The splashing behavior of droplets impinging on rough surfaces is of significant importance for micro-scale engineering applications such as water management in proton exchange membrane fuel cells. In this study, the critical splashing characteristics of 10 μm water droplets impacting surfaces with different roughness levels (0.01–0.8 μm) in a hydrogen environment are investigated numerically. Random rough surfaces are constructed using the Weierstrass–Mandelbrot fractal function, while the coupled level-set and volume-of-fluid method and the Blake dynamic contact angle model are employed to capture interface evolution and dynamic wetting behavior, respectively. The results reveal that (1) a critical dimensionless roughness Rac* = 0.006 (defined as 2Ra/D0) is identified. Below this threshold, the critical Weber number remains largely unaffected by roughness, with corona splash being the dominant mechanism. Above this value, the critical Weber number decreases following a power-law trend with increasing roughness, and the splash mechanism transitions to finger splash. (2) A correlation between the critical Weber number and dimensionless roughness is established as Wec≥K(8cosθ0 )3/5(2Ra/D0)−a, which shows good agreement with experimental data from millimeter-sized droplets, thereby validating the cross-scale applicability of the critical roughness concept. The findings provide theoretical insights for predicting micrometer-sized droplet splashing and optimizing the design of fuel cell flow channel walls.
Li et al. (Wed,) studied this question.