The predictions of several polydisperse kinetic theories are presented in this study for the simple shear flow of a binary mixture of powders with varying sizes in a vacuum under zero gravity. These results are compared to published numerical data obtained using discrete molecular dynamics technique. The theory showing the most accurate results is modified so that the sum of the kinetic stresses of two or more identical solid phases adds to that of a monodisperse system with the same properties. Simulation results obtained in a three-dimensional riser for the flow of air and a binary mixture of glass beads are compared with available experimental data for each solid-phase velocity, concentration, and granular temperature. The predictions of the theory compare reasonably well with experimental data when the value of the linear particle-particle restitution coefficient is lowered to take into account the extra energy dissipation due to collisions between pairs of slightly frictional particles. Published by Elsevier Ltd.