Capillary retraction of a slender fiber into a driven and confined microfluidic droplet

The elastocapillary deformation of flexible objects by a liquid interface has been widely studied from an experimental and theoretical point of view. It has been shown that the equilibria for these systems depends on the surface tension between all three phases as well as the bending modulus of the deformable object. Depending on the liquid/flexible object combination, a plethora of self-assembled structures including coiled droplets, bundled hair and capillary origami have been observed. If these equilibria are well described in the literature, the dynamical approach towards such equilibrium in the presence of a surrounding hydrodynamic flow has been less reported.

This study therefore aims to explore a visco-elasto-capillary relaxation starting from a model non-equilibrium state. For this purpose, the dynamic retraction of a slender fiber into a moving droplet was observed. We have experimentally witnessed such a phenomenon in droplet/fiber pairs prepared in biphasic microfluidic devices under pressure-driven flow. We observed two distinct dynamics depending on the sense of retraction of the fiber compared to the direction of the external-phase flow, and depending on the relative viscosity of the droplet and external phases. Using a minimal model considering an energy balance between the surface energy of the fiber and viscous dissipation, the observed capillary retraction dynamics can be described.