The approach of combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been increasingly used to study the fundamentals of coupled particle–fluid flows. Different CFD–DEM models have been used. However, the origin and the applicability of these models are not clearly understood. In this paper, the origin of different model formulations is discussed first. It shows that, in connection with the continuum approach, three sets of formulations exist in the CFD–DEM approach: an original format set I, and subsequent derivations of set II and set III, respectively, corresponding to the so-called model A and model B in the literature. A comparison and the applicability of the three models are assessed theoretically and then verified from the study of three representative particle–fluid flow systems: fluidization, pneumatic conveying and hydrocyclones. It is demonstrated that sets I and II are essentially the same, with small differences resulting from different mathematical or numerical treatments of a few terms in the original equation. Set III is however a simplified version of set I. The testing cases show that all the three models are applicable to gas fluidization and, to a large extent, pneumatic conveying. However, the application of set III is conditional, as demonstrated in the case of hydrocyclones. Strictly speaking, set III is only valid when fluid flow is steady and uniform. Set II and, in particular, set I, which is somehow forgotten in the literature, are recommended for the future CFD–DEM modelling of complex particle–fluid flow.

This paper presents a simulation study of the packing of uniform fine-spherical particles where the van der Waals force is dominant. It is shown that porosity increases with the decreases of particle size from about 100 to 1 μm and the simulated relationship can match the literature data well. The packing structure of fine particles is qualitatively depicted by illustrative pictures and quantified in terms of radial distribution function, angular distribution, and coordination number. The results indicate that in line with the increase in porosity, the first component of the split second peak and then the other peaks beyond the second one in the radial distribution function gradually vanish; the first peak becomes narrower, with a sharp decrease to the first minimum. As particle size decreases, the peaks at 120° and then 60° in the angular distribution will gradually vanish; the coordination number distribution shifts to the left and becomes narrower. The mean coordination number can decrease to a value as low as two for 1 μm particles, giving a very loose and chainlike structure. The interparticle forces acting on individual particles in a stable packing are analyzed and shown to be related to the packing properties.