The settling of consecutive spheres in viscoplastic fluids

One of the factors contributing to the uncertainties involved in the estimation of particle settling velocity in viscoplastic fluids is the time-dependent effect where the viscous parameters of the fluid change as a particle flows through and shears the medium. These changes, particularly at low shear Reynolds numbers, are reflected in the settling velocity of a following sphere that is released some time after an initial one, with the following sphere having a significantly greater velocity. This study found that changes in both fall velocity and equivalent viscosity can be correlated satisfactorily by a power law equation to the dimensionless form of the time interval between releases, and the rheogram shape factor for the fluid. A collision of particles occurs in cases where the time interval between releases is small, after which the particles combine and travel at a terminal velocity. A new variable, β, which takes into account the different surficial stress of the combined spheres, was introduced to the correlation of Wilson et al. Wilson, K.C., Horsley, R.R., Kealy, T., Reizes, J.A., Horsley, M.R., 2003. Direct prediction of fall velocities in non-Newtonian materials. Int. J. Miner. Process. 71, 17–30] β was found to depend on the rheogram shape factor for the fluid and the shear Reynolds number for the particle. The validity of this approach was supported by experimental data.