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

Authors：Wang, Yi-Feng; Wang, Yi-Bo; He, Xin; Zhang, Ben-Xi; Yang, Yan-Ru; Wang, Xiao-Dong; Lee, Duu-Jong^*

Source：Journal of Fluid Mechanics, 2022, 937: A12.

DOI：10.1017/jfm.2022.115

• drops

This study investigates the dynamics of low-viscosity nanodroplets impacting surfaces with static contact angles from theta = 73 degrees to 180 degrees 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 theta = 180 degrees. 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 beta(max) similar to We(1/5) in the low-Weber-number range (capillary regime) and beta(max) similar to We(2/3)Re(-1/3) (or beta(max) similar to We(1/2)Oh(1/3)) in the high-Weber-number range (cross-over regime) are obtained. Here, We, Re, and Oh are theWeber number, Reynolds number, and Ohnesorge number, respectively. Although the scaling laws are proposed only for the ideal superhydrophobic surface, they are tested valid for. over 73 degrees owing to the ignorable zero-velocity spreading effect. Furthermore, combining the two scaling laws leads to an impact number, We(3/10)Oh(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.