Numerical simulations of a toroidal droplet breakup in viscous oils

Abstract

Toroidal droplets are inherently unstable in viscous oils; they either shrink to a single drop or break into several spherical droplets due to Rayleigh–Plateau instability. In this paper, the breakup dynamics of toroidal droplets in immiscible viscous oils have been numerically investigated. A two-dimensional model combined level-set method is proposed. Numerical results reveal that the initial aspect ratios, interfacial tensions, and outer liquid viscosities play important roles in determining the breakup dynamics of toroidal droplets. The initial aspect ratios dominate the number of split droplets, which is consistent with a linearly scaling law n = 0.57 R0/ a0. By considering key factors of interfacial tension in this process, it is found that interfacial tension is crucial in the initial morphology of the toroidal droplet and helps to retard the unstable breakup dynamics. Interestingly, reducing the interfacial tension stabilizes it against breakup. We further study the effect of viscosity on the breakup dynamics. The surrounding viscous oils contribute to stabilizing the interfacial-tension-driven instabilities and extending the breakup time. Thus, for a toroidal droplet in high viscosity oils and a sufficiently low interfacial tension system, the unstable breakup dynamics could be delayed. Our findings provide a novel fundamental understanding of toroidal droplets and are beneficial to applications involving the manipulation of toroidal droplets.