Dynamics of aqueous ferrofluid droplets at coflowing liquid-liquid interface under a non-uniform magnetic field

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 F m, non-inertial lift force F l, and interfacial tension force F i. Depending on the force ratios, namely, the lift force ratio [ K L = F l / F i] and magnetic force ratio [ K M = F m / F i], three different regimes are identified. The results also reveal that the FFD trajectory and migration length ( L m i g *) depend on the net force ratio [ F R , n e t = F m + F l / F i ] and magnet location x m *. 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.