The lattice-Boltzmann method has been refined to take account of near-contact interactions between spherical particles. First, we describe a comprehensive solution to the technical problems that arise when two discretized surfaces come into contact. Second, we describe how to incorporate lubrication forces and torques into lattice-Boltzmann simulations, and test our method by calculating the forces and torques between a spherical particle and a plane wall. Third, we describe an efficient update of the particle velocities, taking into account the possibility that some of the differential equations are stiff.

• Received 5 July 2002

DOI:https://doi.org/10.1103/PhysRevE.66.046708