  Settling velocity statistics for dilute, non-Brownian suspensions of
polydisperse spheres having a log-normal size distribution are analysed by
Stokesian Dynamics, as a function of the total volume fraction and width of the
size distribution. Several hundred instantaneous configurations are averaged to
obtain reliable statistics. Average velocities for each particle class are
compared to the models proposed by Batchelor, Richardson & Zaki, Davis & Gecol,
and Masliyah-Lockett-Bassoon (MLB). Batchelor's model is shown to give
reasonably accurate predictions when the volume fraction is within 5%. Because
of its complexity, this model is however hardly used in practice, so
lower-order models are needed. We found that while the other hindered settling
models can give reasonably accurate predictions of the velocity of the largest
particles, all of them overestimate - in certain cases by a large margin - the
velocity of the smaller particles. By computing the fluid-particle velocity
slip for each particle class and using Batchelor's model, we explain why
predicting the lower tail of the particle size distribution is challenging, and
propose possible avenues for model improvement. The analysis of velocity
fluctuations suggest quantitative similarities between velocity fluctuations in
monodisperse and polydisperse suspensions.
