We report on lattice-Boltzmann simulations of slow fluid flow past mono- and bidisperse random arrays of spheres. We have measured the drag force on the spheres for a range of diameter ratios, mass fractions and packing fractions; in total, we studied 58 different parameter sets. Our simulation data for the permeability agrees well with previous simulation results and the experimental findings. On the basis of our data for the individual drag force, we have formulated new drag force relations for both monodisperse and polydisperse systems, based on the Carman–Kozeny equations; the average deviation of our binary simulation data with the new relation is less than 5%. We expect that these new relations will significantly improve the numerical modelling of gas–solid systems with polydisperse particles, in particular with respect to mixing and segregation phenomena. For binary systems with large diameter ratios (1:4), the individual drag force on a particle, as calculated from our relations, can differ by up to a factor of five compared with predictions presently favoured in chemical engineering.