Numerical simulation of buoyant drops suspended in Poiseuille flow at nonzero Reynolds numbers

Abstract

Suspensions of two-dimensional buoyant drops in Poiseuille flow are studied at nonzero Reynolds numbers by numerical simulations. The flow is studied as a function of the Froude number, the Reynolds number, the Capillary number and the density ratio. First, the lateral migration of a drop is studied. Results agree with two-dimensional simulations of solid circular cylinders by Feng et al. (J Fluid Mech 261:95–134, 1994; J Fluid Mech 277:271–301, 1994) qualitatively. At a relatively large Reynolds number (120) and a moderate Froude number (43), a drop shows oscillations across the channel and does not obtain a stable equilibrium position. Simulations are also performed at low and moderate area fractions (0.22, 0.44). It is found that the effective viscosity strongly depends on the Froude number for heavy drops (α > 1). The effective viscosity changes with the Froude number for light drops as well (α < 1), but to a lower extent. The distribution and the fluctuation energy of drops across the channel are non-uniform for buoyant drops that depend on the Froude number. The density ratio also affects the distribution and fluctuation energy of drops across the channel. The effect of the Reynolds number on the effective viscosity of the suspension is also investigated.