In this research the PI will develop efficient mesh-based algorithms to simulate the dynamics and interactions of thin liquid structures such as sheets, jets, bubbles, and films. The thin geometry of these liquid phenomena poses tremendous difficulties for traditional techniques, leading to long runtimes and excessive memory consumption. The PI argues that a fundamentally different approach that recognizes and exploits the unique geometry of thin liquids is needed in order to simulate them efficiently and accurately (by analogy with the special treatment of thin elastic bodies such as rods, plates, shells). The project is comprised of three thrusts. First, the PI will develop algorithms for the dynamic simulation of liquid bodies composed of high viscosity threads and sheets, including physical modeling, collision processing, topology changes, and mixed dimensional remeshing. Second, he will address the specific challenges of low viscosity jets and sheets, considering in particular the enhanced influence of surface tension, sheet breakup, and the choice of Eulerian vs. Lagrangian evolution. Finally, he will examine the deformations of films, bubbles, and foams, using a new mesh-based representation for deforming multi-region interfaces, coupled to the fluid dynamics of the surrounding air. In each thrust, the predictive power of the techniques developed will be validated against both experimental observations and theoretical results from the literature.
To these ends, the PI will bring several geometric and computational techniques from the dynamics of thin elastica to bear on the dynamics of thin fluids. The PI believes this cross-pollination of ideas has the potential to provide dramatic improvements in efficiency and accuracy, while yielding computational tools that complement theory and experiment in the study of thin fluid phenomena. By considering a thin material as a lower dimensional object (curve or surface) with an associated thickness, the dimension of the problem can be reduced, yielding improved numerical properties and better allocation of degrees of freedom. This perspective has never before been applied to develop computational techniques for three-dimensional thin liquids. The use of non-manifold meshes to represent mixed bodies of thin liquids also opens up previously unexplored challenges in mixed dimensional remeshing and the handling of topological transitions. Furthermore, the proposed surface tracking representation builds on robust collision-processing techniques originally applied to cloth animation, and will offer the first surface mesh-based technique for the evolution of multi-material interfaces. This will allow for more accurate tracking of bubbles and general multiphase flows than can be achieved with state-of-the-art implicit surface approaches.
Broader Impacts: Thin liquids are crucial to a broad class of problems in computer graphics, engineering, and scientific applications. Liquid animations are increasingly prevalent in visual effects-driven films, yet thin splashes remain among the most difficult effects to animate. Thin threads and sheets of viscous liquids arise in applications from food processing to cosmetics, from the geophysics of the earth's crust to the forming and blowing of elaborate glass artwork. They are the subject of substantial concurrent experimental and theoretical investigation, and complementary computational tools for these problems could offer vital new insights. The potential applications for low viscosity liquids and foams are equally wide-ranging. Project outcomes will be reported at major international venues including the SIGGRAPH conferences, and the associated computational tools will be made publicly available. A variety of education and outreach efforts, some of which specifically target minority middle school students, are also planned.