Bubble Rings and Ink Chandeliers

Albert Chern, Felix Knöppel, Marcel Padilla, Ulrich Pinkall, Peter Schröder



Using variable thickness, viscous vortex filaments various phenomena as underwater bubble rings or the intricate “chandeliers” formed by ink dropping into fluid can be realistically modeled.

Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold classical work in the dynamics of vortex filaments can be extended 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.

Both, the underlying theory and associated practical numerical algorithms are provided by the authors of [1]. Supplement material can be found on the project page https://www3.math.tu-berlin.de/geometrie/wp_padilla/on_bubble_rings_and_ink_chandeliers/ .


  • Marcel Padilla, Albert Chern, Felix Knöppel, Ulrich Pinkall, and Peter Schröder.
    On Bubble Rings and Ink Chandeliers.
    ACM Trans. Graph. 38, 4, Article 129, July 2019.

Dr. Albert Chern   +

University: TU Berlin
E-Mail: chern[at]math.tu-berlin.de

Dr. Felix Knöppel   +

Projects: C07
University: TU Berlin
E-Mail: knoeppel[at]math.tu-berlin.de

Marcel Padilla   +

Projects: A05
University: TU Berlin, Institut für Mathematik, MA 823
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31429278
E-Mail: padilla[at]math.tu-berlin.de
Website: https://www3.math.tu-berlin.de/geometrie/wp_padilla/

Prof. Dr. Ulrich Pinkall   +

Projects: A05, C07
University: TU Berlin, Institut für Mathematik, MA 822
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31424607
E-Mail: pinkall[at]math.tu-berlin.de
Website: http://page.math.tu-berlin.de/~pinkall/

Prof. Dr. Peter Schröder   +