A procedure for the direct numerical simulation (DNS) of the mixing of a passive scalar dissolved in a fluid phase due to the motion of spherical solid particles relative to the fluid is outlined. The procedure is based on solving the fluid flow in between the solid spheres with the lattice Boltzmann method, a molecular dynamics type of approach for the solid particle motion (including hard-sphere collisions), and solving a convection-diffusion equation for the passive scalar. The full resolution (in terms of particle motion, flow of interstitial fluid, boundary conditions at the particle surfaces) implies that only small-scale systems can be considered. In this paper the procedure is applied to a fully periodic system to assess the mixing performance of granular particles, and to a micro-channel in which particles are contained to enhance scalar mixing in laminar flow. (C) 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.