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The solids-flux theory - Confirmation and extension by using partial differential equations.

Diehl, Stefan LU (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)
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author
organization
publishing date
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
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
2008-12-08 10:38:59
date last changed
2017-02-09 11:59:46
@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},
  volume       = {42},
  year         = {2008},
}