Modelling powder mixing in mass flow discharge: A kinematic approach

The dynamics of a powder flowing in a mass flow regime through a storage bin with a conical hopper, is a well studied problem. However, many challenges remain, including quantification of the mixing that occurs during discharge through the hopper. We have formulated a model based on the conservation of volume of the powder and a semi-empirical expression for velocity profile, (see 1], 2]), and used this to estimate mixing parameters. We have specifically considered the case of an inflow which is disposed in homogeneous horizontal layers as it enters the storage bin. When the powder, in successive layers, enters the hopper, it accelerates and its velocity along the longitudinal axis of the hopper is greater than at the walls. Portions of layers high in the hopper may overtake layers closer to the exit resulting in mixing of the layers. Using this model we are able to quantify the percentage of each layer in a given output volume and present results for typical hopper geometries.