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

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 mu m and mm, 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 epsilon. 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 epsilon, 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 degrees between the ejected sheet and the horizontal substrate at 5 atm. Conversely, the splash becomes more depressed with increasing surface tension sigma. 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.