Splash of impacting nanodroplets on solid surfaces

Using molecular dynamics (MD) simulations, this study investigates the splash of water nanodroplets on hydrophilic to hydrophobic surfaces with static contact angles ranging from 30 ° to 105 ° in the ranges of $\mathrm{We}=24.76-525$ and Re = 18.43–65.51. Here, We is the Weber number, describing the ratio of inertial to capillary forces, and Re is the Reynolds number, defined as the ratio of inertial to viscous forces. Two splash patterns, internal breakup and prompt splash, are observed under normal conditions. The mechanisms behind these two patterns are found to be different from those of macroscale impacting droplets. The internal rupture of macroscale droplets is attributed to initial air holes on solid surfaces, whereas it arises from the vibration of a nanometer-thick spreading film for nanodroplets. The internal breakup of nanodroplets relies heavily on surface wettability because the attenuation of vibration is much more drastic on hydrophilic surfaces than hydrophobic surfaces owing to larger viscous dissipation rates. A damped harmonic vibration model is developed to characterize the vibration, which verifies the dependence of internal rupture on surface wettability. The prompt splash of macroscale droplets is initiated by air bubbles under the spreading lamella; however, the Rayleigh-Taylor instability of ejected rims caused by a rapidly decelerated spreading lamella gives rise to the prompt splash of nanodroplets. This mechanism is further verified by comparing the number of fingers predicted by the Rayleigh-Taylor instability theory with that obtained by MD simulations. Corona splash has been observed for macroscale droplets at standard atmospheric pressure conditions, but the present simulations show that an extremely high pressure of 1900 kPa is required to trigger it for nanodroplets.

Figure 1

Initial configuration of a nanodroplet impacting a solid surface.

Figure 2

Snapshots of internal rupture for three static contact angles of (a) ${\theta }_0={30}^{\circ }$, (b) 75 °, and (c) 105 ° at $\mathrm{We}=235$.

Figure 3

The time evolution of the flatness factor, ε = $h/D_0$, for the three contact angles at $\mathrm{We}=235$.

Figure 4

The damping factor as a function of surface wettability (a), and the viscous dissipation as a function of static contact angle (b) at $\mathrm{We}=235$.

Figure 5

Snapshots of the rim breakup behavior of nanodroplets, rim breakup for three static contact angles of (a) ${\theta }_0={30}^{\circ }$, (b) 75 °, and (c) 105 ° at $\mathrm{We}=350$.

Figure 6

The splash threshold for three static contact angles of ${\theta }_0={30}^{\circ }$ and 105 °.

Figure 7

The formation of fingers from the edge of the droplet at $\mathrm{We}=300$.

Figure 8

Comparison of the number of fingers between the calculation using Eq. (16) and MD simulations for surfaces with ${\theta }_0={30}^{\circ }$ and 105 ° in a wide range of Weber numbers.

Figure 9

Snapshots of splash behavior for two ambient pressures of (a) $P=101$ kPa and (b) 1900 kPa at $\mathrm{We}=350$.