Field-controlling patterns of sheared ferrofluid droplets

We investigate how ferrofluid droplets suspended in a wall-bounded shear flow can organize when subjected to an external magnetic field. By tuning the magnitude of the external magnetic field, we find that the ferrofluid droplets form chain-like structures in the flow direction when the magnetic field is weak, while forming a crystal-like pattern in a strong magnetic field. We provide the phase diagram and the critical conditions for this chain-to-crystal transition, by applying both numerical simulations and analytic calculations. We also examine how the organized patterns of the ferrofluid droplets can be controlled by simply changing the direction of the magnetic field. This work demonstrates new aspects of field-controllable ferrofluid droplets as a configurable and reprocessable metamaterial.