The Structure of Bidisperse Suspensions at Low Reynolds Numbers

We present a simulation technique for the direct simulation of the motion of spherical particles suspended in fluids at low Reynods numbers. We use this method to simulate bidisperse suspensions at varying size ratios of the suspended spheres and compare to analytic results of Batchelor for the low concentration regime. We find that the pair correlation functions indicate that three body hydrodynamic effects are significant even at volume fractions of φ = 0.01 and lead to a decrease of the settling velocity of the involved particle species. In order to describe the time evolution of the concentration profiles in a suspension that settles into a condensed sediment layer from an initially well-mixed state, we propose an advection-diffusion model. The functional forms of the required hindered settling and hydrodynamic diffusion terms are chosen to describe not only our simulation results but also match other experimental results and asymptotically known theoretical predictions.