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 (Reo), the internal to external fluid characteristic viscosity ratio (k), the volume fraction of the dispersed phase (Φ) and the power-law index of the continuous phase (no) on the external flow field, pressure drag (Cdp), friction drag (Cdf) and total drag (Cd) coefficients have been analyzed over wide ranges of parameters as follows: 1 ≤ Reo ≤ 200, 0.1 ≤ k ≤ 50, 0.2 ≤ Φ ≤ 0.6 and 0.6 ≤ no ≤ 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.