Continuous Settlement Mathematical Model And Numerical Simulation

The process of settling is a solid-liquid separation process. It is alsoamulti-level and multi-material mixing process, which involves fluid mechanics,applied mathematics, reactor engineering disciplines and so on. Settlingbehavior is a very complex phenomenon that is not easily described fully bypeople. Over time, the need of the process of settling application is increasing, itrises a activity of settling model research of home and abroad. This upsurgedevelops the settling theory, settling model and solid-liquid separationtechnology.Continuous sedimentation of solid particles in a liquid takes place in aclarifier-thickener unit, which has one feed inlet and two outlets. The processcan be modeled by a nonlinear scalar conservation law with point source anddiscontinuous flux function. The chief purpose of this paper is to formulate andpartly analyze a new mathematical model for continuoussedimentation-consolidation processes of flocculated suspensions inclarifier-thickener units. This model appears in two variants for cylindrical andvariable cross-sectional area units, respectively. In both cases, the governingequation is a scalar, strongly degenerate parabolic equation in which both theconvective and diffusion fluxes depend on parameters that are discontinuousfunctions of the depth variable. We present existence and uniqueness results inthe case of varying cross-sectional area and a complete classification of thesteady-state solutions when the cross-sectional area decreases with depth. Theclassification is utilized to formulate a static control strategy for the largediscontinuity called the sludge blanket that appears in steady-state operation.The construction of steady-state concentration profiles attainable in acontinuously operated clarifier-thickener is described. This constructionincorporates an entropy principle, which implies that only those steady states areadmissible for which the solids concentration is increasing downwards.Numerical examples of steady-state profiles are presented. Implication of themathematical model is also demonstrated by steady-state calculations, which lead to new possibilities in thickener design.