Dynamic and steady-state behavior of continuous sedimentation

Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process can be modeled by a nonlinear scalar conservation law with point source and discontinuous flux function. This paper presents existence and uniqueness results in the case of varying cross-sectional area and a complete classification of the steady-state solutions when the cross-sectional area decreases with depth. The classification is utilized to formulate a static control strategy for the large discontinuity called the sludge blanket that appears in steady-state operation. A numerical algorithm and a few simulations are also presented.