The object of this work is to develop methods for the quantitative prediction of all the major features of flow of a gas, together with solid particulate material, through a duct of arbitrary size and inclination. Flows of this sort are of great technical importance in pneumatic transport of particulate material, and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation 100~ in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants. In all these systems the particles tend to distribute themselves over the cross section of the duct in a markedly non-uniform way, making it very difficult to predict the hold up of solid material and the pressure drop along the duct, or even to extrapolate these quantities from measurements made with the same materials in ducts of other sizes. In addition, the crowding of the particles into limited parts of the cross section can lead to undesirable effects, such as recirculation of the solid material against the direction of the main flow.
The key to making useful predictions for these systems is to understand and quantify the mechanism that determines the distribution of particle concentration over the cross section. This understanding must be based on equations of motion for the gas and the particles, so the object of the present work has been to propose such equations of motion and explore their solutions for flow through ducts. These solutions appear to simulate many of the characteristic observed properties of flows of this sort, including the undesirable recirculation patterns referred to above. However, they are unduly sensitive to the values of certain physical properties of the gas and the particles, indicating that turbulent flows must be considered to give a satisfactory account of the situation of greatest technical importance, where suspensions flow at high rates through large ducts. The modelling of turbulent flow of a suspension is difficult, but a start in this direction has been made.