Hindered settling of log-normally distributed particulate suspensions: theoretical models vs. Stokesian simulations

TL;DR

This study compares theoretical models and Stokesian Dynamics simulations to analyze hindered settling velocities in log-normal polydisperse suspensions, highlighting model accuracy limitations and proposing avenues for improvement.

Contribution

It evaluates the accuracy of existing hindered settling models against detailed simulations for polydisperse suspensions, identifying their limitations and suggesting improvements.

Findings

Batchelor's model predicts within 5% for low volume fractions.

Other models overestimate velocities of smaller particles.

Velocity fluctuations are similar in monodisperse and polydisperse suspensions.

Abstract

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.