Eccentric equilibration of buoyant, deformable drops in a channel

The motion of droplets and bubbles under gravity is fundamental to several multiphase processes, including liquid-liquid extraction and emulsion stability and separation. We use a boundary-integral method to simulate the motion of non-neutrally buoyant, deformable droplets between two horizontal, flat plates in a pressure-driven Poiseuille flow at low Reynolds number. Unlike neutrally buoyant drops that always migrate cross-stream to reach a steady state at the channel centerplane when released off-center, the equilibrium position of non-neutrally buoyant drops is determined by a balance between the buoyancy force and the deformation-induced hydrodynamic drift. We study the effect of variation in Bond number, capillary number, drop size, and initial lateral position of a buoyant drop on its lateral migration and the steady-state position. With increasing Bond number, the drop equilibrates closer to one of the walls, drop velocity decreases, and drop deformation increases. We predict a critical Bond number, above which the deformation-induced drift is overpowered by gravity and drops cease to reach a steady state. With increasing capillary number, drops equilibrate closer to the channel centerplane. Above a critical capillary number, however, drops experience large deformation and may not reach a steady state. Drops starting from different initial positions under identical conditions equilibrate at the same lateral position.