Title

The Shrinking Instability of Toroidal Liquid Droplets in the Stokes Flow Regime

Author(s)/Creator(s)

Mark Bowick, Department of Physics, Syracuse University, Syracuse, NYFollow
Zhenwei Yao, Syracuse University

Document Type

Article

Date

3-30-2011

Language

English

Disciplines

Physics

Description/Abstract

We analyze the stability and dynamics of toroidal liquid droplets. In addition to the Rayleigh instabilities akin to those of a cylindrical droplet there is a shrinking instability that is unique to the topology of the torus and dominates in the limit that the aspect ratio is near one (fat tori). We first find an analytic expression for the pressure distribution inside the droplet. We then determine the velocity field in the bulk fluid, in the Stokes flow regime, by solving the biharmonic equation for the stream function. The flow pattern in the external fluid is analyzed qualitatively by exploiting symmetries. This elucidates the detailed nature of the shrinking mode and the swelling of the cross-section following from incompressibility. Finally the shrinking rate of fat toroidal droplets is derived by energy conservation.

Additional Information

6 pages, 7 figures More information at http://arxiv.org/abs/1011.3437

Recommended Citation

Bowick, Mark and Yao, Zhenwei, "The Shrinking Instability of Toroidal Liquid Droplets in the Stokes Flow Regime" (2011). Physics - All Scholarship. 136.
https://surface.syr.edu/phy/136

Source

Harvested from Arxiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.