Shapes of hanging viscous filaments

We discuss the evolution of the shape of viscous filaments (such as honey threads) placed horizontally in the gravitational field. When attaching both ends of the filament to solid walls, the center of the filament falls down. Hence, a catenary forms and extends as a function of time, owing to gravity. However, it was noted by Koulakis et al. that a second shape roughly consisting of three perpendicular pieces (evoking a flying trapeze) is sometimes observed. We try here to understand the origin of this U-shape. We show in particular that its origin is independent of the liquid viscosity, and fixed only by the geometric characteristics (length and radius) of the (initial) filament.