Numerical simulation and modeling of droplet spreading under smaller Weber numbers

Dynamic of droplet spreading on the free-slip surface was studied numerically by using the Front tracking method (FTM), with particularly interesting in the impacting under relatively small droplet inertias (We ≤ 30). Our predictions of dimensionless droplet maximum spreading diameter β_max agree well with the widely-used Wildeman et al.’s [J. Fluid Mech. 805: 636-655 (2016)] model at We>30. The “1/2 rule” (i.e., approximately one half of the initial kinetic energy finally transfer 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 β_max. Droplet spreading can be divided into three distinct regimes according to the deformation styles, namely, the puddle-shaped regime (I), the transition regime (II) and the pizza-shaped regime (III). Surface energy dominates the energy budget in regime (I), while kinetic energy dominates the energy budget in regime (III). A practical model for estimating β _max 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 and previous experiments.