Non-Newtonian effects on fall velocities of pairs of vertically aligned spheres

Many industrial slurries have as their major component a homogenous mixture of fine particles in a carrier fluid, and such mixtures typically display non-Newtonian properties. In addition, slurries often contain a fraction of large particles, which may settle with a terminal velocity that depends on mixture rheological properties and time since prior disturbance. This behaviour was investigated by experiments performed using spheres of various diameters and densities falling in a clear non-Newtonian medium with a yield stress. A mechanism is used to release pairs of spheres at known time differences. Both spheres fall in the same vertical line, with the second sphere having a greater terminal fall velocity than the first, an effect more pronounced for small differences in release time. The ratio of terminal fall velocity to that of an equivalent sphere in an effectively undisturbed medium was correlated against a dimensionless form of the difference in release time. A further dimensionless parameter was required, representing the significance of non-Newtonian behaviour. This parameter, zero for the Newtonian case, is larger for non-Newtonian media. It depends on the shape of the rheogram, but not on the specific function used to express it.