Seminar by Michiko Shimokawa

Breakup of falling droplets by instability of vortex ring

Michiko Shimokawa* and Hidetsugu Sakaguchi†

* Fukuoka Institute of Technology, Fukuoka, Japan.

† Kyushu University, Fukuoka, Japan.

When a droplet with a relatively high density falls into a miscible solution with a relatively low density, the droplet deforms into a vortex ring and the instability of the vortex ring leads to the droplet breaking up spontaneously. Although it is easy to observe this phenomenon with such things as ink and water, it is difficult to clarify the dynamics as the phenomenon occurs in an unsteady state where the falling velocity and the shape of the droplet and vortex ring changes with time. In a previous paper, we showed that Rayleigh-Taylor instability was an important factor for the instability of the vortex ring derived from the droplet breakup [1]. In this presentation, we focus on the number of the breakup and discuss the physical parameters to determine the number through a consideration of the dynamics.

We investigated the number of the breakup in experiments with several density differences between two solutions, viscosities, and droplet radii when a droplet starts to fall. The mode number has a distribution even under the same experimental conditions. We propose a simple model of mode-selection based on the linear Rayleigh-Taylor instability and the growing radius of the vortex ring deformed from the droplet. The model provides the probability distribution and a relationship between the non-dimensional parameter and the average value of the number of the breakup. The theoretical arguments are consistent with experimental results [2].

[1] M. Shimokawa, R. Mayumi, T. Nakamura, T. Takami, and H. Sakaguchi, Phys. Rev. E 93, 062214 (2016).

[2] M. Shimokawa & H. Sakaguchi, Physical Review Fluids, Phys. Rev. Fluids 4, 013603 (2019).