Geometrical and topological confinement in 3D active emulsions

Active shells and droplets are fascinating examples of topological matter, exhibiting striking dynamic states. These behaviors have attracted significant attention, leading to numerous computational and theoretical studies based on the active liquid crystal theory. Most of these studies focus on two cases: thin shells, where active nematics are confined to the droplet surface, and fully filled 3D droplets composed entirely of active liquid crystal. Interestingly, these two systems display distinct dynamics: thin shells undergo periodic oscillations, with four +1/2 topological defects cycling between tetrahedral and planar arrangements, replicating experimental observations, while 3D droplets exhibit rotational and translational instabilities.

In this work, we bridge the gap between these two extremes by introducing a novel framework to describe active liquid crystalline emulsions and by exploring the dynamics of thick active shells, where the shell thickness can be varied [1,2]. We find that the transition between the periodic planar-tetrahedral (P-T) instability and rotational dynamics occurs at intermediate shell thicknesses, accompanied by a topological recombination of defect structures. In the P-T instability, disclination lines connect the four semi-integer defects on both the inner and outer surfaces, with the defects exhibiting analogous oscillatory dynamics. As the shell thickness increases, these disclinations elongate until they collapse into two boojums on both surfaces, leading to the rotational instability. We also examine the case of active chiral liquid crystals, where the helix pitch is comparable to or smaller than the shell thickness. Notably, for sufficiently high activity and chirality, we observe a continuous transition from a morphologically disordered state (akin to Blue Phase III) to active turbulent dynamics. Finally, we construct a full phase diagram based on three control parameters: shell thickness, chirality, and activity.

[1] Bulut A; Sariyar Y; Negro G, and Carenza LN. "Geometrical and topological confinement in 3D active emulsions". In preparation.

[2] Negro G; Head LC; et al. "Controlling flow patterns and topology in active emulsions". arXiv:2402.02960 (2024)