Oscillating path between self-similarities in liquid pinch-off.

Many differential equations involved in natural sciences show singular behaviors; i.e., quantities in the model diverge as the solution goes to zero. Nonetheless, the evolution of the singularity can be captured with self-similar solutions, several of which may exist for a given system. How to characterize the transition from one self-similar regime to another remains an open question. By studying the classic example of the pinch-off of a viscous liquid thread, we show experimentally that the geometry of the system and external perturbations play an essential role in the transition from a symmetric to an asymmetric solution. Moreover, this transient regime undergoes unexpected log-scale oscillations that delay dramatically the onset of the final self-similar solution. This result sheds light on the strong impact external constraints can have on predictions established to explain the formation of satellite droplets or on the rheological tests applied on a fluid, for example.