Sedimentation in emulsions of mono-size droplets at moderate Reynolds numbers

Abstract

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 (I), and the ratio of internal to external fluid viscosity (κ) over the ranges of conditions: 1≤Re_o≤500, 0.2≤I≤0.6 and 0.1≤κ≤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.