document: As already discussed, in dilute flows the choice between the hard sphere and soft sphere models largely depends on the computational time spent to solve the particle equation of motion. For very dilute flows, the hard sphere model is the most natural choice. However, when the collisions can no longer be assumed as binary and instantaneous, the soft sphere model is the only realistic option. It is interesting to know whether the choice of the collision model affects the statistics. Fig. 14 compares the mean velocity obtained from both models with the experimental data. The same comparison is performed for the smooth walls. The differences between the hard and soft sphere models for the smooth walls are almost negligible. However, the differences between the hard and soft sphere models for the rough walls are minor. This is because the rough wall treatment in the soft sphere implementation adds extra virtual walls during the collision of a particle with a wall, which is a more realistic representation of a rough wall compared to the hard sphere rough wall treatment where one random wall is considered. This is because, a soft sphere collision is not instantaneous and occurs over a finite amount of time. Similarly, the same effects are observed on the fluid statistics. However, Fig. 15, which compares the particle velocity fluctuations, shows that the differences are somewhat larger. Additionally, the differences in both particle mean and RMS velocity profiles are because the hard sphere collisions are unfortunately heavily dependent on the tangential coefficient of restitution (ψ); the effects by varying this quantity are shown in Figs. 16 and 17.