Power-law Constitutive Equation Research Articles

The Influence of Exogenous Particles on Saliva Rheology

This study aimed to investigate the effect of exogenous nanoparticles on the rheological properties of artificial saliva. There are four reasons for undertaking this type of research: Firstly, the number of solid particles of various origins present in the air is still high. Secondly, nanoparticles (including silver and gold nanoparticles) are increasingly used in food packaging and can migrate into food. Thirdly, saliva is the first biological fluid that comes into contact with exogenous particles. Finally, the function of saliva is also closely related to its rheological properties. Due to the remarkable properties of nano-objects, nanoparticles of various origins in the body may cause effects that have not been realised until now. Therefore, each type of nanoparticle must be tested in terms of its impact on the body/body fluid. We used silver and gold nanoparticles because they are used in the food industry, and diesel exhaust particles because they are standard components of air pollution. The effect of various nanoparticles (e.g., their size and shape) on the rheology of saliva at two temperatures was investigated. The constants of the power law constitutive equation were also estimated. Studies showing the impact of nanoparticles on the rheology of body fluids are rare because it is one of the less obvious ways of their affecting the human body. However, the results show that nanoparticles are not neutral to the biological fluid, which may translate into a change in its properties and thus disturb its functions.

Experimental Measurement of the Stress Gradient in a Bent Sheet

Stress gradients were experimentally measured in a 316 stainless steel sheet after bending with a press brake. Two different tool radii and three different bend angles were used to produce plastically bent sheets. Microhardness tests were performed across the thickness of the bent sheet, and a correlation between microhardness and strength was experimentally determined and was used to obtain the stress gradient. The position of the experimentally determined neutral plane correlated well with theory. Theoretical calculations of the stress gradient were made using a power law constitutive equation along with a simple mechanics analysis of plastic bending. Four of the six bending experimental conditions had reasonable correlation with the theoretical calculations. Ideas for improving this experimental method are discussed.

Microstructural evolution, high temperature tensile deformation behavior, and deformation mechanism in an Mg–Zn–Y–Ca–Zr alloy processed by multidirectional forging and hot rolling

To explore high temperature ductility, a new Mg-2.70Zn-1.34Y-0.37Ca-0.02Zr (wt.%) alloy has been fabricated by novel multidirectional forging (MDF) and hot rolling. The microstructure and mechanical properties were investigated. The average grain size of MDF + hot rolled alloy is 10.89 ± 0.90 μm refined from the as-cast average grain size of 60.03 ± 0.72 μm. The ultimate tensile strength of 260.51 ± 1.03 MPa, yield strength of 192.29 ± 1.21 MPa, and elongation of 17.83 ± 0.72 % were obtained at room temperature. For high temperature tensile behavior, microstructural examination revealed that continuous dynamic recrystallization and discontinuous dynamic recrystallization are the main softening mechanism in the temperature range of 573–673 K, while dynamic grain growth with bimodal grains and twins is discovered at 723 K in this alloy. X-ray diffraction and scanning electron microscopy –energy dispersive spectroscopy examinations revealed that the constituent phases are composed of α-Mg solid solution and intermetallic compounds of Ca2Mg6Zn3, Mg3YZn6 (I-phase), and Mg3Zn3Y2 (W-phase). The microstructural evolution, such as dynamic recrystallization and dynamic grain growth at desired tensile temperatures, is related to the thermal stability of constituent phases. The elongation to failure of 215.4 % was demonstrated at 673 K and 1.67 × 10−2 s−1, exhibiting high strain rate quasi-superplasticity. A power-law constitutive equation was established. The deformation activation energy of 177.948 kJ/mol and stress exponent of 4.494 revealed that the dominant deformation mechanism of this alloy at elevated temperatures of 573–723 K is dislocation climb controlled by lattice diffusion.

