Shape and stress relaxation in gelling droplets

Encapsulation is a process that enables to protect, transport and deliver active species in dedicated areas. One encapsulation process is the alginate/calcium dripping method, where droplets of a biopolymer, alginate are dripped on a calcium bath where the calcium ions diffuse into the polymer droplets and bind the molecules together to obtain a hydrogel bead. We investigate the shape relaxation of these gelling droplets. We show experimentally and numerically that a gelled layer grows at the surface. Due to volume contraction of the gelling shell, this layer induces tensile stresses and drives the flow of the ungelled liquid core, resulting in the relaxation of the droplets toward spherical shapes. Over time the thickness of this elastic membrane grows hence the bending stiffness required to change its shape eventually balances the surface stresses, which arrests the relaxation process.
These results provide general rules to understand the shape of solidifying materials combining both tension and bending driven deformations.

Godefroid, J., Marcellan, A., Bouttes, D., Barthel, E., and Monteux, C., Soft Matter, 2023