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 ( C dp), friction drag ( C df) and total drag ( C D) coefficients have been presented as functions of the Reynolds number ( Re o) 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 ≤ Re o ≤ 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.