Enhanced droplet breakup dynamics via magnetic force assistance: Unveiling mixed splitting mode

An active manipulation task, such as splitting droplets through the modulation of an external physical magnetic field, is commonly associated with key processes in chemical reactions, drug delivery systems and biomedical applications. This study focuses on the splitting mechanisms of isolated ferrofluid droplets, offering a breakup characteristic for both non-magnetic and magnetic conditions, considering a broad range of flow rate ratios and magnetic Bond numbers (measure of the relative strength of magnetic force to interfacial tension force). By introducing potential flow regimes (permanent, partial, non-splitting and mixed), we specifically investigated the unexplored breakup dynamics of mixed obstruction experimentally and examined the evolution of geometrical parameters in the presence of varying magnetic field strengths. Our experimental observations are enriched with numerical results, shedding light on complex velocity field changes and force dynamics in a mixed regime. The study concludes by presenting phase diagrams that map out how varying magnetic forces influence the breakup behaviour, correlating droplet length, capillary number, Reynolds number and magnetic Bond number. Our results underscore the significant role of magnetic fields in inducing asymmetry at the droplet interface, thereby controlling the formation of ferrofluid sub-droplets of diverse lengths.