Pattern formation in active droplets

Many morphogenic processes in biology -- from embryogenesis to mitosis -- involve a dynamic competition between bulk active stresses and interfacial tension. We mimic this competition experimentally to understand how activity and capillarity compete to generate functionalized structures. A microtubule-driven active liquid is embedded in a binary, polymeric liquid that phase separates, forming active droplets surrounded by a passive background. Fluctuations in active stress near the boundary induce spontaneous curvature changes of the soft interface. We report active analogs of the viscous fingering and Rayleigh-Plateau instabilities in passive liquids: activity competes against surface tension to destabilize the interface. After the nonequilibrium instability occurs, asymmetries between active and capillary stresses break detailed balance, hence breaking time-reversal and up/down symmetry of the interface. We quantify statistical signatures of these symmetries to understand how activity drives far-from-equilibrium pattern formation. Our work shows active droplets display key morphogenic signatures of living cells, a step toward building functional, bioinspired materials.