A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.2166/wst.2020.171 http://hdl.handle.net/11449/199008 |
Resumo: | Sedimentation processes are fundamental to solids/liquid separation in water and wastewater treatment, and therefore a robust understanding of the settlement characteristics of mass fractal aggregates (flocs) formed in the flocculation stage is fundamental to optimized settlement tank design and operation. However, the use of settling as a technique to determine aggregates' traits is limited by current understanding of permeability. In this paper, we combine experimental and numerical approaches to assess settling velocities of fractal aggregates. Using a non-intrusive in situ digital image-based method, three- and two-dimensional fractal dimensions were calculated for kaolin-based flocs. By considering shape and fractal dimension, the porosity, density and settling velocities of the flocs were calculated individually, and settling velocities compared with those of spheres of the same density using Stokes' law. Shape analysis shows that the settling velocities for fractal aggregates may be greater or less than those for perfect spheres. For example, fractal aggregates with floc fractal dimension, Df = 2.61, floc size, df > 320 μm and dp = 7.5 μm settle with lower velocities than those predicted by Stokes' law; whilst, for Df = 2.33, all aggregates of df > 70 μm and dp = 7.5 μm settled below the velocity calculated by Stokes' law for spheres. Conversely, fractal settling velocities were higher than spheres for all the range of sizes, when Df of 2.83 was simulated. The ratio of fractal aggregate to sphere settling velocity (the former being obtained from fractal porosity and density considerations), varied from 0.16 to 4.11 for aggregates in the range of 10 and 1,000 μm, primary particle size of 7.5 μm and a three-dimensional fractal dimension between 2.33 and 2.83. However, the ratio decreases to the range of 0.04-2.92 when primary particle size changes to 1.0 μm for the same fractal dimensions. Using the floc analysis technique developed here, the results demonstrate the difference in settlement behaviour between the approach developed here and the traditional Stokes' law approach using solid spheres. The technique and results demonstrate the improvements in understanding, and hence value to be derived, from an analysis based on fractal, rather than Euclidean, geometry when considering flocculation and subsequent clarification performance. |
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A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometryDensityFlocculationFractal dimensionPorositySettling velocitySedimentation processes are fundamental to solids/liquid separation in water and wastewater treatment, and therefore a robust understanding of the settlement characteristics of mass fractal aggregates (flocs) formed in the flocculation stage is fundamental to optimized settlement tank design and operation. However, the use of settling as a technique to determine aggregates' traits is limited by current understanding of permeability. In this paper, we combine experimental and numerical approaches to assess settling velocities of fractal aggregates. Using a non-intrusive in situ digital image-based method, three- and two-dimensional fractal dimensions were calculated for kaolin-based flocs. By considering shape and fractal dimension, the porosity, density and settling velocities of the flocs were calculated individually, and settling velocities compared with those of spheres of the same density using Stokes' law. Shape analysis shows that the settling velocities for fractal aggregates may be greater or less than those for perfect spheres. For example, fractal aggregates with floc fractal dimension, Df = 2.61, floc size, df > 320 μm and dp = 7.5 μm settle with lower velocities than those predicted by Stokes' law; whilst, for Df = 2.33, all aggregates of df > 70 μm and dp = 7.5 μm settled below the velocity calculated by Stokes' law for spheres. Conversely, fractal settling velocities were higher than spheres for all the range of sizes, when Df of 2.83 was simulated. The ratio of fractal aggregate to sphere settling velocity (the former being obtained from fractal porosity and density considerations), varied from 0.16 to 4.11 for aggregates in the range of 10 and 1,000 μm, primary particle size of 7.5 μm and a three-dimensional fractal dimension between 2.33 and 2.83. However, the ratio decreases to the range of 0.04-2.92 when primary particle size changes to 1.0 μm for the same fractal dimensions. Using the floc analysis technique developed here, the results demonstrate the difference in settlement behaviour between the approach developed here and the traditional Stokes' law approach using solid spheres. The technique and results demonstrate the improvements in understanding, and hence value to be derived, from an analysis based on fractal, rather than Euclidean, geometry when considering flocculation and subsequent clarification performance.UNESP Universidade Estadual Paulista Instituto de Geociências