Numerical study of a vertically eccentric hollow droplet impacting on a small cylinder

doi:10.7523/j.ucas.2025.048

Abstract

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 rebound， breakup-retraction， continuous breakup， and top breakup. 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， the maximum spreading ratio of the hollow droplet during impact is a non-monotonic function of the bubble’s vertical position within the range of parameters considered. 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

CLC Number:

TK124

Linkai YANG, Longmin TANG, Guangzhao ZHOU. Numerical study of a vertically eccentric hollow droplet impacting on a small cylinder[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(2): 145-154.

Figures/Tables 7

Fig.1 Initial setup and relevant parameters

Fig.2 Gas-liquid interface shapes of hollow droplets under different eccentricities at the moment the droplet is cut off

Fig.3 Four typical regimes of the eccentric hollow droplet impact dynamics

Fig.4 Phase diagram of four typical regimes in the parameter space spanned by We and ξ

Fig.5 Key physical quantities as function of time

Fig.6 Variation of the maximum spreading ratio withξ at different We values

Fig.7 Variation of droplet breaking time tc* with ξ at different We values

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