Measurements and prediction of terminal velocity of solid spheres falling through stagnant pseudoplastic liquids

Prediction of the terminal velocity of solid spheres falling through stagnant pseudoplastic fluids is required in several applications like oil well drilling, geothermal drilling, transportation of non-Newtonian slurries and mineral processing. Prior attempts utilized various Newtonian correlations to predict the drag coefficient and from this the terminal velocity with varying degrees of success. We report here carefully derived experimental data for solid spheres falling through non-Newtonian liquids and present them together with measurements reported in the literature, for a total of 80 pairs of Re–CD, and show that the data fall along the same curve. Through nonlinear regression, an equation is derived, similar to the most accurate, simple, five-constant equation proposed for Newtonian liquids, which has not yet been tested for non-Newtonian liquids. The predictions compare favorably with the measurements both for the proposed equation and for the Newtonian equation. With a combination of non-Newtonian data with Newtonian data, from this work and work from other investigators, giving a database of 148 pairs, an improved equation is derived. Analysis of the predictions shows that the Newtonian equation describes extremely well the Newtonian data and furthermore it could be used with good engineering accuracy to predict the terminal velocity of solid spheres falling through stagnant non-Newtonian liquids.