Dynamic Self-Assembly of Spinning Particles

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain and flow-induced interactions. Under specific conditions, a hydrodynamic repulsion balances the centripetal attraction of the magnetized particles, which leads to the formation of an aggregate of several particles. After a short transient, an aggregate of particles is formed that then rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The numerical simulation is based on the Navier-Stokes equations coupled with the Lagrangian tracking of each individual particle. Multi-body interactions (at low but finite Reynolds number) are achieved by a local forcing of the momentum equations of the fluid flow. The agreement with experiments of spinning disks at a liquid-air interface is not only qualitative but also quantitative. Comparisons on the evolution of the characteristic scales of the aggregate with the rotation rate of individual particles clearly show that the numerical results are consistent with the experiments