Preprint 2001-041

A Mathematical Model for Batch and Continuous Thickening of Flocculent Suspensions in Vessels with Varying Cross Section

Abstract: The phenomenological theory of continuous thickening of flocculated suspensions in an ideal cylindrical thickener is extended to vessels having varying cross-section, including divergent or convergent conical vessels. The purpose of this contribution to draw attention to the corresponding mathematical model, whose key ingredient is a strongly degenerate parabolic partial differential equation. For ideal (non-flocculated) suspensions, which do not form compressible sediments, the mathematical model reduces to the kinematic approach by Anestis, who developed a method of construction of exact solution by the method of characteristics. The difficulty lies in the fact that characteristics and iso-concentration lines, unlike the conventional Kynch model for cylindrical vessels, do not coincide, and one has to resort to numerical methods to simulate the thickening process. A numerical algorithm is presented and employed for simulations of continuous thickening. Implications of the mathematical model are also demonstrated by steady-state calculations, which lead to new possibilities in thickener design.

Paper:

Available as PostScript (5.1 Mbytes) or gzipped PostScript (1.3 Mbytes; uncompress using gunzip).

Author(s):

Raymund Bürger

J.J.R. Damasceno, <j.jrdamasceno@ufu.br>

Kenneth Hvistendahl Karlsen <kennethk@mi.uib.no>

Publishing information:

Submitted to a special issue of Int. J. Mineral Process on the occation of the United Engineering Foundation conference "Solid-Liquid Separation Systems III", Davos, September 30 to October 5, 2001

Comments:

Submitted by:

<kennethk@mi.uib.no> October 10 2001.