On the relative motion of a particle in a swarm of different particles

Abstract

The classification of dissimilar particles in a liquid suspension is exploited in many industrial unit operations. To understand and predict fluidization phenomena in general and particle classification in particular, adequate expressions for each of the governing forces—gravity, buoyancy and drag forces—are required. A possible formulation of the effective driving force and friction in multicomponent mixtures is discussed in this paper. A new expression is derived, which is based on a steady-state force balance for the classifying particle. The expression requires only the usual fluidization data of a single particle species such as the terminal velocity and the Richardson and Zaki index. The new expression is compared with some existing classification models with respect to their predictive value for a wide range of classification data. The new expression proved to be accurate over the entire range of known experimental data and can be extended easily to multicomponent fluidized suspensions. We have found strong evidence that the exact formulation of the buoyancy acting on the classifying particle originates from the bulk density of the fluidized suspension, regardless of the ratio of particle sizes. To clarify the relation between the “overall” drag force and the ratio of particle sizes, the “overall” friction on the classifying particle is decomposed into a solid-liquid and a solid-solid component. The particle-particle interaction force is proportional to the product of the hold-up of the fluidized particles and the slip velocity of dense and fluidized particles. In agreement with other authors, we found an increased friction with a decreasing ratio of classifying and fluidized particles. The particle-particle interaction coefficient was correlated with a modified Stokes-Einstein equation.