New drag-coefficient charts for settling spherical and disk particles in shear thinning fluids

Abstract

Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.

Settlement of solid particles in shear-thinning non­-Newtonian fluids is of great importance and has many applications in petroleum operations and chemical processes. In general, the drag coefficient (Cd) of a solid particle depends mainly on the particle Reynolds number (Rep), which is mainly a function of fluid rheology, particle shape and size, and particle slip velocity. A non-Newtonian fluid is broadly defined as one for which the relationship between shear stress and shear rate is not constant (i.e., shear stress is changing with shear rate). For shear-thinning fluids, the apparent viscosity is decreasing with increasing shear rate. For approximate calculations, most engineers used the Newtonian model to predict the drag coefficient of a solid particle in non-Newtonian fluid, because there is no distinct chart for the drag coefficient which includes the effect of changing fluid rheology and particle sphericity. But this approach gives poor and inaccurate results for all flow regimes around the particle. In this study, the effects of fluid rheology, and particle shape and size on settling velocity measurement have been studied experimentally, from which, new drag coefficient charts have been developed for spherical and disk particles when they settled down through various shear-thinning fluids. The flow behavior indices (n) for these fluids ranged from 0.6 to 0.92, and the predicted drag coefficients ranged from 0.1 to 10000 to cover particle Reynolds number from 0.001 to 100. For spherical particles, the new charts showed that the drag coefficient at a given particle Reynolds number is increased as the flow behavior index is decreased (i.e., the fluid became more non-Newtonian), and the drag coefficient is decreased as the particle Reynolds number is increased. But for disk particles, two settling paths were observed. The first one when n is less than 0.8, the particles were settled­-down edge-wise, and the other when n is greater than 0.8, the particles were settled-down base-wise. For both paths, the drag coefficient at a given particle Reynolds number is increased as the flow behavior index is decreased. Finally, a new empirical correlation has been developed which can be used to determine easily and directly the settling velocity, the particle Reynolds number, and the drag coefficient of spherical and disk particles when settles down in shear-thinning fluids.