We present results from a direct numerical simulation of the passive transport of solid particles by a fully developed turbulent channel flow with a Reynolds number of 180 based on the friction velocity and the channel half-width. Three particle sets are studied, ranging in diameter from 0.5 to 1.4 viscous wall units and in aerodynamic time constant from 0.6 to 56 centreline Kolmogorov time scales. We use particle number density histograms and fractal dimensions to show that the level of order in the particle spatial distribution peaks near a Stokes number of unity based on the Kolmogorov time scale. We then quantify the relationship between this spatial distribution and the instantaneous flow topology. The results indicate that the previously reported preferential concentration of particles in low-speed streaks leads to a suppression of particle velocities in the viscous sublayer and buffer region even in the presence of streamwise gravitational acceleration. In other regions of the flow, the particles' non-random spatial distribution is shown to be uncorrelated with the local flow topology. We compare our results with the experimental data of Kulick et al. (1994) and Fessler et al. (1994) and confirm that the latter authors' results were not influenced by turbulence modification.