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Obtaining flow curve for viscoplastic fluids through inclined open-channel apparatus

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Abstract

Non-Newtonian fluids are commonly seen in industrial processes, such as those of the oil and mining industry, and in natural flows, like dam ruptures, landslides or mud flows. The hydrodynamic modeling of such processes/phenomena is directly linked to the rheological properties of the flowing fluid, usually characterized through rheometers. The high cost of rheometers and possible inaccessibility for certain applications demand for research of alternative rheometric methods. In order to assess the problem, the present work discusses a detailed experimental methodology to evaluate if the steady and uniform flow in an inclined channel is able to produce the flow curve for the test fluid carbopol 996 gel and work as an alternative rheometer. In order to estimate the shear rates and shear stresses, we measured the normal depth (ultrasonic technique), specific discharge (manual gravimetric method) and free surface velocity (manually and with laser barrier sensors). Based on the theoretical solutions, a simplified fitting procedure was adopted to make possible the assessment of shear rate and shear stress through the experimental data. The obtained flow curves were then compared with the reference flow curve, determined by a commercial R/S rheometer. Results showed that the experimental methods were able to provide the flow curves within acceptable uncertainty and the defined methodology detailed in the work can estimate satisfactorily the flow curve of non-Newtonian fluids. Finally, we highlighted that the wide channel hypothesis is the strongest condition to be guaranteed in order to obtain precise flow curves through the methodology present in this work.

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Acknowledgements

The authors wish to acknowledge FAPESP for financial support under Process 2015/25518-8. Thanks are also given to CAPES for the first author scholarship (88882.433524/2019-01). Finally, the authors thank Doctor Fabiana de Oliveira Ferreira and Associate Professor Doctor Milton Dall’Aglio Sobrinho for their valuable collaboration.

Funding

This research was funded by São Paulo Research Foundation (FAPESP) under Process 2015/25518-8 and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) for the first author scholarship (88882.433524/2019-01).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering of Ilha Solteira, São Paulo State University, Avenida Brasil, 56, Ilha Solteira, SP, 15385-000, Brazil

    Yuri Taglieri Sáo & João Batista Pereira

  2. Mechanical Engineering Department, Engineering College, Federal University of Rio Grande do Sul, Avenida Sarmento Leite, 425, Porto Alegre, RS, 90050-170, Brazil

    Guilherme Henrique Fiorot

  3. Department of Civil Engineering, Faculty of Engineering of Ilha Solteira, São Paulo State University, Alameda Bahia, 55, Ilha Solteira, SP, 15385-000, Brazil

    Geraldo de Freitas Maciel

Authors
  1. Yuri Taglieri Sáo
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  2. João Batista Pereira
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  3. Guilherme Henrique Fiorot
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  4. Geraldo de Freitas Maciel
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Corresponding author

Correspondence to Geraldo de Freitas Maciel.

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Appendix

Appendix

This Appendix shows the raw data obtained through the methodology described in Sect. 3, presenting measurements of normal depth h, specific discharge q, uncertainties related to specific discharge measurement \(u_q\), free surface velocity \(v_s\) and uncertainties related to free surface velocity measurement \(u_{v_s}\). The Reynolds number \({\rm Re}_H\), Froude number Fr and minimum Froude number \({\rm Fr}_{\rm min}\) are also calculated as indicated by Subsect. 3.3. The mean velocity \(\bar{V}\) for the automatized method was calculated through \(v_s\) measurement [20]. Tables 6, 7, 8, 9, 10, 11 present data corresponding to experimental tests made with channel slopes \(\theta\) of 4, 6, 10, 14, 16 and \(18^{\circ }\) using the Manual Gravimetric Method and the Manual Kinematic Method. Tables 12, 13, 14, 15, 16 presents data obtained through the automatized kinematic method with channel slopes \(\theta\) of 4, 6, 8, 16 and \(18^{\circ }\).

Table 6 Experimental data measured through Manual Gravimetric Method and Manual Kinematic Method for channel slope \(\theta = 4^{\circ }\)
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Table 7 Experimental data measured through manual Gravimetric method and manual Kinematic method for channel slope \(\theta = 6^{\circ }\)
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Table 8 Experimental data measured through manual Gravimetric method and manual Kinematic method for channel slope \(\theta = 10^{\circ }\)
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Table 9 Experimental data measured through manual Gravimetric method and manual Kinematic method for channel slope \(\theta = 14^{\circ }\)
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Table 10 Experimental data measured through manual Gravimetric method and manual Kinematic method for channel slope \(\theta = 16^{\circ }\)
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Table 11 Experimental data measured through manual Gravimetric method and manual Kinematic method for channel slope \(\theta = 18^{\circ }\)
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Table 12 Experimental data measured through Automatized kinematic method for channel slope \(\theta = 4^{\circ }\)
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Table 13 Experimental data measured through automatized kinematic method for channel slope \(\theta = 6^{\circ }\)
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Table 14 Experimental data measured through automatized kinematic method for channel slope \(\theta = 8^{\circ }\)
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Table 15 Experimental data measured through automatized kinematic method for channel slope \(\theta = 16^{\circ }\)
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Table 16 Experimental data measured through automatized kinematic method for channel slope \(\theta = 18^{\circ }\)
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Sáo, Y.T., Pereira, J.B., Fiorot, G.H. et al. Obtaining flow curve for viscoplastic fluids through inclined open-channel apparatus. J Braz. Soc. Mech. Sci. Eng. 43, 278 (2021). https://doi.org/10.1007/s40430-021-02999-2

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  • DOI: https://doi.org/10.1007/s40430-021-02999-2

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