Numerical simulation of a buoyant suspending drop in plane Couette flow: the equilibrium position of the drop*

The lateral migration of a two-dimensional buoyant drop in simple shear flow is studied numerically. For a slightly buoyant drop, the drop migrates to an equilibrium position which is close to the walls depending on whether the drop leads or lags the flow. If the drop is relatively more buoyant, the equilibrium position moves back to the midplane. The equilibrium position of the drop depends on the Froude number of the flow. The behavior has been investigated for various Froude numbers. The equilibrium position also depends on the drop deformation. When the Capillary number is raised, the equilibrium position moves away from the wall. At relatively large Capillary numbers, the drop shape is not stable, and the equilibrium position shows small oscillations due to an unstable drop shape. The effect of the Reynolds number on the equilibrium position has also been studied by a few simulations. It is found that at a relatively large Reynolds numbers (Reh = 80) and a moderate Froude number (Fr = 160) the drop oscillates with a finite amplitude inside the channel. The equilibrium position of the drop agrees qualitatively with perturbation theories and numerical results available for solid particles.