Binary mixtures of active and passive particles on a sphere

We study the cooperation and segregation dynamics of binary mixtures of active and passive particles on a sphere. According to the competition between rotational diffusion and polar alignment, we find three distinct phases: a mixed phase and two different demixed phases. When rotational diffusion dominates the dynamics, the demixing is due to the aggregation of passive particles, where active and passive particles respectively occupy two hemispheres. When polar alignment is dominated, the demixing is caused by the aggregation of active particles, where active particles occupy the equator of the sphere and passive particles occupy the two poles of the sphere. In this case, there exist a circulating band cluster and two cambered surface clusters, which is a purely curvature-driven effect with no equivalent in the planar model. When rotational diffusion and polar alignment are comparable, particles are completely mixed. Our findings are relevant to the experimental pursuit of segregation dynamics of binary mixtures on curved surfaces.