Sedimentation in Emulsions of Mono-size Droplets at Moderate Reynolds Numbers

The steady incompressible flow of a Newtonian fluid through an ensemble of Newtonian fluid spheres has been numerically investigated using a finite difference method based SMAC algorithm. For both, dispersed and continuous phases, the convective terms have been discretized using the QUICK scheme, and diffussive terms with the second-order central differencing scheme. A simple concentric sphere cell model has been employed to account for inter-particle hydrodynamic interactions. Extensive numerical results on pressure drag (Cdp), friction drag (Cdf) and total drag (CD) coefficients have been presented as functions of the Reynolds number (Reo) for the continuous phase, the volume fraction of the dispersed phase (∈), and the ratio of internal to external fluid viscosity (k) over the ranges of conditions: 1 ≤ Reo ≤ 500, 0.2 ≤ ∈ ≤ 0.6 and 0.1 ≤ k ≤ 50. Based on the numerical values of the total drag coefficients obtained in this work, a simple correlation has been proposed which can be used to predict the rate of sedimentation in liquid–liquid systems.