Single particle trajectories, obtained using the Positron Emission Particle Tracking (PEPT) technique, have been used to characterise axial and radial dispersion of granular media in the rolling drum operated in batch and continuous mode. Axial dispersion can be quantified in terms of axial displacement or angle of descent through the active layer, both of which follow a Gaussian distribution. Radial dispersion is quantified in terms of the change in radius of the particle in the passive layer following each passage through the active layer. The distribution of this change is also Gaussian. The mean angle of descent obtained in the continuous (inclined drum) experiments agrees well with the predictions of Saeman [W.C. Saeman, Passage of solids through rotary kilns, Chem. Eng. Prog., 47 (10) (1951), 508-514.]. Furthermore, the axial and radial dispersion coefficients obtained from batch and continuous experiments are comparable, giving confidence in the use of batch data to predict mixing and residence time distribution in continuous operation. The effects of drum speed, drum diameter and drum fill level on the axial and radial dispersion coefficients are inconsistent and it appears that other factors, not considered here, such as particle shape and even electrostatics may be important. Very large differences are observed between the dispersion coefficients of monodisperse sand and polydisperse TiO2. Yet the effects of particle size within the TiO2 system appear relatively small. It is shown that mixing in the active layer can be far from complete: there is a correlation between the radii at which the particle enters and leaves the active layer. The implications for heat transfer models based on penetration theory are discussed. (c) 2005 Elsevier B.V. All rights reserved.