Settling Velocity Analysis of Natural Suspended Particles Using Fractal Approach
Publication: Journal of Environmental Engineering
Volume 146, Issue 12
Abstract
An automated nonintrusive image analysis method is used to measure the settling velocity of particles and characterize their geometric properties using a fractal approach. A range of suspension characteristics is represented by particles collected from four field sites and one laboratory sample of a montmorillonite clay suspension. The field sites are Lake Ontario, Lake Erie, Lake LaSalle (a small lake in Buffalo, New York), and the Buffalo River (also in Buffalo, New York). In fractal descriptions of aggregates, particle areas do not scale with diameter squared, and settling rates vary with size, shape, and porosity. Measured settling rates are found to be less than values estimated by Stokes’ law, which is consistent with other studies of natural floc settling and indicates the flocs are not solid and spherical, as assumed for that law. They also are less than settling predicted with relationships developed for spheres at higher Reynolds number than the range associated with Stokes’ law. A dimensional analysis is performed to determine the relationship of settling rate with size, which is also correlated with other geometric and physical quantities that can be described using fractal geometry. The relationship determined using this approach provides a very good description of the observed settling rates for each of the five samples, and suggests settling velocity varies with particle size, expressed as area equivalent diameter raised to a power of approximately 1.4. Furthermore, a 2- to 7-fold overestimation of the settling velocity of larger aggregates can occur when Stokes’ law is applied. These results are useful for better prediction of particle fate and particle-bound contaminant transport, particularly in estimating contaminant residence time, fate, and overall surface water quality.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors greatly appreciate research funding provided by the Great Lakes Program and the Department of Civil, Structural and Environmental Engineering at the University of New York at Buffalo. Authors are grateful to Jacobs Engineering Co., for providing assistance during manuscript preparation.
References
Adachi, Y., and Y. Tanaka. 1997. “Settling velocity of an aluminum-kaolinite floc.” Water Res. 31 (3): 449–454. https://doi.org/10.1016/S0043-1354(96)00274-6.
Atkinson, J. F., R. K. Chakraborti, and J. E. VanBenschoten. 2005. “Effects of floc size and shape in particle aggregation.” In Flocculation in natural and engineered environmental systems, edited by I. G. Droppo, G. G. Leppard, S. N. Liss, and T. G. Milligan. Boca Raton, FL: CRC Press.
Bouyer, D., C. Coufort, A. Line, and Z. Do-Quang. 2004. “Experimental analysis 447 of floc size distribution under different hydrodynamics in a mixing tank.” AIChE. J. 50 (9): 2064–2081. https://doi.org/10.1002/aic.10242.
Brown, P. P., and D. F. Lawler. 2003. “Sphere drag and settling velocity revisited.” J. Environ. Eng. 129 (3): 222–231. https://doi.org/10.1061/(ASCE)0733-9372(2003)129:3(222).
Bushell, G. C., Y. D. Yan, D. Woodfield, J. Raper, and R. Amal. 2002. “On techniques for the measurement of the mass fractal dimension of aggregates.” Adv. Colloid Interface Sci. 95 (1): 1–50. https://doi.org/10.1016/S0001-8686(00)00078-6.
Chakraborti, R. K., and J. F. Atkinson. 2006. “Dependence of perceived aggregate size on pixel resolution using an imaging method.” J. Water Supply: Res. Tech.—AQUA 55 (7–8): 439–451. https://doi.org/10.2166/aqua.2006.041.
Chakraborti, R. K., J. F. Atkinson, and J. E. Van Benschoten. 2000. “Characterization of alum floc by image processing.” Environ. Sci. Technol. 34 (18): 3969–3976. https://doi.org/10.1021/es990818o.
Chakraborti, R. K., K. H. Gardner, J. F. Atkinson, and J. E. Van Benschoten. 2003. “Changes in fractal dimension during aggregation.” Water Res. 37 (4): 873–883. https://doi.org/10.1016/S0043-1354(02)00379-2.
Chakraborti, R. K., K. H. Gardner, J. Kaur, and J. F. Atkinson. 2007. “In-situ analysis of flocs.” J. Water Supply: Res. Tech.—AQUA 56 (1): 1–11. https://doi.org/10.2166/aqua.2007.063.
Chakraborti, R. K., and J. Kaur. 2014. “Non-invasive measurement of particle settling velocity and comparison with Stoke’s law.” J. Environ. Eng. 140 (2): 04013008. https://doi.org/10.1061/(ASCE)EE.1943-7870.0000790.
