@article{10.1145/3306346.3322962,
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},
year = {2019},
issue_date = {August 2019},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {38},
number = {4},
issn = {0730-0301},
url = {https://doi.org/10.1145/3306346.3322962},
doi = {10.1145/3306346.3322962},
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.},
journal = {ACM Trans. Graph.},
month = {jul},
articleno = {129},
numpages = {14},
keywords = {physical modeling, fluid simulation, differential geometry, geodesics, vorticity methods, vortex filaments}
}