Effects of surface roughness on droplet impact dynamics

Past investigations into droplet impact dynamics have mostly used either relatively smooth substrates or air-trapping superhydrophobic textures. For this reason, existing models for predicting the maximum spreading ratio of impacting droplets (β_max = D_max/D₀) are unable to capture the influence of surface roughness. In this study, we investigate the influence of roughness and substrate wettability on the dynamics of water impacting at Weber numbers where splashing is minimal, with a specific focus on the maximal spreading diameter of Wenzel droplets. The surface mean roughness amplitude, R_a, was varied widely by laser etching substrates comprised of either glass (R_a = 0.012-22.49 µm), PETG (R_a = 1.18-55.04 µm), or aluminum (R_a = 2.21-58.31 µm). The surface wettability ranged from strongly hydrophilic to weakly hydrophobic and depended on the choice of substrate material, the extent of surface roughness, and the roughness-dependent modification of the intrinsic wettability due to the laser or hydrocarbon adsorption. We develop a new energy model for predicting β_max for both elastic (We < 30) and inelastic (We ≥ 30) droplet impact regimes, where surface energy and viscous dissipation terms are modified to incorporate surface roughness effects. We show that the universality of existing (roughness-independent) models for β_max becomes incomplete for roughness ratios of r ≳ 2, whereas our roughness-dependent model has excellent agreement across all r values. By explicitly incorporating surface roughness into the energy balance, we extend the predictive capability of droplet spreading models to achieve an extended predictive framework for water-droplet spreading on rough substrates.