A semi-empirical model for the drag force and fluid–particle interaction in polydisperse suspensions

Fluid flow through stationary or moving particle beds is a common process in industrial units. The two-phase hydrodynamics strongly influences the performances and characteristics of reactors and contactors in general, but the possibility to model comprehensively the details of the two-phase field of motion still lacks. Computational methods and multi-scale modeling are capable of providing essential information at the microscopic scale. In the present paper, recently published data on the fluid-particle interaction obtained at the sub-particle scale are used to propose a semi-empirical model for the calculation of the fluid-particle interaction, named the basis of computer simulations of fluid-solid flows. The proposed approach starts from flow through monodisperse particle beds and leads to a general expression valid over a very wide range of Reynolds' number and porosity and, most notably, accounts for polydispersion in a consistent and general way. Available actual drag force data from lattice-Boltzmann simulations for mono- and bi-disperse systems are fitted by a physically consistent and computationally efficient model, obtaining a very good agreement over a broad range of conditions. The resulting model is validated both against lattice-Boltzmann simulations involving ten different species and against experimental measurements in real two-component beds fluidized by a liquid exhibiting the layer inversion phenomenon. The model is shown to predict well the correct values under a significant variability of operating conditions. Finally a discussion of the application of the model in the context of numerical simulations is presented.