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Synchronized motion and pattern formation of magnetic particle aggregates in variable magnetic field is of growing interest from the point of view of both fundamental science and its applications. In this article, the role of size differences in synchronized motion of magnetic particles under external rotating magnetic field at low Reynolds number flow regimes is considered. Several different motion regimes are observed in simulations as a function of particle size differences and field rotation rate. Simulation indicates phase-like transitions between different motion regimes when particle size differences become significant. It is also shown that particle size differences permit the possibility of locomotion for particle aggregates which cannot be observed for uniform particle sizes.

Magnetically actuated swimming of microscopic objects has been attracting attention partly due to its promising applications in the bio-medical field and partly due to interesting physics of swimming in general. While colloidal particles that are free to move in fluid can be an attractive swimming system due it its simplicity and ability to assemble in situ, stability of their dynamics and the possibility of stable swimming behavior in periodically varying magnetic fields has not been considered. Dynamic behavior of two magnetically interacting colloidal particles subjected to rotating magnetic field of switching frequency is analyzed here and is shown to result in stable swimming without any stabilizing feedback. A new mechanism of swimming that relies only on rotations of the particles themselves and of the particle pair axis is found to dominate the swimming dynamics of the colloidal particle pair. Simulation results and analytical arguments demonstrate that this swimming strategy compares favorably to dragging the particles with an external magnetic force when colloidal particle sizes are reduced.