Magnetically modulated breakup pathways of multi-core compound droplets in simple shear flow

This study examines the deformation and breakup of a three-core compound droplet in a simple shear flow under a uniform magnetic field for two material architectures: ferro-core and ferro-shell. Sharp-interface front-tracking direct numerical simulations are used to clarify how viscous shear, capillary resistance, and magnetic stress interact to drive distinct evolutionary pathways when the magnetic phase is placed in the cores or in the shell. The responses are classified into four outer-shell topological families: F0 (intact), F1 (connected filamentary non-breakup), F2 (compound-only breakup), and F3 (simple-droplet breakup). The results indicate that the Capillary number, Ca, acts as the primary breakup gate, determining whether the system remains on a non-breakup branch or enters a breakup-accessible window. Beyond this threshold, the magnetic-field orientation angle, α, acts mainly as a local post-threshold pathway selector, whereas the magnetic Bond number, Bom, can bias, reroute, or locally restabilize the response depending on the parameter window. Even under identical external controls, ferro-core and ferro-shell may evolve toward different terminal families. This suggests that the location of the magnetic phase affects how magnetic stress is transmitted through the core–shell structure and, in turn, modulates the terminal breakup topology. Breakup in the present system can therefore be interpreted through a consistent control hierarchy comprising Ca-gated access to breakup, α-dependent pathway selection, Bom-induced local bias or rerouting, and architecture-dependent divergence of the terminal topology.