angle in the different wetting regimes. The model is predictive in that it does not use any empirical or correlatory fitting of parameters to experimental data. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. The contact angle is found be strongly dependent on the range of asperity length scale and weakly dependent on the fractal dimension for a surface with stable Cassie state. Based on the fractal description, desired surface roughness characteristics for generating superhydrophobicity on a particular substrate are also derived.
本文提出了一种分形模型来描述多尺度随机粗糙表面的润湿性。通过电沉积和蚀刻等工艺生产的疏水性或超疏水性表面会在表面的多个长度尺度上产生随机粗糙度。本文考虑使用基于 Weierstrass-Mandelbrot (W-M) 函数的分形粗糙模型来描述这种表面，其中分形参数可以从表面的功率谱中唯一确定。通过这种描述，提出了一种模型来评估不同润湿状态下的表观接触角。该模型具有预测性，因为它不使用任何经验或相关性拟合参数来拟合实验数据。在不同处理条件下在几种材料上生成的各种疏水性和超疏水性表面上进行了模型预测的实验验证。结果表明，对于具有稳定 Cassie 状态的表面，接触角强烈依赖于粗糙度长度尺度范围，而对分形维数的依赖性较弱。基于分形描述，还推导出了在特定基底上产生超疏水性所需的表面粗糙度特征。
