The Saturnian droplet

Abstract

Electrohydrodynamic instabilities at liquid interfaces continue to defy our intuition, from the pioneering work of Taylor (Proc. R. Soc. Lond. A, vol. 280, issue 1382, 1964, pp. 383-397) on conical tips of electrified droplets to a recent numerical study by Wagoner et al. (J. Fluid Mech., vol. 904, 2020, R4). The problem studied by Wagoner et al. (2020) consists of a droplet immersed in a more conducting and more dielectric liquid medium, in a strong electrical field. When the droplet is more viscous than the outer medium, the droplet develops a biconcave shape which might eventually evolve to a torus shape (or doughnut). In contrast, when the droplet is less viscous, it adopts a lenticular shape and emits a thin fluid sheet from its equator which in turn breaks up into droplets. These droplets form a ring of satellites around the original droplet, which justifies its appellation 'Saturnian droplet'. The numerical simulations bring light to this complex phenomenon and confirm the robustness of the leaky-dielectric framework (Melcher & Taylor, Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111-146).