Effect of the diameter of falling balls on the apparent viscosity of suspensions of spheres and rods

Neutrally buoyant, non-colloidal suspensions of spheres and rods are studied using falling-ball rheometry. The apparent viscosity of each suspension, calculated according to Stokes's law and corrected for effects due to the cylindrical boundaries of the experimental apparatus, is measured as a function of the volume fraction of particles, φ, and the diameter of the falling ball, d. The apparent viscosities of suspensions of spheres having φ ≤ 0.55 are found to be independent of the ratio of d to the diameter of the suspended sphere, d_s, in the range 1.0 ≤ d/d_s ≤ 6.0. In suspensions of rods of aspect ratio 19.83 and diameter, d_r, of 1.596 mm, the apparent viscosity is independent of d when d/d_r is greater than approximately 6.