Collective Vortical Motion and Vorticity Reversals of Self-Propelled Particles on Circularly Patterned Substrates

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction $\bar\phi$, motility force $F_D$, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of $F_D$. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of $F_D$, the SPPs exclusion from the center is dominated by the confining boundary. At high values of $\bar\phi$, the substrate pattern leads to reversals in the vorticity, which become quasi-periodic with increasing $\bar\phi$. We also found that the substrate pattern is able to separate SPPs based on their motilities.