Viscous droplets impact on rough surfaces

We experimentally investigate the dynamics of viscous droplets impacting on rough surfaces under a broad range of Weber number ($2\le \mathrm{We}\le 1,194$), Ohnesorge number ($0.002\le \mathrm{Oh}\le 2.630$), and average surface roughness ($9.7\mu m\le R_a\le 19.5\mu m$). Three primary impact outcomes—jetting, spreading, and splashing—are observed. Our findings reveal that surface roughness promotes splashing by amplifying perturbations, while liquid viscosity counters this effect by dissipating the kinetic energy of the advancing lamella. We empirically describe the splashing threshold with the relation as $\mathrm{Oh}{\mathrm{Re}}^{\chi \left(R_a\right)}=K\left(R_a\right)$, where the fitting parameter $K\left(R_a\right)$ increases and $\chi \left(R_a\right)$ decreases with greater surface roughness. Moreover, the maximum spreading factor (${\beta }_m$), defined as the ratio of the droplet’s maximum spreading diameter to its initial diameter, shows a pronounced dependence on surface roughness in low-viscosity conditions ($\mathrm{Oh}<0.050$), but this dependence diminishes in high-viscosity regimes ($\mathrm{Oh}\ge 0.050$). This trend results from the interplay between viscous dissipation induced by surface roughness and the intrinsic liquid viscosity. In the low-viscosity regime, the experimental ${\beta }_m$ is consistent with the empirical scaling law of ${\beta }_m=a{(\mathrm{We}/\mathrm{Oh})}^b$, with the fitting constants, $a$ and $b$, varying with surface roughness and liquid properties. In the regime of $0.050<\mathrm{Oh}<1$, ${\beta }_m$ approximates ${(\mathrm{We}/\mathrm{Oh})}^{1/6}$. These findings elucidate the significant role of surface roughness and liquid viscosity in governing droplet impact dynamics and spreading.