**1. Introduction**

Droplets impinging on solid surfaces are pervasive in nature and industrial production, such as pesticide spraying [1], spray cooling, and inkjet printing [2,3]. A further understanding of this phenomenon is of great importance with the increasing demand for droplet manipulation, such as self-cleaning [4], anti-icing [5,6], and energy harvesting [7]. Although many efforts have been made in this field by researchers, the mechanisms of dynamical behaviors for impinging droplets are not fully clarified.

It is important to recognize that impinging droplets experience a process of spreading, retraction, and eventually bouncing off or depositing on surfaces [8–10]. Many experimental investigations have analyzed the dynamical behaviors of droplets. Wang et al. investigated water droplets impinging on pillar-arrayed polydimethylsiloxane (PDMS) surfaces with different solid fractions and suggested that the lower and upper limits of the Weber number (*We*) for the complete rebound of droplets decreased with solid fractions [11]. Hu et al. revealed the asymmetric spreading and retraction processes in the axial and spanwise directions when droplets impinged on ridged superhydrophobic surfaces. They proposed two theoretical models to quantitatively describe the spreading of droplets for size ratios (the ratio of the ridge diameter to the droplet diameter) as smaller and larger than the critical size ratio [12]. Work by Refael et al. showed the dynamical behaviors of droplets impinging on moving liquid surfaces. Droplets can splash, coalesce with, or bounce off liquid surfaces, which depends on the liquid properties and the velocity of droplets and surfaces [13]. Almohammadi et al. investigated the asymmetric spreading of droplets impinging on a

**Citation:** Zhang, H.; Pan, L.; Xie, X. Molecular Dynamics Simulation on Behaviors of Water Nanodroplets Impinging on Moving Surfaces. *Nanomaterials* **2022**, *12*, 247. https:// doi.org/10.3390/nano12020247

Academic Editors: Antonio Gloria and S M Sohel Murshed

Received: 4 December 2021 Accepted: 7 January 2022 Published: 13 January 2022

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moving surface and developed a model predicting the shape of the lamella. They also discussed the effect of surface wettability on droplets in the retraction process [14].

Recently, the exploration of nanodroplets has become a highly debated topic due to the development of micro and nano technology, such as nanoprinting and nanocoating. However, many important details cannot be displayed in experiments. Molecular dynamics (MD) simulations provide a powerful tool to probe the dynamical behaviors of nanodroplets on an atomic scale. The mechanisms of spreading, break-up, bouncing, and other behaviors of nanodroplets are discussed via MD [15–19]. Chen et al. simulated polymer nanodroplets impinging on a solid surface and found that the viscous dissipation of water nanodroplets stemmed from the velocity gradients in both the impinging and spreading directions [20]. Song et al. investigated the deformation behaviors of water nanodroplets in an electric field and observed the deformation hysteresis phenomenon. The distribution of average dipole orientations in water molecules also showed hysteresis [21]. Kwon et al. presented the dynamical behaviors of a water nanodroplet impinging on a stepped surface with different wetting gradients and step heights [22]. They found three phenomena: fully climbing the step, partially climbing the step, and being blocked by the step, which relied on the normalized step height. MD simulations were also adopted to investigate the influences of surfaces vibrating with high frequency on the wetting mechanism, evaporation, and transportation of nanodroplets [23–26].

However, studies on water nanodroplets impinging on moving solid surfaces are still scarce, especially on high-frequency vibrating surfaces. Due to the rapid development of piezoelectric materials, the frequency of surface acoustic waves (SAW), based on the principle of the inverse piezoelectric effect [27], is up to the level of GHz [28–33]. Therefore, high vibrations of surfaces with a frequency on the order of GHz can be realized. In this paper, the dynamical behaviors of water nanodroplets impinging on translation and vibration surfaces are investigated through MD simulations, respectively. The effects of parameters related to translation and vibration on the dynamical behaviors are explored.