Room Temperature Strengthening and High-Temperature Superplasticity of Mg-Li-Al-Sr-Y Alloy Fabricated by Asymmetric Rolling and Friction Stir Processing

Magnesium-lithium alloy is the lightest alloy to date. To explore its room temperature strength and high-temperature ductility, a plate of a new fine-grained Mg-9.13Li-3.74Al-0.31Sr-0.11Y alloy was fabricated by asymmetric rolling, and the rolled plate was subjected to friction stir processing (FSP). The microstructure and mechanical properties at room and elevated temperatures were investigated by optical microscopy, X-ray diffraction (XRD), energy dispersive spectroscopy (EDS), and tensile tester. Grain refinement with an average grain size in the α-Mg phase of 1.65 μm and an average grain size in the β-Li phase of 4.24 μm was achieved in the water-cooled FSP alloy. For room temperature behavior, the ultimate tensile strength of 208 ± 4 MPa, yield strength of 193 ± 2 MPa, and elongation of 48.2% were obtained in the water-cooled FSP alloy. XRD and EDS analyses revealed that the present alloy consists of α-Mg and β-Li phases, Al2Y, Al4Sr, MgLi2Al, and AlLi intermetallic compounds. For high-temperature behavior, the maximum superplasticity or ductility of 416% was demonstrated in this fine-grained alloy with an average grain size of 10 μm at 573 K and 1.67 × 10-3 s-1. A power-law constitutive equation was established. The stress exponent was 2.29 (≈2) (strain rate sensitivity 0.44), and the deformation activation energy was 162.02 kJ/mol. This evidence confirmed that the dominant deformation mechanism at elevated temperatures is grain boundary and interphase boundary sliding controlled by lattice diffusion.

Room-Temperature Strengthening, Portevin-Le Chatelier Effect, High-Temperature Tensile Deformation Behavior, and Constitutive Modeling in a Lightweight Mg-Gd-Al-Zn Alloy

To explore room-temperature strengthening and high-temperature ductility, a lightweight novel Mg-1.85Gd-0.64Al-0.62Zn alloy was fabricated by innovative multidirectional forging and a hot-rolling technique. Microstructures and mechanical properties were studied at room and elevated temperatures with an optical microscope, an X-ray diffractometer, and a tensile tester. An ultimate tensile strength of 260 MPa, yield strength of 171 MPa, and elongation of 20.4% were demonstrated at room temperature. The room-temperature strengthening mechanisms were identified by strengthening the model estimation. A type C Portevin-Le Chatelier effect was discovered and elucidated in this alloy. X-ray diffraction analysis revealed that the phase composition is α-Mg solid solution and (Mg, Al)3Gd, Al7Zn3, and Al2Gd intermetallic compounds. Examination of the microstructure at elevated temperatures revealed that dynamic recrystallization and dynamic grain growth occur. In particular, it was discovered that bimodal microstructures or incomplete dynamic recrystallization microstructures exist in high-temperature deformation. A maximum quasi-superplasticity of 228.4% was demonstrated in this alloy at 673 K and 5.0 × 10-4 s-1. Flow stress curves showed that the present alloy exhibits Sotoudeh-Bate curves or a long intermediate strain-hardening stage followed by a strain-softening stage. A modified Zerilli-Armstrong constitutive equation incorporating the number of dislocations was established. The power-law constitutive equation was established to identify the deformation mechanism. Both constitutive models had good predictability. At 673 K and 5.0 × 10-4 s-1, the stress exponent was 4, and the average deformation activation energy was 104.42 kJ/mol. The number of dislocations inside a grain was 146. This characteristic evidence confirmed that dislocation motion controlled by pipe diffusion dominates the rate-controlling process under this condition.

