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Capillary instability of a Newtonian liquid torus suspended in an immiscible Newtonian medium is computed using a Cahn-Hilliard diffuse-interface model. The main differences between the torus and a straight thread are the presence of an axial curvature and an external flow field caused by the retraction of the torus. We show that the capillary wave initially grows linearly as on a straight thread. The axial curvature decreases the growth rate of the capillary waves while the external flowdoi:10.1017/jfm.2012.572 fatcat:i7l3cuwjergmloemwhbtjessfa