Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in Stokes flow

Applicability of the pseudo-fluid concept in the case of settling monosized rigid spheres in the viscous regime was partially confirmed using theoretical elaborations and empirical data on viscosity of suspensions. Three formulae: by Richardson and Zaki, Hawksley as well as Eq. (28), giving almost identical results for volumetric concentrations phi < 0.55, have overestimated the settling velocities of suspensions comparing with available experimental results and predictions by the rest of analyzed formulae. The most probable reason for this discrepancy is omission of collisions between more than two relatively large (non-Brownian) particles in terms describing the apparent viscosity of the denser suspensions, which behave as non-Newtonian fluids. That discrepancy can be reduced by a replacement of the mean backflow velocity w(f) with the maximum one w(fm) = 2w(f) in the formula for slip velocity, which reduces the relative settling velocity by a factor (1 + phi)(-1). For suspensions with concentration phi < 0.2 the factor (1 + phi)(-1) is equivalent numerically to the voidage (1 - phi). (C) 2011 Elsevier Ltd. All rights reserved.