Mixing behavior of binary non-spherical particles in a horizontal rotating drum: a shape-dependent optimal Froude number model

Horizontal rotating drums are widely used for particulate processing, but particle shape strongly impacts flow and mixing, rendering the conventional Froude number inadequate for non-spherical binary systems. We combine DEM simulations with experiments using spherical, ellipsoidal, and cubic particles of equal diameter and density. Distinct from isolated shape analyses, we introduce average sphericity and sphericity difference as coupled descriptors. We quantify their effects on flow-regime transition, mixing quality, and bed stability via kinetic-energy partitioning and collision dynamics. Furthermore, we resolve energy transfer into impact, shear, and dissipation powers, showing that shape parameters control both collision frequency and energy allocation among normal, tangential, and irreversible pathways. A shape-dependent model linking the mixing index to the Froude number is developed. Results reveal that lower average sphericity advances flow transition and bed disturbance but restricts particle rotation and interlocking, degrading mixing quality. Larger sphericity differences intensify reorientation and asynchronous migration, lowering bed stability and mixing quality while amplifying index fluctuations. The model yields R2 ≥ 0.918 and RMSE ≤ 0.021, confirming its effectiveness. This work offers a quantitative basis for selecting rotational speeds and scaling up industrial drums for non-spherical particle mixing.