The oscillation of a falling ferrofluid droplet induced by a nonuniform magnetic field

Understanding the droplet size and shape control mechanism in a magnetic field is critical for precisely manipulating ferrofluid droplets. Here, we conducted an experimental investigation on the dynamic behavior of a falling ferrofluid droplet under a nonuniform magnetic field produced by current coils. We observed an interesting phenomenon: the uneven distribution of the magnetic field and the jump in magnetic properties at fluid interfaces will cause the Laplace pressure difference on the droplet surface, stimulating the droplet’s oscillation. We also use the Laplace pressure difference equation and the interfacial tension coefficient correlation to model the deformation of ferrofluid droplets and determine the oscillation frequencies and deflection angles. The droplets’ oscillation frequency is related to the magnetic Bond number: f∼${\mathrm{Bo}}_m^{-0.523\sim -0.501}$. The deflection angle of the droplet is further diminished by the superposition of a viscous shear moment and a magnetic moment (7.41^°∼12.90^°). Our research lays the groundwork for precise ferrofluid droplet manipulation in drug delivery and soft robots.