A numerical study of the accelerating motion of a dense rigid sphere in non-Newtonian power law fluids

The equations of motion of an accelerating sphere falling through non-Newto nian fluids with power law index n in the range 0.2 less than or equal to n less than or equal to 1.8 were integrated numerically using the assumption that the drag on the sphere was a function of both power law index and ter minal Reynolds number, Re-t. For 10(-2) less than or equal to Re-t less tha n or equal to 10(3) both dimensionless time and distance travelled by the s phere under transient conditions showed a much stronger dependence on the f low behaviour index, n, for sheer-thinning than for shear-thickening fluids . The form of this dependence is investigated here. Furthermore, results in four typical shear-thinning fluids suggested a strong correlation between the distance and time travelled by the sphere under transient conditions an d the value of the fluid consistency index. The analysis reported herein is , however, restricted to dense spheres falling in less dense fluids, when a dditional effects arising from the Basset forces can be neglected.