Segregation dynamics of dense polydisperse fluidized suspensions modeled using a novel formulation of the direct quadrature method of moments

Computational fluid dynamics (CFD) may be a useful design tool, provided that the mathematical models that we solve with it capture and describe well the most important features of the systems of interest. For fluidized beds, one of these features is the polydispersity of the powders: particles differ in size and alter their size distribution in time and space continuously. To model this key phenomenon, one needs to solve a population balance equation, that is, an equation that governs the evolution of the size distribution. The direct quadrature method of moments (DQMOM) allows doing so in commercial CFD codes at relatively low computational cost. This technique, successfully employed for describing dilute multiphase flows of particles that share the same velocity, still needs testing in the context of dense multiphase flows. Dense polydisperse fluidized powders can segregate or mix, depending on the process operating conditions, and to describe these phenomena one needs to let particles move with different velocities. In this work we use a recent version of DQMOM that has this feature: each quadrature class is advected with its own velocity. The transport equations of this model feature a diffusive-like contribution that allows the powders to mix at the particle length scale. We discuss how to assign a value to the diffusion coefficient and we carry out a sensitivity analysis on the latter; to do so, we simulate the mixing of powders initially segregated using different values for the diffusivity. Successively, after having estimated a suitable value for the latter, we simulate the system dynamics under conditions that should promote segregation, validating the results of the simulations experimentally.