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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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 \(18^{\circ }\).
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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