[en] A droplet on a fiber (of radius r) can adopt two completely different geometries. First, an axisymmetric form, known as the barrel shape (Figure 1, Top). This static configuration is well described by the Laplace equation, so that physical characteristics of the droplet, like the static contact angle ?? or droplet height h0 can be predicted. When ?? remains high (how high is dependent on r and h0), the droplet retains an asymmetric form, the clam-shell shape (Figure 1, Bottom). This time, the Laplace equation is not the relevant equation and, so far, no theoretical analysis of this conformation is known. The transition between the two geometries, the roll-up transition, is of particular industrial interests for the process of the detergency of oils from fabrics, and was therefore intensively investigated by Carroll [1], McHale et al [2], and Eral et al [3]