On the motion of a falling ferrofluid droplet pair under a nonuniform magnetic field

The controlled assembly of ferrofluid droplets under magnetic fields is pivotal for applications in droplet robotics, drug delivery, and microreactors. This study investigates the dynamics of a ferrofluid droplet pair falling in a non-uniform magnetic field, focusing on magnetic and dipole forces influencing their trajectories. Gravity and viscous forces caused the ferrofluid droplets to rotate counterclockwise (1°–10°) when no magnetic field was present. In a non-uniform magnetic field, the pair of droplets falls vertically and oscillates. The magnetic dipole moment would control the motion (0.1–10 μN·m). The interaction force between droplets transitions from repulsive (19° < θ < 48.4°) to attractive (θ ≤ 19°), with clockwise deflection occurring when the contact angle exceeds 48.4°. These findings provide a theoretical basis for precise droplet manipulation in advanced applications.