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SUMMARYThe discrete element method (DEM) is widely used in calculating powder systems. The DEM makes it possible to determine the complicated phenomena related to particle flowability. However, DEM has a fatal problem, which is that the number of calculated particles is restricted due to excessive calculation costs. Consequently, we have developed a large-scale model of the DEM, which is called the coarse grain model. The coarse grain particle represents a group of the original particles. Therefore, a large-scale DEM simulation can be performed using an extremely small number of the calculated particles. In our previous studies, the coarse grain model was applied in gas-solid and solid-liquid flow systems. It is anticipated that the coarse grain model will be used in various powder systems. In the current study, the coarse grain model has been applied to a two-dimensional bubbling fluidized bed. The adequacy of the coarse grain model was proved by a comparison with the original particle behavior. The simulation results obtained using the coarse grain model showed good agreement with the results for the original system. Moreover, the calculation speed with the coarse grain model was shown to be much faster than the calculation speed of the original model.

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In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.