“Animating bubble interactions in a liquid foam” by Busaryev, Dey, Wang and Ren

Bubbles and foams are important features of liquid surface phenomena, but they are difficult to animate due to their thin films and complex interactions in the real world. In particular, small bubbles (having diameter <1cm) in a dense foam are highly affected by surface tension, so their shapes are much less deformable compared with larger bubbles. Under this small bubble assumption, we propose a more accurate and efficient particle-based algorithm to simulate bubble dynamics and interactions. The key component of this algorithm is an approximation of foam geometry, by treating bubble particles as the sites of a weighted Voronoi diagram. The connectivity information provided by the Voronoi diagram allows us to accurately model various interaction effects among bubbles. Using Voronoi cells and weights, we can also explicitly address the volume loss issue in foam simulation, which is a common problem in previous approaches. Under this framework, we present a set of bubble interaction forces to handle miscellaneous foam behaviors, including foam structure under Plateau’s laws, clusters formed by liquid surface bubbles, bubble-liquid and bubble-solid coupling, bursting and coalescing. Our experiment shows that this method can be straightforwardly incorporated into existing liquid simulators, and it can efficiently generate realistic foam animations, some of which have never been produced in graphics before.

1. Adams, B., Pauly, M., Keiser, R., and Guibas, L. J. 2007. Adaptively sampled particle fluids. ACM Transactions on Graphics (SIGGRAPH) 26 (July). Google ScholarDigital Library
2. Aurenhammer, F. 1987. Power diagrams: properties, algorithms and applications. SIAM Journal on Computing 16, 78–96. Google ScholarDigital Library
3. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. of SIGGRAPH ’98, E. Fiume, Ed., Computer Graphics Proceedings, Annual Conference Series, ACM, 43–54. Google ScholarDigital Library
4. Bargteil, A. W., Goktekin, T. G., O’brien, J. F., and Strain, J. A. 2006. A semi-Lagrangian contouring method for fluid simulation. ACM Transactions on Graphics 25 (January), 19–38. Google ScholarDigital Library
5. Bargteil, A. W., Wojtan, C., Hodgins, J. K., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Transactions on Graphics (SIGGRAPH) 26 (July). Google ScholarDigital Library
6. Brakke, K. A. 1992. The Surface Evolver. Experimental Mathematics 1, 2, 141–165.Google ScholarCross Ref
7. Brochu, T., Batty, C., and Bridson, R. 2010. Matching fluid simulation elements to surface geometry and topology. ACM Transactions on Graphics (SIGGRAPH) 29 (July), 47:1–47:9. Google ScholarDigital Library
8. Cazals, F., Kanhere, H., and Loriot, S. 2011. Computing the volume of a union of balls: a certified algorithm. INRIA 2009 no 7013 Technical report, August, 1–19.Google Scholar
9. Chentanez, N., and Müller, M. 2011. Real-time Eulerian water simulation using a restricted tall cell grid. ACM Transactions on Graphics (SIGGRAPH) 30 (Aug.), 82:1–82:10. Google ScholarDigital Library
10. Choi, K.-J., and Ko, H.-S. 2002. Stable but responsive cloth. ACM Transactions on Graphics (SIGGRAPH) 21 (July), 604–611. Google ScholarDigital Library
11. Cleary, P. W., Pyo, S. H., Prakash, M., and Koo, B. K. 2007. Bubbling and frothing liquids. ACM Transactions on Graphics (SIGGRAPH) 26 (July). Google ScholarDigital Library
12. Durian, D. J. 1995. Foam mechanics at the bubble scale. Physical Review Letters 75 (Dec), 4780–4783.Google ScholarCross Ref
13. Durikovic, R. 2001. Animation of soap bubble dynamics, cluster formation and collision. Computer Graphics Forum 20, 3, 67–.Google ScholarCross Ref
14. Edelsbrunner, H. 2001. Geometry and Topology for Mesh Generation. Cambridge University Press, England. Google ScholarDigital Library
15. Enright, D., Marschner, S., and Fedkiw, R. 2002. Animation and rendering of complex water surfaces. ACM Transactions on Graphics (SIGGRAPH 2002) 21 (July), 736–744. Google ScholarDigital Library
16. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graphical Models and Image Processing 58 (September), 471–. Google ScholarDigital Library
17. Gardiner, B., Dlugogorski, B., and Jameson, G. 2000. The steady shear of three-dimensional wet polydisperse foams. Journal of Non-Newtonian Fluid Mechanics 92, 151–166.Google ScholarCross Ref
18. Greenwood, S. T., and House, D. H. 2004. Better with bubbles: enhancing the visual realism of simulated fluid. In Proc. of SCA. Google ScholarDigital Library
