Abstract
The dynamic of droplet spreading on a free-slip surface was studied experimentally and numerically, with particularly interest in the impacts under relatively small droplet inertias (We≤30). Our experimental results and numerical predictions of dimensionless droplet maximum spreading diameter βmax agree well with those of Wildeman et al.’s widely-used model at We>30. The “1/2 rule” (i.e., approximately one half of the initial kinetic energy Ek0 finally transferred into surface energy) was found to break down at small Weber numbers (We≤30) and droplet height is non-negligible when the energy conservation approach is employed to estimate βmax. As We increases, surface energy and kinetic energy alternately dominates the energy budget. When the initial kinetic energy is comparable to the initial surface energy, competition between surface energy and kinetic energy finally results in the non-monotonic energy budget. In this case, gas viscous dissipation contributes the majority of the dissipated energy under relatively large Reynolds numbers. A practical model for estimating βmax under small Weber numbers (We≤30) was proposed by accounting for the influence of impact parameters on the energy budget and the droplet height. Good agreement was found between our model predictions and previous experiments.