Dynamics of compound droplet splitting in Poiseuille flow across microfluidic channels

Droplet-based methods have become essential in several fields, including chemical analysis, biological diagnostics, and lab-on-a-chip technologies, in microfluidic systems. The precise manipulation and control of droplets is critical for the efficient functioning of these applications. A fundamental challenge remains in fully understanding the complex dynamics of droplets within confined microchannel geometries, particularly when multiple phases, such as core-shell droplets, are involved. While significant advances have been made in the modeling of droplet behavior within microchannels, most existing models focus on single-phase droplets or binary fluid systems. This work uses a phase field method to analyze a compound droplet splitting process in a microchannel with several geometries, including Y-shaped channels, flat T-shaped junctions, and curved T-shaped junctions. This study takes into account the impacts of the capillary number (Ca), the wettability of the microchannel walls, and the core-to-shell fluid viscosity ratio (λ) of the droplet. The investigation explores the mechanics of droplet splitting, deformation, and time at the junction. Because of the prominent bifurcating tip of the Y-shaped channel, droplet splitting happens even at low capillary numbers. In contrast, hydrophilic channel walls facilitate droplet splitting, whereas neutral and hydrophobic surfaces do not. Droplet stability is improved by high viscosity ratios (λ = 10:1), which delay the breakup of the droplet. High Ca generally exhibits in droplet splitting, whereas low Ca leads to non-breakup and moving through any one branch of the microchannel. The droplet splitting and non-splitting characteristics exhibited in the flat and curved T-shaped junctions are almost the same. Overall, the Y-shaped bifurcated microchannel with hydrophilic walls, where the droplet sticks to the wall is the most effective arrangement for droplet breakup. The flat and curved T-shaped junctions display almost alike dynamic behavior, exhibiting splitting regimes for the capillary number from 1.8 to 2 for the flat T-shaped channels and 2 to 2.2 for the curved T-shaped channels, while the Y-shaped bifurcating junction is observed to favor splitting regimes over a broader range of capillary numbers (0.05 ≤ Ca), but only in hydrophilic channels. These droplets exhibit distinct behaviors under varying flow conditions, and understanding these behaviors is essential for improving droplet manipulation techniques in applications such as biochemical analysis, drug development, and chemical synthesis.