A Numerical Study of Drop Motion in Poiseuille Flow

The cross-stream migration of a deformable drop in two-dimensional Poiseuille flow at finite Reynolds numbers is studied numerically. In the limit of a small Reynolds number (<1), the motion of the drop depends strongly on the ratio of the viscosity of the drop fluid to the viscosity of the suspending fluid. For a viscosity ratio 0.125, the drop moves toward the centre of the channe while for the ratio 1.0, it moves away from the centre until halted by wall repulsion. The rate of migration increases with the deformability of the drop. At higher Reynolds numbers (5-50), the drop either moves to an equilibrium lateral position about halfway between the centerline and the wall according to the so-called Segre-Silberberg effect or undergoes oscillatory motions. The steady-state position depends only weakly on the various physical parameters of the flow but the length of the transient oscillations increases as Reynolds number is raised, the density of the drop is increased, or the viscosity of the drop is decreased. Once the Reynolds number is high enough, the oscillations appear to persist forever and no steady state is observed. The numerical results are in good agreement with experimental observations, especially for drops that reach steady-state lateral position.