Transactions on Graphics (Proceedings of SIGGRAPH Asia 2017)

Simulating the behavior of soap films and foams is a challenging task. A direct numerical simulation of films
and foams via the Navier-Stokes equations is still computationally too expensive. We propose an alternative
formulation inspired by geometric flow. Our model exploits the fact, according to Plateau's laws, that the
steady state of a film is a union of constant mean curvature surfaces and minimal surfaces. Such surfaces are
also well known as the steady state solutions of certain curvature flows. We show a link between the
Navier-Stokes equations and a recent variant of mean curvature flow, called *hyperbolic mean curvature
flow*, under the assumption of constant air pressure per enclosed region. We thus introduce hyperbolic mean
curvature flow to describe film dynamics. Instead of using hyperbolic mean curvature flow as is, we propose to
replace curvature by the gradient of the surface area functional. This formulation enables us to robustly handle
non-manifold configurations; such junctions connecting multiple films are intractable with the traditional
formulation using curvature. We also add explicit volume preservation to hyperbolic mean curvature flow, which
in fact corresponds to the pressure term of the Navier-Stokes equations. Our method is simple, fast, robust, and
consistent with Plateau's laws, which are all due to our reformulation of film dynamics as a geometric flow.