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Electric potential distribution in nanoscale electroosmosis has been investigated using the nonequilibrium molecular dynamics (NEMD), whose results are compared with the continuum based Poisson-Boltzmann (PB) theory. If the bin size of the MD simulation is no smaller than a molecular diameter and the focusing region is limited to the diffusion layer, the ionic density profiles on the bins of the MD results agree well with the predictions based on the Poisson-Boltzmann theory for low and moderate bulk ionic concentrations. The PB equation breaks down at high bulk ionic concentrations, which is also consistent with the macroscopic description.

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.