Species interactions in binary particulate systems

In many models for binary particulate systems, the relative motion between two particle species is modeled by diffusion. Recently, two-equation models have been used to improve diffusion models. While two-equation models are significant improvements to diffusion models and are applicable in modeling dilute systems, they are still theoretically inadequate for dense systems. This inadequacy directly results from the assumption that the species interaction forces in the two momentum equations sum to zero. In fact, the sum of the two forces is not zero but the divergence of an interspecies stress [ Zhang, Ma and Rauenzahn Phys. Rev. Lett. 97 048301 (2006)]. Introduction of this interspecies stress amends the inadequacy in two-equation models. The main objective of the present paper is to examine the importance of this newly introduced interspecies stress relative to other known stresses in the system. For this purpose we numerically simulate the simplest possible granular system. The interspecies stress is of the same order of magnitude as other stresses for dense systems. Additionally, we also examine properties of the species interaction force under different conditions.