Second-order moment of kinetic theory of granular flow for multi-type particles

In this study, a numerical method, second-order moment of kinetic theory of granular flow for multi-type particles (SOM-KTGF-MP) is proposed. The SOM-KTGF is used for particle flow with higher concentration and high inertia where inter-particle collisions exist; however, the particle fluctuation is far from equilibrium to satisfy the Boussinesq hypothesis. The model, SOM-KTGF-MP, is derived here as an extension of SOM-KTGF for mono-sized particles to be applied to multi-type particles with different sizes, densities, and other properties. In SOM-KTGF-MP, the conservation equations of the volume fraction, mean velocity, and second-order moment of the fluctuating velocity of particles are solved for each type of particle species in the multi-type mixture. A binary mixture of particles in a simple shear flow was predicted using the SOM-KTGF-MP method. The result was in good agreement with the prediction made by the discrete molecular dynamics method, when considering the non-equipartition of particle velocity between particle species and the non-equipartition of energy between the normal components of the second-order moment of the fluctuating velocity of particles. The SOM-KTGF-MP method increased the fidelity of the prediction of the binary mixture flow of particles based on the kinetic theory.