Numerical simulation of buoyant drops suspended in a shear flow: suspensions at low and moderate areal fractions

Suspension of buoyant drops at low and moderate areal fractions is studied at non-zero Reynolds numbers in simple shear flow. The flow is studied as a function of the Capillary number, the Reynolds number, the Froude number and the density ratio. It is found that the effective viscosity decreases with Capillary number. The normal stress difference increases with Capillary number. The effective viscosity and normal stress difference also depend on the Reynolds number. At a relatively low area fraction (ϕ = 0.22 ) the normal stress difference decreases with Froude number and becomes negative at large Froude numbers. At a moderate areal fraction (ϕ = 0.44 ) the behavior of the suspension is similar to the relatively low areal fraction, except that the normal stress difference is always positive. Also, the flow weakly depends on the Froude number at moderate areal fraction. The density distribution of buoyant drops across the channel is non-uniform. (paper)