On Bubble Rings and Ink Chandeliers

Left part: the reconnection of two bubble rings. Our algorithm output (left) vs real life footage (right).
Right part: the breakdown of an inkdrop into an ink chandelier. Real footage (left) vs our output (right).

Abstract

We introduce variable thickness, viscous vortex filaments. These can model such varied phenomena as underwater bubble rings or the intricate "chandeliers" formed by ink dropping into fluid. Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold we are able to extend classical work in the dynamics of vortex filaments through inclusion of viscous drag forces. The latter must be accounted for in low Reynolds number flows where they lead to significant variations in filament thickness and form an essential part of the observed dynamics. We develop and document both the underlying theory and associated practical numerical algorithms.

Submission Video

Bonus Video

Quick Summary

• Extended the vortex filament model
• Used variable thickness
• Added viscosity and gravity
• Reproduced bubble rings
• Reproduced ink chandeliers
• Deep insights about vortex filaments

Talk

Acknowledgements

This work was supported in part by the DFG Collaborative Research Center TRR 109 "Discretization in Geometry and Dynamics," the Caltech Center for Information Science and Technology, and the Einstein Foundation Berlin. Additional support was provided by SideFX software.

Bibtex

@article{Padilla:2019:BRI:3306346.3322962,
  author = {Padilla, Marcel and Chern, Albert and Kn\"{o}ppel, Felix and Pinkall, Ulrich and Schr\"{o}der, Peter},
  title = {On Bubble Rings and Ink Chandeliers},
  journal = {ACM Trans. Graph.},
  issue_date = {July 2019},
  volume = {38},
  number = {4},
  month = jul,
  year = {2019},
  issn = {0730-0301},
  pages = {129:1--129:14},
  articleno = {129},
  numpages = {14},
  url = {http://doi.acm.org/10.1145/3306346.3322962},
  doi = {10.1145/3306346.3322962},
  acmid = {3322962},
  publisher = {ACM},
  address = {New York, NY, USA},
  keywords = {differential geometry, fluid simulation, geodesics, physical modeling, vortex filaments, vorticity methods},
}