Magnetofluidic-based controlled droplet breakup: effect of non-uniform force field

We report the breakup dynamics of a magnetically active (ferrofluid) droplet in a T-shaped Lab on a Chip (LOC) device under the modulation of a non-uniform magnetic field. We adhere to high-speed imaging modalities for the experimental quantification of the droplet splitting phenomenon, while the underlying phenomenon is supported by the numerical results in a qualitative manner as well. On reaching the T-junction divergence, the droplet engulfs the intersection fully and eventually deforms into the dumbbell-shaped form, making its bulges move towards the branches of the junction. We observe that the asymmetric distribution of the magnetic force lines, acting over the T-junction divergence, induces an accelerating motion to the left of the moving bulge (since the magnet is placed adjacent to the left branch). We show that the non-uniform force field gradient allows the formation of a hump-like structure inside the left moving bulge, which triggers the onset of augmented convection in its flow field. We reveal that this augmented internal convection developed in the left moving volume/bulge, on becoming coupled to the various involved time scales of the flow field, leads to the asymmetric splitting of the droplet into two sister droplets. Our analysis establishes that, at the critical strength of the applied forcing, as realized by the critical magnetic Bond number, the flow time scale becomes minimum at the left branch of the channel, leading to the formation of larger sized sister droplets therein. Inferences of the present analysis, which demonstrates a plausible means of independently controlling the size of the sister droplet by manoeuvring the applied force field gradient, will provide a potential solution for rapid droplet splitting, which typically finds significant importance in point-of-care diagnostics.