The motion of a neutrally buoyant and non-neutrally buoyant drop at finite Reynolds numbers

Three-dimensional simulations are presented on the motion of a drop between two parallel plates in plane Poiseuille flow at a finite-Reynolds-number. 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. The computations are based on an improved implementation of the front tracking method at finite Reynolds numbers that include convective terms. The elliptic pressure equation is solved by a multigrid method when the density of the drop is different from the suspending fluid and by a fast Poisson solver (FISHPACK) when the densities are equal. Both neutrally buoyant and non-neutrally buoyant drops are studied. The gravity force is imposed along the flow direction. A neutrally buoyant drop lags the fluid slightly and the wall effect balances the effect of the curvature of the velocity profile, giving rise to an equilibrium lateral position about halfway between the wall and the centerline (the Segre-Silberberg effect). Results are presented over a range of density ratios. As the density ratio increases, the equilibrium position moves closer to the wall. In the non-neutrally buoyant case, a drop that is slightly buoyant, stabilized at a position close to the wall or the centerline, depending on whether it leads or lags the undisturbed fluid. For larger density ratios, however, the final equilibrium position shifts towards the centerline. The accuracy of the method is assessed by comparison with the other simulations and experiments.

کلیدواژه ها:

Neutrally buoyant drop ، Poiseuille flow ، Reynolds number ، Density ratio