Chancelier, J. P., G. Chebbo, and E. Lucas-Aiguir. 1998. “Estimation of settling velocities.” Water Res. 32 (11): 3461–3471. https://doi.org/10.1016/S0043-1354(98)00114-6.
Droppo, I. G., B. G. Krishnappan, and C. Jaskot. 2006. “Evaluation of a laser-assisted particle sizing/settling velocity determination technique.” Hydrol. Proc. 20 (9): 1885–1893. https://doi.org/10.1002/hyp.5949.
Droppo, I. G., and E. D. Ongley. 1992. “The state of suspended sediment in the freshwater fluvial environment: A method of analysis.” Water Res. 26 (1): 65–72. https://doi.org/10.1016/0043-1354(92)90112-H.
Dyer, K. R., and A. J. Manning. 1999. “Observation of the size, settling velocity and effective density of flocs, and their fractal dimensions.” J. Sea Res. 41 (1–2): 87–95. https://doi.org/10.1016/S1385-1101(98)00036-7.
Elimelech, M., J. Gregory, X. Jia, and R. A. Williams. 1995. Particle deposition and aggregation—Measurement, modeling and simulation. London: Butterworth-Heinemann.
Fair, G. M., and J. Geyer. 1954. Water supply and waste-water disposal. Hoboken, NJ: Wiley.
Gibbs, R. J. 1982. “Floc breakage during HIAC light-blocking analysis.” Environ. Sci. Technol. 16 (5): 298–299. https://doi.org/10.1021/es00099a012.
Gregory, J. 1989. “Fundamentals of flocculation.” Crit. Rev. Environ. Control 19 (3): 185–230. https://doi.org/10.1080/10643388909388365.
Gregory, J. 1998. “The role of floc density in solid-liquid separation.” Filtr. Sep. 35(4):367–371. https://doi.org/10.1016/S0015-1882(97)87417-4.
Gruy, F. 2012. “Modelling of aggregate restructuring in a weakly turbulent flow.” Colloids Surf. A: Physicochem. Eng. Aspects 395 (2012): 54–62. https://doi.org/10.1016/j.colsurfa.2011.12.003.
Guérin, L., C. Francesa, A. Liné, and C. Coufort-Saudejaud. 2019. “Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments.” Colloids Surf. A: Physicochem. Eng. Aspects 560 (Jan): 213–222. https://doi.org/10.1016/j.colsurfa.2018.10.017.
Jiang, Q., and B. E. Logan. 1991. “Fractal dimensions of aggregates determined from steady state size distributions.” Environ. Sci. Technol. 25 (12): 2031–2038. https://doi.org/10.1021/es00024a007.
Johnson, C. P., X. Li, and B. E. Logan. 1996. “Settling velocities of fractal aggregates.” Environ. Sci. Technol. 30 (6): 1911–1918. https://doi.org/10.1021/es950604g.
Keyvani, A., and K. Strom. 2013. “A fully-automated image processing technique to improve measurement of suspended particles and flocs by removing out-of-focus objects.” Comput. Geosci. 52 (Mar): 189–198. https://doi.org/10.1016/j.cageo.2012.08.018.
Khelifa, A., and P. S. Hill. 2006. “Models for effective density and settling velocity of flocs.” J. Hydraul. Res. 44 (3): 390–401. https://doi.org/10.1080/00221686.2006.9521690.
Kim, D., Y. Son, and J. Park. 2018. “Prediction of settling velocity of nonspherical soil particles using digital image processing.” In Advances in civil engineering, 1–8. London: Hindawi Publishing Corporation.
Klimpel, R. C., C. Dirican, and R. Hogg. 1986. “Measurement of agglomerate density in flocculated fine particle suspensions.” Part. Sci. Technol. 4: 45–59. https://doi.org/10.1080/02726358608906441.
Kysela, B., Z. Chara, and P. Ditl. 2008. “Aggregates settling velocity—Direct in situ measurement.” Sep. Sci. Technol. 43 (7): 1610–1620. https://doi.org/10.1080/01496390801973821.
Larsen, T. 2000. “Measuring the variations of the apparent settling velocity for fine particles.” Water Res. 34 (4): 1417–1418. https://doi.org/10.1016/S0043-1354(99)00235-3.
Li, X., and Y. Yuan. 2002. “Settling velocities and permeabilities of microbial aggregates.” Water Res. 36 (12): 3110–3120. https://doi.org/10.1016/S0043-1354(01)00541-3.
Logan, B. E. 1999. Environmental transport processes. New York: Wiley.
MacDonald, I. T., and J. C. Mullarney. 2015. “A novel ‘flocdrifter’ platform for observing flocculation and turbulence processes in a lagrangian frame of reference.” J. Atmos. Oceanic Technol. 32 (3): 547–561. https://doi.org/10.1175/JTECH-D-14-00106.1.
