Equilibrium positioning of buoyant, deformable drops in a channel

We investigate the motion and positioning of density-mismatched, deformable drops in pressure-driven flow through horizontal rectangular microchannels using three-dimensional boundary-integral simulations and complementary experiments. For neutrally buoyant drops at a moderate undeformed drop diameter to channel height ratio (D/H≲0.5), we observe off-center equilibrium positions in addition to positioning at the channel centerline over intermediate viscosity ratio ranges, with the range of viscosity ratio narrowing with increasing D/H. When a buoyant drop is released from the channel centerline (or elsewhere), it migrates laterally under gravity until reaching an equilibrium position determined by the balance between buoyancy and deformation-induced hydrodynamic lift forces, independent of initial position. Through systematic parametric studies spanning Bond numbers Bo=0–3, capillary numbers Ca=0.1–0.7, drop-to-medium viscosity ratios λ=0.05–10, and confinement ratios D/H=0.15–1.2, we demonstrate that drops can be predictably positioned at various heights between the wall and centerline by tuning the flow conditions. Larger drops migrate closer to the centerline due to stronger deformation-induced lift forces and thus have higher steady-state velocity, while increasing the Bond number drives drops toward the wall and promotes deformation. We identify critical combinations of Bo, Ca, and D/H, beyond which drops undergo breakup rather than reaching steady states. Higher-viscosity drops settle farther from the centerline due to suppressed internal circulation and weaker deformation-induced lift. Quantitative comparison with experiments shows reasonable agreement, with discrepancies potentially due to surfactant contamination that suppresses interfacial mobility and weakens centering mechanisms.