절삭 시뮬레이션에 사용되는 구성방정식 종류별 절삭력 예측

The constitutive equation shows the difference in the predicted result value related to cutting according to the coefficient value and type. Therefore, in this study, the cutting force and chip shape obtained from the cutting test for each cutting condition were applied as standards. And the simulation results applying the constitutive equation were compared. The constitutive equations used in this study are the Power-Law, Johnson-Cook, and S-K constitutive equations. Since the Power-Law constitutive equation is basically applied to the cutting simulation, it was used as the internal material property, and the Johnson-Cook constitutive equation and the S-K constitutive equation determined the coefficient value and performed simulation as a user property. As a result, it was confirmed that the tangential force and chip shape prediction in the cutting force and chip shape prediction of AAl7075 material were valid through simulation using the S-K constitutive equation.

Laboratory study on the rheology properties of nanoparticle-stabilized supercritical CO2 foam

Adding nanoparticles (NPs) into surfactant solution has been widely employed in improving foam stability in CO2 Enhanced Oil Recovery (EOR) applications. To help understand the foam flow characteristics in porous media, the rheology behavior of the NP-stabilized CO2 foam is experimentally investigated in this paper. The foam fluid is treated as a non-Newtonian fluid obeying the power law constitutive equation, and the effect of CO2 phase state, oil presence as well as solution salinity on the power law index, and the apparent viscosity of the NP-stabilized foam is scrutinized. Different rheology behavior between the NP-stabilized gaseous CO2 foam and the supercritical CO2 (ScCO2) foam is revealed in the both power law index and the apparent viscosity results. The NP-stabilized gaseous CO2 foam shows the rheology transition behavior from shear thickening to shear thinning with increasing shear rates and supplies maximal foam apparent viscosity of 27.7 mPa s, whereas the NP-stabilized ScCO2 foam shows the universal shear thickening behavior in the studied shear rate range with much higher maximum apparent viscosity of 95.8 mPa s. It is found the apparent viscosity of the NP-stabilized ScCO2 foam could reach up to 210.9 mPa s under the oil presence conditions, while 5 wt% NaCl existence in the aqueous solution could result in slightly lower apparent viscosity of 80.3 mPa s.

Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to non-uniform surface heat flux. After the flow field is determined by solving the continuity and the momentum equations, the energy equation is handled by employing the separation of variables method. The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C. The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length, using Duhamel's Theorem. Furthermore, an approximate analytic solution is determined, employing an integral approach to solve the boundary layer equations. With respect to the comparison, the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%. Interestingly, with decreasing the power-law index, the discrepancy between the two presented methods significantly reduces. Eventually, the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow's thermal characteristics and structure are elaborately discussed. It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation's accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube. In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m2and when the power-law index is 0.25, the maximum arterial wall temperature is found to be about 311.56 K.

Room temperature strengthening mechanisms, high temperature deformation behavior and constitutive modeling in an Al-3.25Mg-0.37Zr-0.28Mn-0.19Y alloy

To improve the ambient strength and high temperature ductility, a novel Al-3.25Mg-0.37Zr-0.28Mn-0.19Y (wt.%) alloy has been fabricated by multidirectional forging and warm rolling. Microstructures and mechanical properties were investigated by light microscope, X-ray diffraction apparatus, transmission electron microscope, and tensile tester. The ultimate tensile strength, yield strength, and elongation of 354.67 ± 0.04, 254 ± 3 MPa, and 18.47% were achieved in the processed alloy, respectively, at room temperature. The maximum superplasticity of 412.5% was demonstrated in this fine-grained (grain size of 8.80 ± 1.06 μm) alloy at 793 K and 8.33 × 10−4 s−1. An ambient strengthening sequence was obtained: grain boundary strengthening > dislocation strengthening > Orowan strengthening > solid solution strengthening. The occurrence of Portevin–Le Chatelier effect or serrated flow in as-annealed alloy was confirmed by theoretical model estimation and experimental evidence. Microstructural evolution and flow stress curves confirmed that dynamic recovery and dynamic grain growth occurred at elevated temperatures; Sotoudeh-Bate curves were discovered at higher temperatures and lower strain rates. Solute Mg, dynamic grain growth, and flow localization were responsible for the formation of Sotoudeh-Bate curves. Modified Johnson–Cook constitutive equation considering dislocation variables and power-law constitutive equation were established. In this fine-grained alloy at 793 K and 8.33 × 10−4 s−1, the number of dislocations inside a grain was 6, the stress exponent was 2, the grain size exponent was 2, and the average activation energy for deformation was 140.10 kJ/mol. These pieces of evidence demonstrated that grain boundary sliding accommodated by intragranular dislocation controlled by lattice diffusion governs the rate-controlling process.

