Surface roughness has been known to facilitate droplet breakup, but the effects of surface morphology on the breakup threshold have not yet been quantitatively clarified. In this paper, numerical simulations are carried out to investigate the fate of a shear-thinning droplet impacting on specially designed randomly rough surfaces. By resorting to a total of 1380 in-silico experiments, deposition state diagrams are constructed, which can offer three types of state as a function of the Weber number and the surface morphology quantified by the root-mean-square roughness (Rr) and the Wenzel roughness parameter (Wr). Results show that it is Rr rather than Wr that can effectively promote droplet splash. Furthermore, critical velocities that can ensure a non-splashing state are identified for different sized droplets impacting on surfaces with different morphologies. This quantitative information has great potential to facilitate operational optimization in a wide range of applications demanding non-splash droplets.

已知表面粗糙度会促进液滴破裂，但表面形态对破裂阈值的影响尚未定量阐明。在本文中，进行数值模拟以研究剪切稀化液滴撞击专门设计的随机粗糙表面的命运。通过总共 1380 次计算机模拟实验，构建了沉积状态图，它可以提供三种类型的状态作为韦伯数和由均方根粗糙度 ( Rr ) 和表面形貌量化的函数Wenzel 粗糙度参数 ( Wr )。结果显示是Rr而不是Wr能有效促进飞沫飞溅。此外，对于影响具有不同形态的表面的不同尺寸的液滴，确定了可以确保非飞溅状态的临界速度。这种定量信息具有很大的潜力，可以促进需要非飞溅液滴的广泛应用中的操作优化。