Generic path for droplet relaxation in microfluidic channels

In two-phase microfluidics, droplets often undergo deformations that drive them away from their circular equilibrium shape. Herein we concentrate on the relaxation of symmetrical deformations to a circle driven by surface tension effects, which are predominant at the micrometer scales. Working in a Hele-Shaw cell, we report a generic pathway for these types of relaxations. We simulate numerically the interface shape evolution and investigate it using linear stability analysis. Finally, we characterize this universal aspect of relaxation using a purely geometrical model that is tested in experiments.