Scaling laws governing droplet spreading and merging dynamics on solid surfaces: a molecular simulation study

This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged droplet and the associated energy conversion. The process is primarily controlled by the amount of energy converted into kinetic energy after dissipation. At high impact velocities, the energy conversion efficiency becomes constant, with only about 1% lost due to surface adhesion-an effect that diminishes with increasing velocity. Factors such as impact velocity, droplet size, surface texture, and wettability significantly influence the jumping velocity. Scaling laws are developed for the maximum spreading time, spreading factor, and restitution coefficient based on the Weber (We) and Reynolds (Re) numbers, which differ from those for single droplet impacts. On superhydrophobic surfaces, the spreading time is approximated as $t_{\mathrm{sp}}\approx 3r/V_i$ , and its dimensionless form scales linearly with $W{e}^{0.31}$ . The general scaling law for the spreading factor is ${\beta }_{\max }\sim W{e}^{0.5\alpha }R{e}^{\alpha }$ , where $\alpha =0.1$ for velocity-dependent and $\alpha =0.24$ for velocity-independent spreading regimes.