A kinematic model of continuous separation and classification of polydisperse suspensions

Kinematic models for polydisperse suspensions are based on specifying the solid–fluid relative velocity for each solids species as a function of the local solids concentrations. One such model, the Masliyah–Lockett–Bassoon (MLB) model, is employed herein to simulate continuous separation and classification of polydisperse suspensions. To this end, the clarifier-thickener (CT) setup for the continuous separation of suspensions is extended to a generalized clarifier-thickener (GCT). Discharge streams (or products) are described by new singular sink terms. Combining the GCT setup with the MLB model yields a system of nonlinear conservation laws with a discontinuous flux and a new non-conservative transport term describing the sinks. A numerical algorithm for the solution of this equation is presented along with numerical examples. The model describes the GCT unit with all critical design parameters, and predicts the composition of the overflow, underflow and discharge streams and the spatio-temporal evolution of the solids species concentrations inside the unit.