Magnetic manipulation of pairwise interactions between droplets in simple shear flows

Droplets dispersed in another immiscible liquid are frequently encountered in polymer blending process where the microscale structure of a polymer blend, developed during processing, is dependent on the droplet distribution. Here, using the level set method, we perform numerical investigations to explore the interaction behavior between a pair of equal-sized ferrofluid droplets in simple shear flows under uniform magnetic fields in the Stokes flow limit (Re ≤ 0.03). The results show that there exists a critical Capillary number Ca_cr, beyond which the droplets demonstrate separation through a sliding over motion, instead of coalescence. Application of a magnetic field along α = 0° (parallel to the flow) results in a faster coalescence phenomenon between droplets, whereas a magnetic field along α = 45° leads to separation followed by a reversal motion. However, at α = 90° (perpendicular to the flow), a critical magnetic field strength appears where the droplets show a reversing motion behavior, instead of passing over motion leading to coalescence. Moreover, the outcome of a collision event is found to be dependent on the initial vertical offset between the droplets.