Droplet penetration through a prewetted hole array

Droplet penetration through prewetted hole arrays was investigated experimentally and theoretically, with particular attention to the effects of film thickness, hole diameter, and Weber number. It was found that complete penetration is confined to a finite radial zone centered on the impact axis, whose width decreases with increasing film thickness but increases with the Weber number and the hole diameter. The initial radial distribution of jet velocities penetrating the plate exhibits a characteristic radial decay with an arc-like envelope, which serves as the governing scaling parameter. A semi-empirical model based on the classical stagnation potential-flow theory, accounting for capillary resistance, was developed to predict the initial velocity of the penetrating jet. An energy balance for the pendant droplet forming at the hole exit yields a threshold jet velocity separating jet retraction from breakup. This threshold, combined with the spatially decaying velocity field, enables the prediction of both the threshold Weber number for complete penetration and the normalized width of the complete-penetration zone. Model predictions agree quantitatively with experimental measurements across a range of film thicknesses and hole diameters. It is suggested that the liquid film pre-wetting the plate acts as a hydrodynamic cushion, redistributing the impact momentum radially and thereby suppressing penetration.