Equilibrium position of a buoyant drop in simple shear flow

The lateral migration of a deformable drop in simple shear flow at finite Reynolds numbers is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objectives of this study are to investigate the equilibrium position of a deformable drop in simple shear flow. It was found that the equilibrium position of the lighter drops is closer to the walls than the heavier drops at each Reynolds number. Also, the equilibrium position moves closer to the walls with increasing the Reynolds number at a fixed density ratio. The final equilibrium position of a drop at higher Reynolds numbers is slightly higher than the equilibrium position of a drop at lower Reynolds numbers. At the equilibrium position from the wall, the migration velocity is zero, while the velocity of the drop in the flow direction and rotational velocity of the drop is finite. The equilibrium position is independent of the initial position of the drops and depends on the density the drop to ambient fluid and the shear Reynolds number

Keywords:

shear flow , finite difference , front tracking , density ratio , Reynolds number