This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a plane 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. A hydrodynamic repulsion balances the centripetal attraction of the magnetized particles and leads to the formation of an aggregate of several particles that 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 repulsion force between the particles is shown to be the result of the secondary flow generated by each particle at low but nonzero Reynolds number. Comparisons are made with analogous experiments of spinning disks at a liquid–air interface, where it is found that the variation in the characteristic scales of the aggregate with the rotation rate of individual particles are consistent with the numerical results.

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