e Ciências ExatasFaculty of Engineering and Informatics University of BradfordUNESP Universidade Estadual Paulista Instituto de Geociências e Ciências ExatasUniversidade Estadual Paulista (Unesp)University of BradfordMoruzzi, R. B. [UNESP]Bridgeman, J.Silva, P. A.G. [UNESP]2020-12-12T01:28:10Z2020-12-12T01:28:10Z2020-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article915-924http://dx.doi.org/10.2166/wst.2020.171Water Science and Technology, v. 81, n. 5, p. 915-924, 2020.1996-97320273-1223http://hdl.handle.net/11449/19900810.2166/wst.2020.1712-s2.0-85086681629Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengWater Science and Technologyinfo:eu-repo/semantics/openAccess2021-10-22T22:17:27Zoai:repositorio.unesp.br:11449/199008Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:11:41.016516Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
title |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
spellingShingle |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry Moruzzi, R. B. [UNESP] Density Flocculation Fractal dimension Porosity Settling velocity |
title_short |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
title_full |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
title_fullStr |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
title_full_unstemmed |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
title_sort |
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry |
author |
Moruzzi, R. B. [UNESP] |
author_facet |
Moruzzi, R. B. [UNESP] Bridgeman, J. Silva, P. A.G. [UNESP] |
author_role |
author |
author2 |
Bridgeman, J. Silva, P. A.G. [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) University of Bradford |
dc.contributor.author.fl_str_mv |
Moruzzi, R. B. [UNESP] Bridgeman, J. Silva, P. A.G. [UNESP] |
dc.subject.por.fl_str_mv |
Density Flocculation Fractal dimension Porosity Settling velocity |
topic |
Density Flocculation Fractal dimension Porosity Settling velocity |
description |
Sedimentation processes are fundamental to solids/liquid separation in water and wastewater treatment, and therefore a robust understanding of the settlement characteristics of mass fractal aggregates (flocs) formed in the flocculation stage is fundamental to optimized settlement tank design and operation. However, the use of settling as a technique to determine aggregates' traits is limited by current understanding of permeability. In this paper, we combine experimental and numerical approaches to assess settling velocities of fractal aggregates. Using a non-intrusive in situ digital image-based method, three- and two-dimensional fractal dimensions were calculated for kaolin-based flocs. By considering shape and fractal dimension, the porosity, density and settling velocities of the flocs were calculated individually, and settling velocities compared with those of spheres of the same density using Stokes' law. Shape analysis shows that the settling velocities for fractal aggregates may be greater or less than those for perfect spheres. For example, fractal aggregates with floc fractal dimension, Df = 2.61, floc size, df > 320 μm and dp = 7.5 μm settle with lower velocities than those predicted by Stokes' law; whilst, for Df = 2.33, all aggregates of df > 70 μm and dp = 7.5 μm settled below the velocity calculated by Stokes' law for spheres. Conversely, fractal settling velocities were higher than spheres for all the range of sizes, when Df of 2.83 was simulated. The ratio of fractal aggregate to sphere settling velocity (the former being obtained from fractal porosity and density considerations), varied from 0.16 to 4.11 for aggregates in the range of 10 and 1,000 μm, primary particle size of 7.5 μm and a three-dimensional fractal dimension between 2.33 and 2.83. However, the ratio decreases to the range of 0.04-2.92 when primary particle size changes to 1.0 μm for the same fractal dimensions. Using the floc analysis technique developed here, the results demonstrate the difference in settlement behaviour between the approach developed here and the traditional Stokes' law approach using solid spheres. The technique and results demonstrate the improvements in understanding, and hence value to be derived, from an analysis based on fractal, rather than Euclidean, geometry when considering flocculation and subsequent clarification performance. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T01:28:10Z 2020-12-12T01:28:10Z 2020-03-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.2166/wst.2020.171 Water Science and Technology, v. 81, n. 5, p. 915-924, 2020. 1996-9732 0273-1223 http://hdl.handle.net/11449/199008 10.2166/wst.2020.171 2-s2.0-85086681629 |
url |
http://dx.doi.org/10.2166/wst.2020.171 http://hdl.handle.net/11449/199008 |
identifier_str_mv |
Water Science and Technology, v. 81, n. 5, p. 915-924, 2020. 1996-9732 0273-1223 10.2166/wst.2020.171 2-s2.0-85086681629 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Water Science and Technology |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
915-924 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1808129031926710272 |