In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the differences with the basic viscous string model and with its viscous rod model extension. In particular, an elliptic deformation of the torus section appears because of surface tension effects, and this cannot be described by viscous string nor viscous rod models. Furthermore, we study the Rayleigh-Plateau instability for periodic deformations around the perfect torus, and we show that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop. Conversely, a rotating torus is dynamically attracted toward a stationary solution, around which the instability can develop freely and split the torus in multiple droplets.
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