## Preprint 2013-15

## Fernando Betancourt, Raimund Bürger, Stefan Diehl, Camilo Mejías:

### Advance methods of flux identification for Clarifier-Thickener simulation models

### Abstract:

Mathematical models for the simulation of batch settling and continuous clarifier-thickeners can usually be expressed as a convection-difusion partial diferential equation (PDE). Reliable numerical methods require that the nonlinear flux function of this PDE has been identified for a given material. This contribution summarizes, and applies to experimental data, a recent approach [R. Burger and S. Diehl, Inverse Problems 29 (2013) 045008] for the flux identification in the case of a suspension that shows no compressive behaviour. The experimental Kynch test and the Diehl test, which are based on an initially homogenous suspension either filling the whole settling column or being initially located above clear liquid, respectively, provide data points that represent a convex and concave, respectively, suspension-supernate interface. A probably convex (concave) smooth approximation of this interface is obtained by solving a constrained least-squares minimization problem. The interface-approximating function can be converted uniquely into an explicit formula for a convex (concave) part of the flux function.

This preprint gave rise to the following definitive publication(s):

**Fernando BETANCOURT, Raimund BüRGER, Stefan DIEHL, Camilo MEJíAS: ***Advance methods of flux identification for Clarifier-Thickener simulation models*. Minerals Engineering, vol. 63, pp. 2-15, (2014).