Advanced methods of flux identification for clarifier–thickener simulation models

• Clarifier–thickener simulators rely on the batch settling flux for given materials.
• A new method of flux identification from batch settling data is presented.
• Concentrated ranges of volume fraction are covered.
• The identified flux portions are convex or concave. This facilitates their use in simulators.
• Applications to synthetical and experimental data are presented.

Mathematical models for the simulation of batch settling and continuous clarifier–thickeners can usually be expressed as a convection–diffusion partial differential 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 [Bürger, R., Diehl, S., 2013. Inverse Problems 29, 045008] for the flux identification in the case of a suspension that shows no compressive behavior.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 provably 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.