fluids Article Rheological Characterization of Non-Newtonian Mixtures by Pressure Pipe Tests Armando Carravetta , Oreste Fecarotta , Riccardo Martino and Maria Cristina Morani *   Citation: Carravetta, A.; Fecarotta, O.; Martino, R.; Morani, M.C. Rheological Characterization of Non-Newtonian Mixtures by Pressure Pipe Tests. Fluids 2021, 6, 419. https://doi.org/10.3390/ fluids6110419 Academic Editor: Francisco J. Galindo-Rosales Received: 12 October 2021 Accepted: 16 November 2021 Published: 20 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Civil, Architectural and Environmental Engineering (DICEA), University of Naples, “Federico II”, 80125 Napoli, Italy; arcarrav@unina.it (A.C.); oreste.fecarotta@unina.it (O.F.); riccardo.martino@unina.it (R.M.) * Correspondence: mariacristina.morani@unina.it; Tel.: +39-081-768-3453 Abstract: The rheological behavior of non-Newtonian fluids in turbulent conditions is an important topic in several fields of engineering. Nevertheless, this topic was not deeply investigated in the past due to the complexity of the experimental tests for the assessment of the constitutive parameters. Pressure pipe tests on Herschel-Bulkley mixtures were proven to be suitable for exploring turbulent conditions, but discrepancies with the results of tests performed in laminar flow were detected. These contradictions could be attributed to the inconsistencies of the Herschel-Bulkley model (HB) for high shear rate flows, proven by Hallbom and Klein, who suggested a more general “yield plastic” model (HK). Hence, in this study, a procedure for the estimation of the rheological parameters of both HB and HK models in pressure pipe tests is defined and rated on a complete set of experiments. The HK model performed much better than HB model in the turbulent range and slightly better than the HB model in the laminar range, confirming the consistency of the “yield plastic” model. The rheological parameters obtained by the proposed procedure were used to numerically model a dam-break propagation of a non-Newtonian fluid, showing significant differences in terms of process evolution depending on the constitutive model. Keywords: rheology; non-Newtonian flow; pipe flow; Herschel-Bulkley model; Hallbom and Klein model 1. Introduction Non-Newtonian flows are present in many applications, such as mining, chemical engineering, environmental and civil engineering, etc. The non-Newtonian behavior can be generated by the internal structure of pseudohomogenous mixtures [1,2], such as in the case of foams, emulsions, suspensions, pastes, and polymer solutions, or by the particle interaction in heterogeneous mixtures, such as in mine tailings, mineral suspensions, wastewater sludges, and drilling muds. The non-Newtonian rheological behavior is generally well described by the Herschel- Bulkley equation [3]: τ = τ y + k . γ n (1) where τ (Pa) is the shear stress, . γ (s −1 ) is the shear rate, τ y (Pa) is the yield stress, n (-) is the flow behavior index, and k (Pa s n ) is the flow consistency index. It is worth pointing out that the flow consistency index has a noncoherent unit of measurement depending on n. With regard to the yield stress (τ y ), it is the stress value at which the deformation begins: such a minimum stress is required to break the internal ‘structure’ of the mixture before any relative movement can occur. The HB rheological model describes both shear thinning (n < 1) and dilatant (n > 1) behavior [2], and it is equivalent to the Bingham plastic model [4] for n = 1, the power-law model for τ y = 0, and the Newtonian model [5] for n = 1 and τ y = 0. The HB model has been generally employed for its simplicity and ability to quantify the presence of yield stress and has been applied to several fluids, including sediment mixtures and sewage sludge [6,7]. Fluids 2021, 6, 419. https://doi.org/10.3390/fluids6110419 https://www.mdpi.com/journal/fluids