Considering particle size distribution for various threshold velocities

In previous works we have shown that by defining threshold velocities, such as: pickup from a layer of particles, critical, wind threshold, incipient motion, boundary saltation, minimum pressure, minimum fluidization and terminal, in terms of the modified Reynolds number as a function of the modified Archimedes number a Generalized Master-Curve can be plotted. Using the Generalized Master-Curve, the ratio between various threshold velocities can be determined easily. However, all the threshold velocities were defined for mono-sized particles. In this paper, the various threshold velocities will be analyzed for particle size distribution. The analysis provides practical guides for various engineering cases, such as: selecting the appropriate fluidization velocity for maximum fluidization and minimum entrainment, selecting the conveying velocity in pneumatic systems and how it will affect the height of the layer of particles at the pipe bottom and whether it is stationary or moving.