Double Bubbles Sans Toil and Trouble:
Discrete Circulation-Preserving Vortex Sheets
for Soap Films and Foams

Fang Da Christopher Batty Chris Wojtan Eitan Grinspun
Columbia University University of Waterloo IST Austria Columbia University


Simulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional many-phase Navier-Stokes solver, even though their visual appearance is completely dominated by the thin liquid surface. We depart from earlier work on soap bubbles and foams by noting that their dynamics are naturally described by a Lagrangian vortex sheet model in which circulation is the primary variable. This leads us to derive a novel circulation-preserving surface-only discretization of foam dynamics driven by surface tension on a non-manifold triangle mesh. We represent the surface using a mesh-based multimaterial surface tracker which supports complex bubble topology changes, and evolve the surface according to the ambient air flow induced by a scalar circulation field stored on the mesh. Surface tension forces give rise to a simple update rule for circulation, even at non-manifold Plateau borders, based on a discrete measure of signed scalar mean curvature. We further incorporate vertex constraints to enable the interaction of soap films with wires. The result is a method that is at once simple, robust, and efficient, yet able to capture an array of soap films behaviors including foam rearrangement, catenoid collapse, blowing bubbles, and double bubbles being pulled apart.


[MP4], [YouTube], [more bubbles]
Technical Report:
[Columbia Academic Commons]
Poster at TWIG 2015:
Hindsight (Improvement):
[Convergence and Stability at Multi-Bubble Junctions]
Houdini Plugin (by Sergen Eren):


In its derivation of Equation (9), this paper incorrectly argues that the material derivative commutes with the gradient due to linearity of differentiation. Please see Pozrikidis [2000] for a more involved derivation of the same equation of motion (Equation 3.20 in that paper) which does not rely on the gradient commuting with the material derivative.


    author = "Fang Da and Christopher Batty and Chris Wojtan and Eitan Grinspun",
    title = "Double Bubbles Sans Toil and Trouble: Discrete Circulation-Preserving Vortex Sheets for Soap Films
             and Foams",
    journal = {ACM Trans. on Graphics (SIGGRAPH 2015)},
    year = 2015

This work was supported in part by the NSF (Grant IIS-1319483), ERC (Grant ERC-2014-StG-638176), NSERC (Grant RGPIN-04360-2014), Adobe, and Intel. We would also like to thank Henrique Teles Maia, Dingzeyu Li, Yonghao Yue, Papoj Thamjaroenporn and Rohan Sawhney for their assistance.