A THREE-DIMENSIONAL STUDY OF THE MOTION OF A DROP IN PLANE POISEUILLE FLOW AT FINITE REYNOLDS NUMBERS

Three-dimensional simulations are presented on the motion of a neutrally buoyant dropbetween two parallel plates at a finite-Reynolds-number in plane Poiseuille flow, under conditionsof negligible gravitational force. The full Navier-Stokes equations are solved by a finitedifference/front tracking method that allows a fully deformable interface between the drop and thesuspending medium and the inclusion of the surface tension. In the limit of a small Reynoldsnumber ( 1), the direction of motion of the drop depends on the ratio of the viscosity of the dropfluid to the viscosity of the ambient fluid. At finite Reynolds numbers, the drop migrates to anequilibrium lateral position about halfway between the wall and the centerline (the Segre-Silberberg effect). Results are presented over a range of capillary number, Reynolds number,viscosity ratio and drop size. As the Reynolds number increases or capillary number or viscosityratio decreases, the equilibrium position moves closer to the wall. The drop velocity is observed toincrease with increasing capillary number and viscosity ratio, but decreases with increasingReynolds number. The drops are more deformed with increasing the capillary number or viscosityratio. The drop deformation increases slightly with increasing Reynolds number at constantcapillary number. The equilibrium position of the three-dimensional drop is close to that predictedby two-dimensional simulations. But the translational velocities do not agree quantitatively withtwo-dimensional simulations.