This work numerically examines droplet transport through a trifurcating microchannel utilizing the coupled Navier–Stokes equation with the phase field approach, with a focus on various aspects of droplet dynamics: deformation, breakup, and directional sorting across a broad range of capillary numbers (Ca) and droplet lengths (Ld). The simulations reveal multiple distinct regimes, including symmetric and asymmetric breakup, selective entry into the upper, middle or lower branches without breakup, and a stuck regime at the junction. At higher Ca, where viscous forces outweigh interfacial tension, breakup dominates, while at lower Ca, droplet routing is primarily governed by the vectorial balance of resultant velocities rather than the channel's high flow rate. A transient stuck phenomenon is observed at intermediate Ca values for droplets with smaller lengths, which diminishes as Ld increases. To encapsulate these findings, a comprehensive regime map is developed, capturing the nuanced dependency of droplet dynamics on Ca and Ld. These results contribute a predictive framework for tailoring multifurcating microchannel architectures in droplet-based technologies, with potential applications in lab-on-a-chip diagnostics, emulsification systems in food engineering, and controlled dispersion in microreactor environments.
Pandey et al. (Fri,) studied this question.