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dc.contributor.authorMoruzzi, R.B.
dc.contributor.authorBridgeman, John
dc.contributor.authorSilva, P.A.G.
dc.date.accessioned2020-06-20T08:45:02Z
dc.date.accessioned2020-07-21T09:24:52Z
dc.date.available2020-06-20T08:45:02Z
dc.date.available2020-07-21T09:24:52Z
dc.date.issued2020-03
dc.identifier.citationMoruzzi RB, Bridgeman J and Silva PAG (2020) A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry. Water Science & Technology. 81(5): 915-924.en_US
dc.identifier.urihttp://hdl.handle.net/10454/17920
dc.descriptionYesen_US
dc.description.abstractSedimentation 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 ¼ 2.61, floc size, df > 320 μm and dp ¼ 7.5 μm settle with lower velocities than those predicted by Stokes’ law; whilst, for Df ¼ 2.33, all aggregates of df > 70 μm and dp ¼ 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 performanceen_US
dc.description.sponsorshipRodrigo B. Moruzzi is grateful to São Paulo Research Foundation (Fundação de Amparo à Pesquisa do Estado de São Paulo – FAPESP) Grant 2017/19195-7 for financial support and to CNPq for the fellowship Grant 301210/2018-7.en_US
dc.language.isoenen_US
dc.relation.isreferencedbyhttps://doi.org/10.2166/wst.2020.171en_US
dc.rights©IWA Publishing 2020. The definitive peer-reviewed and edited version of this article is published in Water Science & Technology 81(5): 915-924, 2020, https://doi.org/10.2166/wst.2020.171 and is available at www.iwapublishing.com
dc.subjectDensityen_US
dc.subjectFlocculationen_US
dc.subjectFractal dimensionen_US
dc.subjectPorosityen_US
dc.subjectSettling velocityen_US
dc.titleA combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometryen_US
dc.status.refereedYesen_US
dc.date.Accepted2020-03-31
dc.date.application2020-04-10
dc.typeArticleen_US
dc.date.EndofEmbargo2021-04-11
dc.type.versionAccepted Manuscripten_US
dc.description.publicnotesThe full-text of this article will be released for public view at the end of the publisher embargo on 11 Apr 2021.
dc.date.updated2020-06-20T07:45:10Z
refterms.dateFOA2020-07-24T15:08:59Z


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