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 Fm, non-inertial lift force Fl, and interfacial tension force Fi. Depending on the force ratios, namely, the lift force ratio [KL=Fl/Fi] and magnetic force ratio [KM=Fm/Fi], three different regimes are identified. The results also reveal that the FFD trajectory and migration length (Lmig*) depend on the net force ratio [FR,net=Fm+Fl/Fi] and magnet location xm*. 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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