Touchdown dynamics of a liquid droplet on a patterned substrate: A generalized lumped parameter-based model

Droplet dynamics post-impingement on a solid surface is of immense technological importance due to its applicability in self-cleaning, anti-frosting, anti-biofouling, anti-icing, thermal management, and inkjet printing. While sustained droplet oscillation is desirable in some applications, a fast seizure of oscillations after the surface touchdown of the droplets is necessary for others. The post-impingement dynamics is a complex non-linear interaction of the fluid and solid properties and a common framework to characterize the short-time response of a droplet is provided here. We describe these post-impact droplet dynamics on a patterned surface in terms of lumped simple harmonic oscillator parameters. We delineate the effect of the substrate and fluid properties and attribute the same to one or more terms in the dynamical model of the oscillator, describing an analogy between the terms. Our analogy gives a universal mapping between the fluid-solid parameters and droplet dynamics, making it feasible to predict with accuracy the post-impact behavior. Here for the first time, we developed a simplified universal approach to predict the droplet oscillation dynamics impacting any solid surface for a broad range of fluid and solid properties and impingement conditions.