Multi-scale Modelling of Liquid Suspensions of Micron Particles in the Presence of Nanoparticles

A combined continuous, discrete, and statistic mechanics (CCDS) method is proposed to model micron particle dynamics in the presence of nanoparticles – a highly asymmetric system. The CCDS method treats the liquid medium as a continuum and the micron particles as a discrete phase, whereas the statistics mechanics method is used to treat the nanoparticles. The treatment of the nanoparticles involves the use of the Ornstein-Zernike equation with Percus-Yevick approximation based on the hard-sphere interaction. Such an approach enables the effective coupling between different length scales. Sedimentation of micron particles in the presence of nanoparticles is used as a case study for the CCDS method. It is shown that, at a high salt concentration where electrostatic repulsive force is significantly screened, the structural force induced by both monodisperse and bidisperse nanoparticles could overcome the van der Waals attractive force between the micron particles and thus prevent particle flocculation. It is also shown that the introduction of disparity in the system complicates the effective interactions between the micron particles and consequently the particle dynamics.