A three-dimensional study of the motion of a drop in plane Poiseuille flow at finite Reynolds numbers

Abstract– Three-dimensional simulations are presented on the motion of a neutrally buoyant drop between two parallel plates at a finite-Reynolds-number in plane Poiseuille flow, under conditions of negligible gravitational force. The full Navier-Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the drop and the suspending medium and the inclusion of the surface tension. In the limit of a small Reynolds number (<1), the direction of motion of the drop depends on the ratio of the viscosity of the drop fluid to the viscosity of the ambient fluid. At finite Reynolds numbers, the drop migrates to an equilibrium 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 viscosity ratio decreases, the equilibrium position moves closer to the wall. The drop velocity is observed to increase with increasing capillary number and viscosity ratio, but decreases with increasing Reynolds number. The drops are more deformed with increasing the capillary number or viscosity ratio. The drop deformation increases slightly with increasing Reynolds number at constant capillary number. The equilibrium position of the three-dimensional drop is close to that predicted by two-dimensional simulations. But the translational velocities do not agree quantitatively with two-dimensional simulations.