Experimental and fractal analysis on wettability of rough structures

The influence of a rough structure on wettability has been widely studied, but the quantitative relationship between surface wettability and structure with the same roughness has been largely ignored. In this work, a model describing the contact angle of rough surfaces with the same roughness is proposed based on fractal parameters. Hydrophilic or hydrophobic multiscale aluminum alloy random rough surfaces were prepared by chemical etching with different solutions. The fractal dimension and the scale parameter of the rough structures are determined by the fractal roughness model based on the Weierstras–Mandelbrot function. The influences of chemical etching parameters on fractal parameters and wettability were studied by using the extreme variance method. In addition, the theoretical contact angles calculated by the Wenzel and Cassie-Basic models based on fractal parameters are compared with the measured results. Although the Wenzel model is more suitable for the chemical-treated structures, there is a gap between the predicted value and the measured value as it ignores the air gaps between the liquid and the rough surface. The coefficients of the Wenzel model are modified and verified according to the experimental results. For the chemical-treated rough structures, the error between the measured and theoretical values of the modified Wenzel model is about 10%.