From Single Particle Drag Force to Segregation in Fluidised Beds

Discrete Element Modelling has been successfully applied in combination with fluid flow solvers (CFD) to tackle important multi-phase process engineering problems. However, until recently most of the DEM-CFD studies have dealt with monodisperse particulate systems. The reason for that is that DEM requires knowledge of the force exerted by the flowing fluid on each particle. While numerous expressions are available for homogenous systems, the presence of size polydispersion or the presence of solids mixtures complicate particle-level formulations of the drag force considerably and a general model is still lacking. In the present contribution a drag force model for polydisperse system is introduced and discussed. The expression was originally proposed in the literature on the basis of lattice-Boltzmann simulation results for flow through random polydisperse systems. However, its theoretical foundations were not fully recognised. The proposed formula requires the introduction of an average diameter, whose definition will be proved to be rigorously derivable provided that appropriate consistency constraints are considered. No other fitting or adjustable parameters are involved. In the case of a binary mixture of differently sized particles the resulting drag force is shown to depend both on size ratio and local volume fraction of the solids. Such precious particle-level information is then shown to be extendable to the macroscopic scale with attractive potentialities. On this basis, solution to the (open) problem of the segregation direction in a gas-fluidized bed of binary solids endowed with contrasting density and size differences will be suggested.