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Updated: Jun 28, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
The solids-flux theory--confirmation and extension by using partial differential equations
1Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden. diehl@maths.lth.se
Water Research
|October 18, 2008
Summary
Solids-flux theory, used for decades in wastewater treatment, is refined by new mathematical analysis. This study confirms and extends flux theory, offering insights into secondary settling tank control and dynamic behavior.
Area of Science:
- Environmental Engineering
- Fluid Dynamics
- Applied Mathematics
Background:
- Solids-flux theory has been a cornerstone for designing and operating secondary settling tanks for 50 years.
- It relies on mass conservation and batch-settling flux functions (Kynch assumption) for stationary conditions.
- The theory models continuous sedimentation using one-dimensional conservation laws with discontinuous coefficients.
Purpose of the Study:
- To mathematically confirm and extend existing solids-flux theory.
- To investigate the dynamic behavior of settling tanks.
- To explore the control possibilities and limitations within the flux theory framework.
Main Methods:
- Utilized a one-dimensional conservation law with discontinuous coefficients to model sedimentation.
- Employed recent mathematical analysis to interpret and extend classical flux theory.
- Applied calculations to an ideal settling tank with a defined batch-settling flux.
Main Results:
- Confirmed and extended previous statements of solids-flux theory.
- Derived new conclusions regarding the dynamic behavior of settling tanks.
- Presented mathematical results in the form of convenient operating charts for practical application.
Conclusions:
- Recent mathematical advancements provide a more robust understanding of solids-flux theory.
- The study enhances the understanding of secondary settling tank dynamics and control.
- Operating charts derived from this analysis can aid in practical design and operation.
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