## 5 Conclusions  
In this work, the performance of discrete and continuum approaches for modeling the solids motion inside a rotating drum at different regimes has been studied. To achieve this, a pilot-plant rotating drum experiment filled with DAP spherical particles with a 4-mm diameter, was mounted with a plexiglass cover to observe the flow patterns using a high-speed camera. The DEM simulations were performed with the open-source code LIGGGHTS(R), while a VOF solver of the OpenFOAM(R) platform was adopted for the continuum approach. To account for the granular flow dynamics in this context, an implementation of the \(\mu(I)\)-rheology was made on the general structure of the viscosity models library of the code. For evaluating the performance of the computational approaches, four different test cases at different regimes were considered. The accuracy of the results was analyzed in terms of solids distribution, particles velocities, and mixing patterns. The main findings may be summarized as follows:  
* The solids distribution for each regime was correctly predicted with both techniques, except for the slumping regime, which could not be captured by the CM approach. This was attributed to the use of a high-viscosity threshold instead of a yield criterion in the implementation of the rheology model. In the fastest regimes, DEM predicted more splashing of particles than the experimental observations;
* The velocity of the particles predicted by the models was mostly in agreement with the experimental results. Neither of the computational models stood out over the other in this regard as both tend to detach more from the experimental observations where the material flow backwards relative to the rotation of the drum;
* The rate of mixing of two different materials in a cascading regime was well predicted by both models, reaching a fairly similar level of mixing at different instants in time. While the DEM results were in very good agreement with the experiments, the CM predicted a slower dragging of the material as the system was accelerated but reaching similar steady-state profiles of the interface between the bed of particles and the air. This drawback might be attributed to the lack of non-local effects and a yield criterion that reign over the inertial regime at slow speeds;
* In the rolling regime, CM saved around 20% of computational time compared to DEM, both with an optimized set of numerical parameters. This suggests that, when the dimensions of the problem shifted from pilot-plant to industrial-scale, CM might still be suitable while the computational costs of DEM might become prohibitive. In general, both techniques were able to predict the granular flow patterns in most of the regimes analyzed. The CM model used in this work needs to incorporate more phenomenological features to predict with the same level of accuracy as DEM for lab and pilot-plant scales. This indicates that a more comprehensive rheological model is needed but it is yet to be proven if an Euler-Euler approach (such as the Two-Fluids Model) instead of VOF could yield more accurate predictions. The results of this study suggest that a continuum model based on the \(\mu(I)\)-rheology (with a pressure-dependent viscosity and a yield criterion) enhanced with non-local effects, in contrast to DEM, would be an interesting approach for simulating industrial-scale rotating drums, by meeting both accuracy and computational cost requirements. Conceptualization: C.M.V., S.M.D. and N.M.N. ; Methodology: C.M.V., S.M.D., S.E.B., G.D.P. and N.M.N. ; Supervision: N.M.N., S.E.B. and J.M.R. provided the experimental facilities. All the authors contributed to the discussion, the writing, and the revision of the paper. All authors read and agreed to the published version of the manuscript. This research was funded by ANPCyT grant PICT 2016-2908, ASACTEI grant 1010-009-16, ASACTEI grant AC-00010-18, Universidad Tecnologica Nacional through Research Program ASUTNRA0007817 and CONICET for the funding through doctoral and postdoctoral scholarships.