New model for single spherical particle settling velocity in power law (visco-inelastic) fluids

Abstract

Particle settling in a non-Newtonian power law fluid is of interest to many industrial applications, including chemical, food, pharmaceutical, and petroleum industry. Conventionally, the Newtonian model for the drag coefficient prediction is extended to non-Newtonian fluids. The approach of merely replacing a viscosity term in Newtonian correlation with a power law apparent viscosity is reported to be inadequate. In this investigation, the inadequacy of the Newtonian model to correlate the data of single solid spherical particle moving in power law liquids is demonstrated. An approach presented earlier by Shah has been adopted to re-analyze the previously published data of particle settling in various non-Newtonian fluids from five different investigations. The particle settling velocity data have been correlated with two dimensionless quantities – drag coefficient C d and particle Reynolds number Re – as C d 2 - n Re 2 versus Re, rather than the conventional correlation of C d versus Re. A new model to predict the settling velocity of a spherical particle moving in inelastic power law liquids is presented, which reduces to the expected Newtonian fluid limit. It is shown that the Shah’s method predicts the particle settling velocity data much closer to the experimental data than the Newtonian standard drag curve that has been widely used by many researchers. The new model is valid for a wide range of power law flow behavior index n (0.281–1.0) and particle Reynolds number Re (0.001–1000). The paper is concluded by presenting an illustrative example to calculate the settling velocity of a spherical particle in non-Newtonian liquid.