A new modelling approach to slurry transport in dynamic beds based upon combining space and time-averaged Navier-Stokes equations with a new type of cell model is described. The resulting Ergun-like equation is used to correlate pressure drop with time-averaged distributions of the porosity, superficial fluid velocity and solids velocity for data derived from positron-emission-particle-tracking (PEPT) experiments in a scaled industrial tumbling mill fitted with lifter bars, pulp lifters and a discharge grate and run with particles and re-circulating slurry. (C) 2010 Elsevier Ltd. All rights reserved.