The Discrete Element Method (DEM) was used to investigate the mechanics of adhesive units, the building blocks of adhesive mixtures, formed by a randomised distribution of fine particles of different shape (spherical, tetrahedral and triangular bipyramidal) on the surface of spherical carrier particles. Binary collision between like adhesive units was simulated for different surface coverage ratios (SCRs; 0.5, 0.7 and 1) at a fixed surface energy (interfacial adhesion strength). The obtained data was analysed in terms of effective mechanical properties (restitution coefficients), physical stability of the adhesive units and redistribution of fines. The effect of the fine particle shape was predominant for low SCRs, and adhesive units formed from tetrahedral fines exhibited the largest physical stability. However, this effect diminished with increasing SCR, for which an extensive network of contact chains dominated the dynamics. These results point towards ways to improve the flowability and integrity of adhesive mixtures during handling.