Abstract: This paper presents a direct numerical simulation study of the effect of bubble vertical eccentricity on the behavior of a hollow droplet impacting on a super-hydrophobic cylindrical target. Based on the topological changes the droplet undergoes during impact, four typical regimes are identified: direct bounce, break-retract, break-break, and top break. The transitions between these regimes are analyzed in relation to the dimensionless parameters including the Weber number and bubble eccentricity ratio. Furthermore, the temporal evolution of key physical quantities, such as the spreading ratio, velocity, and kinetic energy, is discussed for each regime. Quantitative analysis further reveals that, with the range of parameters considered, the maximum spreading ratio of the hollow droplet during impact is a non-monotonic function of the bubble's vertical position. For relatively large Weber numbers, a smaller degree of bubble eccentricity facilitates droplet spreading. On the other hand, the dimensionless rupture time demonstrates an approximately linear relationship with the bubble eccentricity ratio, while exhibiting only a weak correlation with the Weber number.

Key words: hollow droplet, bubble eccentricity, droplet impact, topological change