The solids-flux theory - Confirmation and extension by using partial differential equations.
(2008) In Water Research 42(20). p.4976-4988- Abstract
- The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and... (More)
- The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1262174
- author
- Diehl, Stefan LU
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Water Research
- volume
- 42
- issue
- 20
- pages
- 4976 - 4988
- publisher
- Elsevier
- external identifiers
-
- wos:000262055900010
- pmid:18926553
- scopus:56949104343
- pmid:18926553
- ISSN
- 1879-2448
- DOI
- 10.1016/j.watres.2008.09.005
- language
- English
- LU publication?
- yes
- id
- 101ffb5f-464f-4064-a607-f0196ccc6f31 (old id 1262174)
- alternative location
- http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V73-4TJ6F94-3-1&_cdi=5831&_user=745831&_orig=search&_coverDate=12%2F31%2F2008&_sk=999579979&view=c&wchp=dGLbVlb-zSkzV&md5=b2b5f0e708a1003b4c6d6e77f7e3463d&ie=/sdarticle.pdf
- date added to LUP
- 2016-04-01 14:39:31
- date last changed
- 2022-02-04 22:04:52
@article{101ffb5f-464f-4064-a607-f0196ccc6f31,
abstract = {{The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.}},
author = {{Diehl, Stefan}},
issn = {{1879-2448}},
language = {{eng}},
number = {{20}},
pages = {{4976--4988}},
publisher = {{Elsevier}},
series = {{Water Research}},
title = {{The solids-flux theory - Confirmation and extension by using partial differential equations.}},
url = {{http://dx.doi.org/10.1016/j.watres.2008.09.005}},
doi = {{10.1016/j.watres.2008.09.005}},
volume = {{42}},
year = {{2008}},
}