Curvature Controlled Phase Separation in Self-Propelled Colloidal Particle Systems

In many biological systems, the curvature and topology of the surfaces, on which cells or other organisms live, influence their collective properties. We find that Gaussian curvature also affects active colloidal systems and can lead to new dynamic phases like cyclic phase separation and dissipation states or positionally targeted clustering. We explain these phenomena by studying computationally the phase behavior of active particles confined to the surfaces of positively curved spheres and negatively curved gyroids. We show that geometrical effects decrease or increase the critical density of motility induced phase separation (MIPS) for positive or negative curvature, respectively, while topological effects dominate at very high curvature. We also prove theoretically that the change in the onset of clustering can be explained by the nature of parallel lines in spherical and hyperbolic space. Lastly, we observe that the dense MIPS clusters fluidize upon introducing curvature due to the increase of defect patterns within the crystalline order. Our findings demonstrate a promising tool to design the emergent behavior of active colloids and indicate a mechanism to control their clustering and dynamics for robotic and other applications.