Scaling laws of the maximum spreading factor for impact of nanodroplets on solid surfaces

This study investigates the dynamics of low-viscosity nanodroplets impacting surfaces with static contact angles from θ = 73° to 180° via molecular dynamics (MD) simulations. Two typical morphologies of impacting nanodroplets are observed at the maximum spreading state, a Hertz-ball-like in a low-Weber-number range and a thin-film-like in a high-Weber-number range. Only inertial and capillary forces dominate the impact for the former, whereas viscous force also becomes dominant for the latter. Regardless of morphologies at the maximum spreading state, the ratio of spreading time to contact time always remains constant on an ideal superhydrophobic surface with θ = 180°. With the help of different kinematic approximations of the spreading time and scaling laws of the contact time, scaling laws of the maximum spreading factor β_max ∼ We^1/5 in the low-Weber-number range (capillary regime) and β_max ∼ We^2/3Re^-1/3 (or β_max ∼ We^1/2Oh^1/3) in the high-Weber-number range (cross-over regime) are obtained. Here, We, Re, and Oh are the Weber number, Reynolds number, and Ohnesorge number, respectively. Although the scaling laws are proposed only for the ideal superhydrophobic surface, they are tested valid for θ over 73° owing to the ignorable zero-velocity spreading effect. Furthermore, combining the two scaling laws leads to an impact number, We^3/10Oh^1/3 = 2.1. This impact number can be used to determine whether viscous force is ignorable for impacting nanodroplets, thereby distinguishing the capillary regime from the cross-over regime.