# Modeling of the Sedimentation Process of Monodisperse Suspension

Modeling of the Sedimentation Process of Monodisperse Suspension

Rząsa Mariusz Łukasiewicz Ewelina

Department of Computer Science, Opole University of Technology, Opole, Poland

Department of Thermal Engineering and Industrial Facilities, Opole University of Technology, Opole, Poland

Page:
50-61
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DOI:
https://doi.org/10.2495/CMEM-V10-N1-50-61
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Revised:
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Accepted:
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Available online:
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| Citation

OPEN ACCESS

Abstract:

During coagulation, particles with a flocculent shape and an irregular structure are formed in water. In the model sedimentation water presented in this study, three fractions of particles were distinguished and the method of calculating the sedimentation rate presented. Each fraction sediments in a different way due to different forces acting on particles of different shapes. The particles of fraction I are similar in shape to spherical particles, the particles of fraction II are non-spherical particles, and the particles of fraction III are porous agglomerates, for which the formula for liquid flow through a porous bed has been adopted. For the proposed theoretical sinking model for three types of suspensions composed of particles of each fraction, experimental tests were carried out, which confirmed the model predictions. The results for the sedimentation velocity of the monodisperse suspension of fractions I, II, and III are very similar to predictions: for fraction I, the discrepancy between theoretical and experimental results was 9%; for fraction II, 11%; and for fraction III, 17%. This proves a correctly selected methodology, and the proposed model can be used to calculate the sedimentation velocity of monodisperse suspen- sions of various shapes.

Keywords:

flocculation, monodisperse suspension, sedimentation modeling

References

[1] Podgórni, E. & Rząsa, R.M., Investigation of the effects of salinity and temperatureon the removal of iron from water by aeration, filtration and coagulation. Polish Journalof Environmental Studies, 23(6), pp. 2157–2161, 2014. https://doi.org/10.15244/pjoes/24927

[2] Shannon, M.A., Bohn, P.W., Elimelech, M., Georgiadis, J.G., Marinas, B.J. & Mayes,A.M., Science and technology for water purification in the coming decades. Nature,452, pp. 301–310, 2008.

[3] Tzoupanos, N.D. & Zouboulis, A.J., Coagulation-flocculation processes in water/wastewater treatment: The application of new generation of chemical reagents, 6th IASME/WSEAS International Conference on HEAT TRANSFER, THERMAL ENGINEERINGand ENVIRONMENT (HTE’08) Rhodes, Greece, August 20–22, 2008.

[4] Rosendahl, L., Using a multi-parameter particle shape description to predict the motionof non-spherical particle shapes in swirling flow. Applied Mathematical Modelling,24(1), pp. 11–25, 2000. https://doi.org/10.1016/s0307-904x(99)00023-2

[5] Sümer, M., Helvaci, P. & Helvaci Ş.Ş., Solid-Liquid Two Phase Flow, Elsevier, 2008.

[6] Sharma, M., Gupta, M. & Katy, P., A review on viscosity of nanofluids. InternationalJournal of Management, Technology And Engineering, 8(9), pp. 1413–1425, 2018.

[7] Barnea, E. & Mizrahi, J., A generalized approach to the fluid dynamics of particulatesystems. Part I. General correlation for fluidization and sedimentation in solid multiparticlesystems. The Chemical Engineering Journal, 5(2), pp. 171–189, 1973. https://doi.org/10.1016/0300-9467(73)80008-5

[8] Hashin, Z. & Shtrikman, S., A variational approach to the theory of the elastic behaviourof multiphase. Journal of the Mechanics and Physics of Solids, 11(2), pp. 127–140,1963. https://doi.org/10.1016/0022-5096(63)90060-7

[9] Happel, J. & Epstein, N., Viscous flow in multiparticle systems: cubical assemblage ofuniform spheres. Industrial & Engineering Chemistry, 46, pp. 1187–1194, 1954.

[10] Kelbaliyev, G. & Ceylan, K., Development of new empirical equations for estimationof drag coefficient, shape deformation, and rising velocity of gas bubbles or liquiddrops. Chemical Engineering Communications, 194, pp. 1623–1637, 2007. https://doi.org/10.1080/00986440701446128

[11] Rosendahl, L., Using a multi-parameter particle shape description to predict the motionof non-spherical particle shapes in swirling flow. Applied Mathematical Modelling,24(1), pp. 11–25, 2000. https://doi.org/10.1016/S0307-904X(99)00023-2

[12] Zastawny, M., Mallouppas, G., Zhao, F. & van Wachem, B., Derivation of drag and liftforce and torque coefficients for non-spherical particles in flows. International Journalof Multiphase Flow, 39, pp. 227–239, 2012. https://doi.org/10.1016/j.ijmultiphaseflow.2011.09.004

[13] Hölzer, A. & Sommerfeld, M., New simple correlation formula for the drag coefficientof non-spherical particles. Powder Technology, 184(3), pp. 361–365, 2008. https://doi.org/10.1016/j.powtec.2007.08.021

[14] Maron, S.H. & Pierce, P.E., Application of Ree-Eyring generalized flow theory to suspensionsof spherical particles. Journal of Colloid Science, 11(1), pp. 80–90, 1956.https://doi.org/10.1016/0095-8522(56)90023-X

[15] Sanjeevi, S.K.P., Kuipers, J.A.M. & Padding, J.T., Drag, lift and torque correlationsfor non-spherical particles from Stokes limit to high Reynolds numbers. InternationalJournal of Multiphase Flow, 106, pp. 325–337, 2018. https://doi.org/10.1016/j.ijmultiphaseflow.2018.05.011

[16] Leva, M., Weintraub, M., Grummer, M., Pollchik, M. & Storch, H.H., Fluid FlowThrough Packed and Fluidized Systems, Bulletin 504, Bureau of Mines, United StatesGovernment Office, Washington, 1951.

[17] Kozeny, J., Über kapillare Leitung des Wassers im Boden, Hölder-Pichler-Tempsky,A.-G. [Abt.] Akad. d. Wiss, Wiedeń, 1927.