The shape and behaviour of a granular bed in a rotating drum using Eulerian flow fields obtained from PEPT

Non-invasive single-particle tracking techniques, such as positron emission particle tracking (PEPT), provide useful information about the behaviour of a representative particle moving in a bulk of similar particles in a rotating drum. The Lagrangian trajectories that they yield can be used to study, for example, particulate diff usion or granular interaction. However, often the Eulerian flow fi elds of the entire granular bed are more useful-- they can be used to study segregation, for instance, or the evolution of the free surface of the bed. In this work, we present a technique for converting Lagrangian trajectories to Eulerian flow fields via a time-weighted residence time distribution (RTD) of the tracked particle. We then perform PEPT experiments on a mono-disperse bed of spherical particles in a cylindrical drum, rotated at various rates, and use the RTD procedure to obtain flow fi elds of the bed. We use these flow fi elds to investigate the e ffect of drum rotational speed on the shape and behaviour of a granular bed in a rotating drum, and the insights gained thereby to defi ne a comprehensive set of surfaces{ such as the bulk free surface{ to divide the bed into regions of distinct granular behaviour. We further defi ne scalar bed features-- such as the centre of circulation of the bed-- that can be used to quantitatively compare the behaviour of granular beds in rotating drums operated under various conditions