| In recent years, the thickener units for a very important equipment of solid-liquid separation are widely used in chemical engineering, mineral processing, food industry, the pulp-and-paper ,wastewater treatment, and so on. The study of sedimentation theory began in the early 20th century, it has improved greatly after nearly a century of development. But the research of thickener in design theory, experimental theory and mathematical model is very little. the mathematical model of the thickener unit is studied by sedimentation theory and a small continuously operated thickener device in laboratory. Its results can take some guidance directly to the design and operation of industrial machines, it can also predict settling velocity, bottom flow concentration and so on. Therefore, the paper has a certain practical significance.The chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifier-thickener units. This model appears in a variable cross-sectional area units, In the case,the governing equation is a scalar, strongly degenerate parabolic equation. We introduce a simple finite difference scheme and the software of model is writed by VB. Numerical examples illustrate that the model realistically describes the dynamics of flocculated suspensions in clarifier-thickeners.The paper contains six parts: The first part makes a brief description for the content of this article. The second part formulates a mathematical model for the clarifier-thickener. The third part describes the finite difference scheme of the model ,and the initial and boundary problem. The fourth part analyzes batch settlement and a small continuously operated thickener device in laboratory. The fifth part compares the difference of simulation results and actual results, and proves the feasibility of the model. The sixth part is the conclusion of the paper. |
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