Computational fluid dynamics (CFD) is extensively employed to investigate dense fluidized suspensions Most mathematical models assume that the powder is monodisperse or is formed by few solid phases of particles with constant size Real powders, nevertheless, are polydisperse, with their particle size distribution continuously changing in time and space. To account for this Important feature, models have to include a population balance equation (PBE). which needs to be solved along with the customary fluid dynamic transport equations The recently developed direct quadrature method of moments (DQMOM) permits solving PBEs in commercial CFD codes at relatively low computational cost. This technique, nevertheless, still needs testing in the context of dense multiphase flows In this work we implement DQMOM within the CFD code Fluent to study the mixing of two polydisperse fluidized suspensions initially segregated. Each node of the quadrature represents a distinct solid phase advected with its own velocity. Simulating this apparently simple system highlights a problem related to the numerical solution of the DQMOM transport equations these do not feature diffusive terms. but the numerical diffusion generated by the finite-volume integration method alters the model predictions, leading to wrong results To solve this, the PBE needs to account for diffusion: this yields source terms in the transport equations of the quadrature weights and nodes that ensure the latter are correctly predicted