Vorticity Determines the Force on Bodies Immersed in Active Fluids

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem relate forces responsible for this density and current induced by---but far away from---the body. In general, force is composed two contributions: due strength dipolar field component particles leaving boundary, generating nonvanishing vorticity polarization. We derive numerically corroborate results periodic systems, which are fundamentally different from unbounded systems with that scale area system. demonstrate localized close body points at local curvature changes, enabling rational design particle shapes desired propulsion properties.