Modeling liquid droplet impact on a micropillar-arrayed viscoelastic surface via mechanically averaged responses

Abstract

Droplet impact on a substrate is an intriguing phenomenon that widely exists in our daily life and a broad range of industrial processes. However, droplet impact dynamics on soft textured surfaces are less explored and the underlying mechanisms remain elusive. Here, we report numerical simulation of droplet impact dynamics on a micropillar-arrayed soft surface using BASILISK, which involves a multiscale geometric domain containing the micropillars and droplet that are in the order of $\text{μ}\mathrm{m}$ and $\mathrm{m}\mathrm{m}$, respectively. As such, the volume of fluid (VOF) method is coupled with the finite volume method (FVM) to build the fluid fields and track their interface. From a conceptual point of view, the micropillared substrate is formed by imposing interstitial gaps into the otherwise intact soft material, whose viscoelastic properties can be quantified by gap density ϵ. Via a five-parameter generalized Maxwell model, the viscoelastic properties of the micropillared substrate can be approximated by its equivalent elastic response in the Laplace–Carson (LC) space, and the averaged bulk strain of the micropillared substrate in the real space is obtained by the inverse LC transform. Moreover, through parametric studies of splash extent, it turns out that for a specific ϵ, the splash is dramatically intensified with increasing impact velocity $U_i$. The splash also turns more violent with increasing ambient pressure $P_a$, which is evidenced by a larger splash angle of ${114.44}^{\circ }$ between the ejected sheet and the horizontal substrate at 5 atm. Conversely, the splash becomes more depressed with increasing surface tension σ. Overall, the splash magnitudes of our simulations agree well with those predicted by the Kelvin-Helmholtz instability theory. By leveraging the LC transform in the fluid-viscoelastic solid interactions, our simulation methodology captures the main features of droplet impact dynamics on microstructured viscoelastic surfaces by means of the mechanically averaged responses while avoiding the predicament of domain scale inconsistency.

Keywords:

• Droplet impact dynamics
• micropillar-arrayed viscoelastic substrate
• finite volume method
• volume of fluid method
• Laplace-Carson transform
• Kelvin-Helmholtz instability

Acknowledgments

The authors would like to thank Mr. Arnaud Antkowiak for helping build the primary simulation model via BASILISK.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementary Materials

The droplet impact movies of the spreading and splashing processes for various cases, shown in Figure 5, Figure 11, Figure 12, and Figure 14, can be found through the following link: https://github.com/comilf/Supplemental-Movies-Used.

Additional information

Funding

This work is partially supported by National Science Foundation (NSF) [grant numbers 2133017 and 1808931].