Simulation of concentrated suspensions using the force-coupling method

The force-coupling method (FCM) represents the dynamics of low Reynolds number suspension flows through a distributed, low-order, finite force-multipole expansion and provides an efficient, matrix-free method to solve the mobility problem for the particle motion. In concentrated suspensions, strong short-range lubrication forces are generated between particles in close proximity as fluid in the intervening gap is displaced by the relative motion of the particles. These forces, together with near-surface contact forces, play an important role in the suspension rheology and self-diffusion of particles. However these forces lead to ill-conditioned problems for determining the particle stresses and particle motion in large systems of particles at higher volume fractions. A robust and effective iteration scheme for determining the particle stresslets is described together with a new scheme for including lubrication forces as near-field corrections to the FCM resistance problem. Both the lubrication and far-field interactions are solved as fully coupled systems in O ( N p log ( N p ) ) operations, for N p particles, using preconditioned conjugate gradient solvers. Numerical results for particles settling under gravity, particle pairs in linearly varying flows and in concentrated suspensions are compared with previous theoretical results and simulations. Numerical simulations with more than 4000 non-Brownian, spherical particles in a homogeneous shear flow provide results on the pair-distribution function and Lagrangian velocity correlations. The extension of the methods to simulate bidisperse systems or wall-bounded suspensions are discussed.