We report the dynamical behaviour of aqueous ferrofluid droplets (FFDs) of different sizes and concentrations at the interface of coflowing immiscible oils in a microchannel in the presence of the magnetic field. We show that the migration and sorting phenomena are governed by the interplay between magnetic force , non-inertial lift force , and interfacial tension force . Depending on the force ratios, namely, the lift force ratio ] and magnetic force ratio [], three different regimes are identified. The results also reveal that the FFD trajectory and migration length () depend on the net force ratio and magnet location . Finally, size-based sorting of FFD is demonstrated, which shows a remarkable improvement in terms of the size range and resolution compared to when the magnetic field is not present.
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