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.