19. Herzhafta, B., Kakadjianb, S., and Moanc, M. 2005. Measurement and modeling of the flow behavior of aqueous foams using a recirculating pipe rheometer. Colloids and Surfaces A: Physicochem. Eng. Aspects 263, 153–164.Google ScholarCross Ref
20. Hong, J.-M., and Kim, C.-H. 2003. Animation of bubbles in liquid. Computer Graphics Forum 22, 3, 253–262.Google ScholarCross Ref
21. Hong, J.-M., Lee, H.-Y., Yoon, J.-C., and Kim, C.-H. 2008. Bubbles alive. ACM Transactions on Graphics 27 (August), 48:1–48:4. Google ScholarDigital Library
22. Hou, Q., and Zhou, K. 2011. A shading reuse method for efficient micropolygon ray tracing. ACM Transactions on Graphics (SIGGRAPH Asia) 30 (Dec.), 151:1–151:8. Google ScholarDigital Library
23. Kelager, M. 2009. Vertex-based simulation of dry foam. In Master Thesis, University of Copenhagen, Denmark.Google Scholar
24. Kim, B., Liu, Y., Llamas, I., Jiao, X., and Rossignac, J. 2007. Simulation of bubbles in foam with the volume control method. ACM Transactions on Graphics (SIGGRAH) 26 (July). Google ScholarDigital Library
25. Kim, Y., Seol, Y., Lai, M.-C., and Peskin, C. S. 2011. The immersed boundary method for two-dimensional foam with topological changes. Communications in Computational Physics.Google Scholar
26. Kraynik, A. M., Reinelt, D. A., and van Swol, F. 2003. Structure of random monodisperse foam. Physical Review E 67.Google Scholar
27. Kraynik, A. M., Reinelt, D. A., and van Swol, F. 2004. Structure of random foam. Physical Review Letters 93, 20.Google ScholarCross Ref
28. Kück, H., Vogelgsang, C., and Greiner, G. 2002. Simulation and rendering of liquid foams. In Proc. of Graphics Interface, 81–88.Google Scholar
29. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM Transactions on Graphics (SIGGRAPH) 23 (Aug.), 457–462. Google ScholarDigital Library
30. Losasso, F., Talton, J., Kwatra, N., and Fedkiw, R. 2008. Two-way coupled SPH and particle level set fluid simulation. IEEE Transactions on Visualization and Computer Graphics 14 (July). Google ScholarDigital Library
31. Mihalef, V., Unlusu, B., Metaxas, D., Sussman, M., and Hussaini, M. Y. 2006. Physics based boiling simulation. In Proc. of SCA. Google ScholarDigital Library
32. Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In Proc. of SCA. Google ScholarDigital Library
33. Piazza, L., Gigli, J., and Bulbarello, A. 2008. Interfacial rheology study of espresso coffee foam structure and properties. Journal of Food Engineering 1984, 3, 420–429.Google ScholarCross Ref
34. Redenbach, C., Shklyar, I., and Andr, H. 2012. Laguerre tessellations for elastic stiffness simulations of closed foams with strongly varying cell sizes. International Journal of Engineering Science 50, 1, 70–78.Google ScholarCross Ref
35. Sin, F., Bargteil, A. W., and Hodgins, J. K. 2009. A point-based method for animating incompressible flow. In Proc. of SCA, ACM, New York, NY, USA, SCA ’09, 247–255. Google ScholarDigital Library
36. Stam, J. 1999. Stable fluids. In Proc. of SIGGRAPH ’99, Computer Graphics Proceedings, Annual Conference Series, 121–128. Google ScholarDigital Library
37. Sullivan, J. M. 1998. The geometry of bubbles and foams. Foams and Emulsions (NATO ASI volume E) 354, 379–402.Google Scholar
38. Taylor, J. E. 1976. The structure of singularities in soap-bubblelike and soap-film-like minimal surfaces. Annals of Mathematics 103, 3 (May), 489–539.Google ScholarCross Ref
39. Thürey, N., Sadlo, F., Schirm, S., Müller-Fischer, M., and Gross, M. 2007. Real-time simulations of bubbles and foam within a shallow water framework. In Proc. of SCA, 191–198. Google ScholarDigital Library
40. Thürey, N., Wojtan, C., Gross, M., and Turk, G. 2010. A multi-scale approach to mesh-based surface tension flows. ACM Transactions on Graphics (SIGGRAPH) 29 (July), 48:1–48:10. Google ScholarDigital Library
41. Wang, H., Miller, G., and Turk, G. 2007. Solving general shallow wave equations on surfaces. In Proc. of SCA, 229–238. Google ScholarDigital Library
42. Weaire, D., and Hutzler, S. 2001. The Physics of Foams. Oxford University Press.Google Scholar
43. Weaire, D., Pittet, N., Hutzler, S., and Pardal, D. 1993. Steady-state drainage of an aqueous foam. Physical Review Letters 71, 6, 2670–2673.Google ScholarCross Ref
44. Wicke, M., Ritchie, D., Klingner, B. M., Burke, S., Shewchuk, J. R., and O’Brien, J. F. 2010. Dynamic local remeshing for elastoplastic simulation. ACM Transactions on Graphics (SIGGRAPH) 29 (July), 49:1–49:11. Google ScholarDigital Library
45. Zheng, W., Yong, J.-H., and Paul, J.-C. 2006. Simulation of bubbles. In Proc. of SCA, 325–333. Google ScholarDigital Library