Hydrodynamics of a Compound Drop in Plane Poiseuille Flow

We numerically investigate the hydrodynamics of a compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core-shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. We also find that the migration of the compound drop affects the eccentricity of the core significantly. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in stable state pushes the compound drop towards the walls, and the revolving core in limit-cycle state makes the compound drop to oscillate at its equilibrium position. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and increase in any parameter sufficiently causes a transition from limit-cycle state to stable state.