AbstractSolids dispersion due to the simultaneous diffusion (random particle motion) and classification (segregation) of fluidized spheres has been investigated. The model developed permits calculation of the mean concentration of spheres of both sizes in a mixture of two sizes of fluidized spheres as a function of bed length. Fick's law has been applied to the diffusional phenomenon. A hypothesis has been advanced and confirmed which permits calculation [Equation (5)] of the classification velocity for each size of sphere in a fluidized mixture. Calculation of the classification velocities in a mixture of spheres is based on the relation of void fraction to superficial velocity for the individual sizes of spheres. To facilitate carrying out these calculations, a generalized equation has been developed for the relation of void fraction to superficial velocity in terms of the Galileo number (d3gΔρρƒ/μ2) and sphere‐to‐column diameter ratio. Measurement of the bead size gradients (change in bead size with bed length) at steady state fluidization was used to investigate dispersion. Closely sized glass beads of 0.1 and 0.2 cm. diameters were fluidized with liquids of 1 and 15 cps. at void fractions of 0.5 to 0.8 in 2.5 and 5.0 cm. columns. Lead beads of 0.12 cm. diameter were also used. Further, several experiments were conducted by a method which is analogous to that used in molecular diffusion cells.