Loading...
A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry
Moruzzi, R.B. Bridgeman, John Silva, P.A.G.
Moruzzi, R.B.
Bridgeman, John
Silva, P.A.G.
Publication Date
2020-03
End of Embargo
Supervisor
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
Peer-Reviewed
Yes
Open Access status
Accepted for publication
2020-03-31
Institution
Department
Awarded
Embargo end date
Additional title
Abstract
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 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 performance
Version
Accepted Manuscript
Citation
Moruzzi 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.
Link to publisher’s version
Link to published version
Link to Version of Record
Type
Article