Simulation of bidisperse colloidal centrifugal sedimentation using a mixture viscosity model

Abstract

Understanding the sedimentation behavior of bidisperse colloidal suspensions is critical in determining their stability and separation. While centrifugation is often used to accelerate separation, the settling of bidisperse colloids and their phase separation under these conditions is complex and difficult to predict explicitly. As an alternative, this work proposes a one-dimensional advection-diffusion model that uses an effective maximum volume fraction with a bidisperse viscosity scheme, which reflects important characteristics of bidisperse sedimentation while remaining computationally efficient. The influence of Derjaguin-Landau-Verwey-Overbeek interactions on packing fraction and dispersion viscosity is also considered. A numerical implementation is described using an adaptive finite-difference solver, which can be used for concentration profile and settling rate prediction of both species under variable acceleration. Validation experiments with silica suspensions in two size ratios (500:800 and 100:500 nm) and various total concentrations are performed using an analytical centrifuge, with results also being compared to Richardson-Zaki empirical predictions. The model is shown to be a very good fit to the data for both size ratio dispersions at three mixing ratios, with differences <10%. Slightly higher levels of variation were detected for the 500:800 nm system, owing to the smaller size ratio and resulting greater effect of uncounted secondary hydrodynamic factors, which enables the limits of the mixture viscosity model to be established. Nevertheless, this work highlights that mixture viscosity modeling combined with effective maximum volume fraction modifications can provide critical insights into the effect of bidisperse suspension dynamics on separation efficiencies.