Analysis and optimization of a multicascade method for the size fractionation of poly-dispersed particle systems via sedimentation or centrifugation

Sedimentation and centrifugation can be used to sort particles by size, using a multistep (multicascade) method in which particles in the sediment are removed and the content of the supernatant is processed again, repeating the cycle several times. This paper proposes a theoretical analysis of this process, based on a one-dimensional model, with a view to identify parameters that are optimal to obtain a relatively monodispersed suspension, starting from a log-normal particle size distribution. We found that a rational choice of the sedimentation/centrifugation time enables to control the amount of particles outside of the desired size range (impurities). Surprisingly, the multistep method does not converge, as multiple steps are worse than 2 steps. Band sedimentation, in which a particle-rich layer is overlaid on clear fluid, offers substantial benefits in terms of impurity reduction with respect to starting from a completely mixed situation. An application to graphene fractionation is discussed.