The mixing of solids is a fundamentally important unit operation in the pharmaceutical, food and agricultural industries, as well as many others. The efficiency and quality of mixing can have a significant bearing on downstream processability and product quality. In spite of the fact that the equipment, usually batch blenders without impellers such as tumbling bins and V-Blenders or with impellers such as ploughshare mixers, is well established, there remains considerable uncertainty in the optimisation of mixing. Simple laboratory/pilot scale mixers based on the rotating drum, such as the hoop mixer and the Turbula, are commonly used and yet also little understood in terms of performance. These mixers add additional rotational and/or translational movements to the cylindrical rotation of the drum to deliver significant improvements in mixing, particularly in the longitudinal axis. Discrete Element Modelling (DEM), in which a flowing or deforming granular system is modelled by considering the movement of each individual particle and its interaction (momentum and energy exchange) with neighbours and boundaries, has recently become accessible to relatively non-expert users. The reasons for this include: increasing confidence in its capability; user-friendly graphical interfaces of commercial software packages; and the fact that top end personal computers now have sufficient memory and computational speed to enable many problems to be solved in weeks rather than months. The purpose of the work reported here is to evaluate the power of DEM to help understand flow processes and explain mixing mechanisms in mixing equipment based on the rotating drum. The commercial package EDEM (from DEM Solutions) was used. For speed and simplicity the modelled system comprised monosized smooth glass beads. Three mixers were selected: horizontal rotating drum, the hoop mixer and the Turbula. The rate and extent of mixing, quantified using a "segregation index" based on contacts between two discretely labelled but otherwise identical fractions, was shown to depend on equipment motion, operating speed and the initial distribution of the fractions. The well known characteristics of the horizontal drum operating in rolling mode were demonstrated: excellent transverse mixing and poor axial mixing; both improving with speed as the depth of the active layer is shown to increase. The hoop mixer incorporates off-axis rotation, causing periodic tilting of the cylinder axis. This results in a considerable improvement in axial mixing. Interestingly, at low speeds the hoop mixer and simple rotating drum exhibit similar transverse mixing but increasing speed has the opposite effect: improving transverse mixing in the drum while worsening it in the hoop. Axial mixing in the hoop mixer, on the other hand improves with speed. The Turbula displays a very interesting relationship with speed. At low speeds, its transverse mixing performance is the same as the horizontal drum and hoop mixer but decreases significantly with increasing speed, going through a minimum at medium speed before recovering completely at high speed. Axial mixing is comparable, showing the same trend. It appears that the motion in the Turbula goes through some sort of transition that has a profound effect on mixing performance. The implication is that unless this is understood, it will be difficult a priori to identify optimum operating conditions. The power of DEM lies in the fact that the complete trajectory of each particle is recorded: it is possible to follow the movement, deformation and breakup of clusters of particles. From this it should be possible to elucidate the dominant flow mechanisms and to identify those that have the most impact on mixing. This presents a challenge to develop methodologies for cluster analysis and visualisation and is the subject of on-going work. Other work is focussed on experimental validation of the DEM predictions. (C) 2011 Elsevier B.V. All rights reserved.