Mathematical model of vertical air classifiers

A theoretical concept is presented for the description of the separation process in a vertical gravitational air classifier. Particle movements within the classification zone are described by two types of transport: a convective transport, which represents the average movement of the particles and is characterized by the mean absolute particle velocity u; and a mixing transport, which comprises all transport due to deviations from the average particle displacement and is characterized by the mixing coefficient E.

The main assumptions of the model are that particle inertia is negligible and that the transport parameters u and E are constant along the height of the classification zone. The removal of the particles from the classification zone is described by rate equations. At the heavy fraction exit the removal rate is assumed to be linearly proportional to the fall velocity of the particle and the relative particle concentration at the heavy fraction exit. At the light fraction exit the removal rate is assumed to be linearly proportional to the superficial air velocity and the relative particle concentration at the light fraction exit.

Expressions are derived for the separation curve and for the mean residence time of the particles. The mean residence time of the particles is an indirect measure of the throughput capacity of the classifier. The relation between separation efficiency and mean residence time of the particles is calculated. The theoretical concept is experimentally verified for particles with small inertia at low particle concentrations in the classification zone. On the basis of the relation between separation efficiency and mean residence time of the particles conclusions are drawn with regard to the design of vertical gravitational air classifiers for separating usable components from mixed municipal waste. Obviously, these conclusions are valid only within the assumptions made in the model. Examples of possible designs illustrate these conclusions. It can be concluded from theory that suppression of particle mixing and accelerated removal of the particles from the classification zone yields the highest separation efficiency at comparable particle residence times.