Size matching effect on Wenzel wetting on fractal surfaces

Materials with fractal structures may show distinct features of wetting. Here we report the characteristics of wetting of liquid caps on fractal surfaces in the Wenzel wetting regime. It shows that the relationship between the apparent and Young's contact angles is associated with the size-matching degree or discrepancy between the liquid caps and substrate. An explicitly fractal-dimension-and size-related equation is developed to bridge over the apparent contact angle and the Young's contact angle, and validated by the experimental results of water wetting on nanostructured fractal surfaces reported in the literature. The features of the Wenzel wetting of liquid caps on fractal surfaces are also discussed. This work enables us to understand the wetting regimes on fractal surfaces, and may pave a path for the rational uses of fractal structures to control liquid wetting.