A ligament, after pinch-off, breaks into main droplets and much smaller satellite droplets. Satellite droplets form due to pinch-off asymmetry, yet their size distribution remains poorly understood. We investigate the satellite droplet formation in ligament breakup, considering both viscosity and stretching effects. The ligament with viscosity m = 1–1000 mPa s and initial radius R = 400–740 mm, is stretched bidirectionally at a constant acceleration a = 0:002–25 m/s2, see Fig. 1(a). Results show that viscosity reduces while stretching enlarges the satellite radius, with experimentally observed radii ranging from Rs = 2–290 mm, see Fig. 1(b,c). Two limits regimes are identified: an inviscid limit with Rs;in(We) 0:33We0:45 +0:045, and a viscous limit with Rs;vis(Ca) = F(Ca)Oh2:23. A two-dimensional model [1] is applied to predict the satellite radius. In most cases, numerical results agree well with experiments, see Fig. 1(b). However, we observed that at high viscosities, satellite droplets remain undetectable in experiments (see Fig. 1(d)), even when numerical predictions yield Rs 20 mm. Preliminary analysis suggests that this discrepancy may arise because thermal fluctuations disrupt the classical pinch-off process [2]. Our results can be applied to control the satellite size in various industrial applications.
Contributors
Xiaofeng Wei (1), Fangye Lin (2), Chengxi Zhao (3), Dongyun Wang (1), and Benoit Scheid (4)
1. College of engineering, Zhejiang Normal University, 321004 Jinhua, China
2. Ningbo Innovation Center, Zhejiang University, 315048 Ningbo, China
3. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China
4. TIPs - Fluid Physics Unit, Universit´e Libre de Bruxelles C.P. 165/67, 1050 Brussels, Belgium
References
[1] X. Wei, J. Rivero-Rodr´ıguez, J. Zou, and B. Scheid, Journal of Fluid Mechanics, 922 (2021), A14.
[2] M. Brenner, X. Shi, and S. Nagel, Physical Review Letters, 73 (1994), 3391.
