  Antibubbles, which consist of a shell of a low-density fluid inside a
high-density fluid, have several promising applications. We show, via extensive
direct numerical simulations (DNSs), in both two and three dimensions (2D and
3D), that the spatiotemporal evolution of antibubbles can be described
naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a
binary fluid. Our DNSs capture elegantly the gravity-induced thinning and
breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar
order parameter field $\phi$, which varies continuously across interfaces, so
we do not have to enforce complicated boundary conditions at the moving
antibubble interfaces. To ensure that our results are robust, we supplement our
CHNS simulations with sharp-interface Volume-of-Fluid (VoF) DNSs. We track the
thickness of the antibubble and calculate the dependence of the lifetime of an
antibubble on several parameters; we show that our DNS results agree with
various experimental results; in particular, the velocity with which the arms
of the antibubble retract after breakup scales as $\sigma^{1/2}$, where
$\sigma$ is the surface tension.
