| The process of fluid particle flow is encountered in numerous applications. In nature or industry, we deal with both highly concentrated flow, where the solid phase interactions are dominant, or more dilute flow where the interaction between the solid and fluid is becoming more important.To understand the behavior of fluid particle flow, one may first need to understand granular flows where the interstitial fluid effects may be neglected. In granular media, the particle-particle interaction is dissipative, thus modeling the flow behavior is non-trivial.The purpose of this work is to investigate the effect of particle properties (e.g. size, particle density) on granular flow behavior using the kinetic theory approach.The kinetic theory is extended to a multi-type (size and/or density) mixture of particles, where each type of particles is represented by a phase, with an average velocity and a fluctuating velocity. We solved the Boltzmann's equation for each particulate phase using the Chapman-Enskog procedure by adding a perturbation to the Maxwellian velocity distribution function. In our mathematical model, the momentum equation for each particulate phase includes phase interaction due to collisional pressure and particle-particle drag force.Our model was applied to simple shear flow of binary and ternary mixture of particles. In the parameter range studied, the rheological behavior of a binary mixture showed a good quantitative agreement with the molecular dynamics simulation calculation of Galvin et al. (2004) and predicted qualitatively well the experiment of Savage and Sayed (1984) and Feitosa and Menon (2002). Furthermore, the investigation of a ternary granular mixture showed interesting results: the fluctuations were strongly damped and the granular mixture showed less resistance to the flow when the number of particulate phases with smaller particle size increased in the mixture, while the total particle concentration remained unchanged.This model predicted well segregation by size when applied to couette shear flow. The calculated numerical values for flow parameters using our model compared well with the experiment of Karion and Hunt (1999). |
