Abstract
Fluidized bed bioreactors are widely used in wastewater treatment applications. Such reactors employ gel beads or hard particles covered with a biofilm layer. These particles lose more energy due to deformation when they collide than particles with high mechanical resistance. This energy loss can result in heterogeneity in particle distribution, increasing the drag on them, which, if not considered properly, can lead to problems in reactor design and operation. Therefore, it is important to know how much energy is dissipated by particles with low mechanical strength during collisions. In this context, the coefficient of restitution of alginate particles synthesized using different cationic solutions was determined experimentally. The influence of the Young’s modulus, size and roughness of the particles, as well as the impact velocity, on the coefficient of restitution was investigated. Results indicate that the coefficient of restitution is directly proportional to the particle Young's modulus and inversely proportional to the impact velocity. A correlation is proposed to estimate the coefficient of restitution as a function of particle density, Young’s modulus, impact velocity and maximum deformation in the elastic regime, with R2 = 0.9219. This correlation provides a potential tool for determining the coefficient of restitution to be used in simulating the dynamics of the flow in fluidized bed bioreactors in wastewater treatment.
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Data availability
The data presented in the article are available in the public repository of the Federal University of São Carlos, at the website https://repositorio.ufscar.br/handle/ufscar/12660.
Abbreviations
- c 0 :
-
Compressional wave velocity (m/s)
- d:
-
Particle diameter (m)
- e :
-
Coefficient of restitution (-)
- E :
-
Young’s modulus (Pa)
- R a :
-
Average roughness (μm)
- V 1 :
-
Impact velocity (m/s)
- εmax :
-
Maximum deformation of particles in the elastic regime (-)
- ρ:
-
Particle density (kg/m3)
- σ:
-
Standard deviation (units as required
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Funding
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001, and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP, processes n° 2018/16036–8 and 2018/20711–2).
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All authors contributed to the manuscript conception. The experimental steps, such as material preparation, experimental collision tests and data analysis, were carried out by KRBM. All steps were supervised by GCL, the project coordinator. JRG contributed to the definition of the project and helped in discussing the results. All authors commented and contributed to previous versions of the article. All authors read and approved the final manuscript.
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Melo, K.R.B., Grace, J.R. & Lopes, G.C. A new correlation for the coefficient of restitution of particles with low mechanical resistance for modeling wastewater treatment biofilm reactors. Clean Techn Environ Policy 24, 623–632 (2022). https://doi.org/10.1007/s10098-021-02079-y
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DOI: https://doi.org/10.1007/s10098-021-02079-y