Maggi, F. 2013. “The settling velocity of mineral, biomineral, and biological particles and aggregates in water.” J. Geophys. Res. Oceans 118 (4): 2118–2132. https://doi.org/10.1002/jgrc.20086.
Manning, A., P. Friend, N. Prowse, and C. Amos. 2007. “Estuarine mud flocculation properties determined using an annular mini-flume and the LabSFLOC system.” Cont. Shelf Res. 27 (8): 1080–1095. https://doi.org/10.1016/j.csr.2006.04.011.
Many, G., X. D. de Madron, R. Verney, F. Bourrin, P. R. Renosh, F. Jourdin, and A. Gangloff. 2019. “Geometry, fractal dimension and settling velocity of flocs during flooding conditions in the Rhône ROFI.” Estuarine Coastal Shelf Sci. 219 (Apr): 1–13. https://doi.org/10.1016/j.ecss.2019.01.017.
Moruzzi, R. B., J. Bridgeman, and P. A. G. Silva. 2020. “A combined experimental and numerical approach to the assessment of floc settling velocity using fractal geometry.” Water Sci. Technol. 81 (5): 915–924. https://doi.org/10.2166/wst.2020.171.
Stokes, G. G. 1850. “On the effect of the internal friction of fluids on the motion of pendulums.” In Transactions of the Cambridge Philosophical Society IX, 8. London: Cambridge Philosophical Society.
Strom, K., and A. Keyvani. 2011. “An explicit full-range settling velocity equation for mud flocs.” J. Sediment. Res. 81 (12): 921–934. https://doi.org/10.2110/jsr.2011.62.
Sun, S., M. Weber-Shirk, and L. W. Lion. 2016. “Characterization of flocs and floc size distributions using image analysis.” J Environ. Eng. Sci. 33 (1): 25–34. https://doi.org/10.1089/ees.2015.0311.
Syvitski, J. P. M., K. W. Asprey, and K. W. G. Leblanc. 1995. “In-situ characteristics of particles settling within a deep-water estuary.” Deep Sea Res. Part II 42 (1): 223–256. https://doi.org/10.1016/0967-0645(95)00013-G.
Tambo, N., and Y. Watanabe. 1979. “Physical aspect of flocculation process—I. Fundamental treatise.” Water Res. 13: 429–439.
Tang, P., J. Greenwood, and J. A. Raper. 2002. “A model to describe the settling behavior of fractal aggregates.” J. Colloid Interface Sci. 247 (1): 210–219. https://doi.org/10.1006/jcis.2001.8028.
Tang, P., and J. A. Raper. 2002. “Modelling the settling behavior of fractal aggregates—A review.” Powder Tech. 123 (2–3): 114–125. https://doi.org/10.1016/S0032-5910(01)00448-X.
Thonon, I., J. R. Roberti, H. Middelkoop, M. van der Perk, and P. A. Burrough. 2005. “In situ measurements of sediment settling characteristics in floodplains using a LISST-ST.” Earth Surf. Processes Landforms 30 (10): 1327–1343. https://doi.org/10.1002/esp.1239.
Vahedi, A., and B. Gorczyca. 2012. “Predicting the settling velocity of flocs formed in water treatment using multiple fractal dimensions.” Water Res. 46 (13): 4188–4194. https://doi.org/10.1016/j.watres.2012.04.031.
Vahedi, A., and B. Gorczyca. 2014. “Settling velocities of multifractal flocs formed in chemical coagulation process.” Water Res. 53 (Apr): 322–328. https://doi.org/10.1016/j.watres.2014.01.008.
Van Rijn, L. C. 2007. Manual sediment transport measurements in rivers, estuaries and coastal seas. Delft, Netherlands: Aqua Publications.
Williams, R. A., S. J. Peng, and A. Naylor. 1992. “In-situ measurement of particle aggregation and breakage kinetics in concentrated suspension.” Powder Tech. 73 (1): 75–83. https://doi.org/10.1016/0032-5910(92)87009-Y.
Zhang, Z., J. Zhao, S. Xia, C. Liu, and X. Kang. 2007. “Particle size distribution and removal by a chemical-biological flocculation process.” J. Environ. Sci. 19 (5): 559–563. https://doi.org/10.1016/S1001-0742(07)60093-X.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 146 • Issue 12 • December 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Nov 1, 2019
Accepted: Jul 22, 2020
Published online: Sep 30, 2020
Published in print: Dec 1, 2020
Discussion open until: Feb 28, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.