Migration of ferrofluid droplets in shear flow under a uniform magnetic field

Manipulation of droplets based on physical properties (e.g., size, interfacial tension, electrical, and mechanical properties) is a critical step in droplet microfluidics. Manipulations based on magnetic fields have several benefits compared to other active methods. While traditional magnetic manipulations require spatially inhomogeneous fields to apply forces, the fast spatial decay of the magnetic field strength from the source makes these techniques difficult to scale up. In this work, we report the observation of lateral migration of ferrofluid (or magnetic) droplets under the combined action of a uniform magnetic field and a pressure-driven flow in a microchannel. While the uniform magnetic field exerts negligible net force on the droplet, the Maxwell stresses deform the droplet to achieve elongated shapes and modulate the orientation relative to the fluid flow. Hydrodynamic interactions between the droplets and the channel walls result in a directional lateral migration. We experimentally study the effects of field strength and direction, and interfacial tension, and use analytical and numerical modeling to understand the lateral migration mechanism.