Hydrodynamic simulations of sedimenting dilute particle suspensions under repulsive DLVO interactions

We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope $K$ of the concentration-dependent sedimentation velocity and the range $\chi$ of the electrostatic repulsion normalized by the average particle-particle distance. When $\chi \to 0$, the particles are too far away from each other to interact electrostatically and $K=6.55$ as predicted by the theory of Batchelor. As $\chi$ increases, $K$ likewise increases as if the particle radius increased in proportion to $\chi$ up to a maximum around $\chi=0.4$. Over the range $\chi=0.4-1$, $K$ relaxes exponentially to a concentration-dependent constant consistent with known results for ordered particle distributions. Meanwhile the radial distribution function transitions from a disordered gas-like to a liquid-like form. Power law fits to the concentration-dependent sedimentation velocity similarly yield a simple master curve for the exponent as a function of $\chi$, with a step-like transition from 1 to 1/3 centered around $\chi = 0.6$.