Effective diameter for group motion of polydisperse particle mixtures

An analysis is conducted on the effective mean diameter for fluidized beds and other two-phase flows for which the drag and gravitational forces are the primary determinants of particle motion. This work was motivated by Eulerian-based computational treatments of particles which assume a single group velocity for a polydisperse collection of particles within a computational cell. For particles in the inertial-dominated regime (e.g. Rep>2000), it is found that the Sauter mean diameter is the effective mean diameter regardless of particle shape, particle size number distribution, particle density distribution, or net volume fraction. However, the effective mean diameter is the volume-width diameter for particles which are in the creeping flow regime (Rep≪1), e.g. in micro-fluidized beds. Expressions for the effective diameter for solid spherical particles at intermediate Reynolds numbers are given for a log-normal probability distribution function and for binary mixtures. Finally, comparison with two experimental data sets shows a qualitative validation of the derived effective diameter for the group motion of polydisperse mixtures.