Study on the lateral migration of a ferrofluid droplet in a plane Poiseuille flow under uniform magnetic fields

Droplet dispersion in another immiscible fluid is important in a variety of technological processes that involve liquid-liquid extraction where phase separation is crucial to the purification of the product. In this study, we investigate the lateral migration of a ferrofluid droplet in a plane Poiseuille flow under uniform magnetic fields by means of a numerical simulation, which uses a level set method to track the droplet interface between the two phases. Focusing on low droplet Reynolds number (i.e.,${Re}_{d}\le 0.05$ ), the results indicate that the magnetic field plays a pivotal role in the motion trajectory of the droplet and the final equilibrium position in the channel. When the magnetic field acts in a direction parallel to the flow direction (i.e., $\alpha =\thinspace 0^{^{\circ}})$, the droplet settles closer to the bottom wall with increasing magnetic field strength, while at $\alpha =\thinspace {45}^{^{\circ}}$ the droplet settles closer to the center. Also, variation of initial droplet sizes results in different equilibrium positions along the channel. Furthermore, at $\alpha =\thinspace {90}^{^{\circ}}$ the droplet finds its equilibrium position at the channel center irrespective of different magnetic field strengths and droplet sizes.