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In this paper, recent advances in the discrete-element method (DEM) for describing motion, deposition, agglomeration or aggregation of a large number of adhesive spherical particles immersed in fluid flows, termed as adhesive particulate flow, are reviewed. The constitutive equations together with the length and time scales of DEM are compared with those of other similar Lagrangian particle methods, e.g., molecular dynamics (MD), Brownian dynamics (BD), dissipative particle dynamics (DPD). The adhesive contact force and torque models in the presence of different adhesive effects are examined, including van der Waals force, ligand-receptor binding, liquid bridging force, interface adhesion, and sintering forces, all of which play an important role in DEM formulations for different types of adhesive particulate flow problems of interest in energy, combustion and environmental fluid mechanics problems. A …