Non-Brownian suspensions: simulation and linear response

We have developed and applied numerical techniques to study the dynamics of non-Brownian suspensions of spheres in viscous fluids. The numerical approaches reproduce experimental results like the mean settling velocity and pressure drops in particle arrays for solid volume fractions up to about 0.30 in 3D. In two dimensions we study the correlations between the velocity and the density distribution at small particle Reynolds numbers Re≈1 under the influence of gravity both by full hydrodynamic simulations and by linear analysis of corresponding continuum equations. For the case of the stratification of a dense homogeneous fluids on top of a less dense one, classical Rayleigh–Taylor theory predicts exponential growth of the arising initial velocity fluctuations. We find, however, that the system is driven by the initial density inhomogeneities that necessarily exist in a particulate suspension. The corresponding velocity modes saturate exponentially. The spatial correlation length of the emerging fingers grows in time until it reaches a limit, which, in our simulations, depends on the system size.