Drag on ensembles of fluid spheres translating in a power-law liquid at moderate Reynolds numbers

Abstract

This work elucidates the role of power-law rheology on the sedimentation velocity of an ensemble of mono-size spherical Newtonian droplets (free from surfactants) translating in a power-law continuous phase numerically by solving the momentum equations of both phases. A simple sphere-in-sphere cell model has been used to account for inter-drop interactions. In particular, in this study, the effects of the Reynolds number (Re_o), the internal to external fluid characteristic viscosity ratio (κ), the volume fraction of the dispersed phase (Φ) and the power-law index of the continuous phase (n_o) on the external flow field, pressure drag (C_dp), friction drag (C_df) and total drag (C_d) coefficients have been analyzed over wide ranges of parameters as follows: 1 ≤ Re_o ≤ 200, 0.1 ≤κ≤ 50, 0.2 ≤ Φ ≤ 0.6 and 0.6 ≤ n_o ≤ 1.6. Based on the extensive numerical results obtained in this work, a simple predictive correlation has been proposed for the total drag coefficient, which can be used to predict the rate of sedimentation of ensembles of Newtonian fluid spheres in power-law liquids in a new application.