Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

The drag coefficient of a solid particle depends mainly on
the particle Reynolds number, particle sphericity, and fluid
rheology. The sphericity of a solid particle is the degree to
which the shape of a solid particle approaches that of a sphere.
Non-Newtonian fluids are those fluids which do not show
linear relationship between shear stress and shear rate.
Practically, the apparent viscosity for shear-thinning fluids is
decreasing with increasing shear rate. Settlement of solid
particles in shear-thinning fluids is of great importance and has
many applications in drilling operations, chemical industry, and
mining processes.
In this study, the combined effects of particle sphericity and
fluid rheology on settling velocity measurement have been
studied experimentally. Fifty irregular-shape solid particles
with different sphericities (ranged from 0.575 to 0.875), and
four shear-thinning fluids with flow behavior indices (ranged
from 0.60 to 0.92) were used.
A new drag coefficient charts have been developed for
irregular-shape solid particles when they settled down through
various shear-thinning fluids, which cover laminar to transient
flow regimes around the particles. These charts show linear
relationships between the drag coefficient and particle
Reynolds number for all fluids, which have the same slope but
with different intercepts.
These charts show that the drag coefficient at a given
particle Reynolds number is increased as the flow behavior
index is decreased (i.e. as the fluid becomes more non-
Newtonian), which means higher resistance to particle
movement. And, for a given fluid rheology, the drag coefficient
is decreased as the particle Reynolds number is increased,
which means less resistance to particle movement (i.e. faster
slip velocity).
Finally a general equation has been developed for irregularshape
particles when they settle down in various shear-thinning
fluids, which can be used to calculate easily and directly the
settling velocity and the particle Reynolds number of these
particles. This equation can also be used for spherical and disk
particles.