Effect of Composition on the Compressibility and Shear Strength of Dredged Cohesive Sediment

Progressively, more dredged sediments are being reused for engineering projects. For example, the Marker Wadden is a new wetland constructed in lake Markermeer, the Netherlands, with dredged cohesive sediments originating from the bed of the lake. Such dredged sediments are often dominated by cohesive sediment particles with varying amounts of sand and organic matter. In addition, during and after the construction process, the material consolidates and is often compressed from a very loose state into a significantly denser condition. To assess the mechanical behavior of this material, the compressibility of the Markermeer dredged sediment samples with various sand and organic matter contents was analyzed with incremental loading oedometer tests, whereas the undrained shear strength was studied using the fall cone test. The behavior was theoretically analyzed assuming a fractal structure of the sediment and applying power law constitutive equations for effective stress, hydraulic conductivity, and undrained shear strength. These constitutive equations, usually used at low initial sediment densities, worked well at the relatively high initial densities studied and proved to be a useful tool to identify the transition fines content TFC. The constitutive equations were put in context with indicators traditionally used in soil mechanics. Samples, each with an identical composition of the fines fraction (particles< 63 μm), but with a sand content varying from 9 to 40%, showed the same compressibility and undrained shear strength behavior when considering the sand a filler material. For a natural sand content of 70%, the behavior was dominated by sand. The organic matter oxidation was observed to drastically decrease the compressibility and the shear strength, and even to decrease the amount of sand needed to exhibit sand-dominated behavior, showing the importance of the reactivity or state of organic matter on the TFC.

Microstructures, hot tensile deformation behavior and constitutive modeling in a superlight Mg-2.76Li-3Al-2.6Zn-0.39Y alloy

To explore the ductility and deformation nature, a new Mg-2.76Li-3Al-2.6Zn-0.39Y alloy has been successfully fabricated by decreasing-temperature multidirectional forging and hot rolling. The maximum elongation to failure of 223.0% was demonstrated in this alloy at a temperature of 633 K and a strain rate of 1.67 × 10-4 s-1. Flow stress curves and microstructural examination showed that continuous dynamic recrystallization occurred in this alloy at different temperatures and strain rates in most cases, but the flow hardening phenomena appeared at a temperature of 603 K at a strain rate of 5 × 10-4 s-1 and at 573, 603 and 633 K at a strain rate of 1.67 × 10-4 s-1. A criterion of grain size changing rate was proposed to judge the occurrence of microstructural evolution mechanisms. A modified Johnson-Cook constitutive model established in this alloy was incorporated into dislocation models to realize the estimation of the dislocation density and the number of dislocations under specific conditions. A power-law constitutive equation was established in this alloy. The relationship between average grain size and Zener-Hollomon parameter was established. It was found that the stress exponent was 3.26, and the average experimental activation energy for deformation was 143.67 kJ/mol; the dislocation density was 3.25 × 1013 m-2, and the number of dislocations was 59 at 633 K and 1.67 × 10-4 s-1. All of these results indicate that the predominant deformation mechanism of this alloy under this condition is dislocation glide creep controlled by lattice diffusion.

Constitutive equation of compacted graphite iron (GJV450) at high temperature and high strain rate

Compacted graphite iron (CGI) is an ideal material for the cylinder block and cylinder head of diesel engine because of its excellent physical and mechanical properties. At present, the researches on CGI mainly focused on experimental study of machining CGI, there are few studies on the cutting simulation of CGI, especially the high-speed machining simulation of CGI, and the constitutive equation of CGI at high temperature and high strain rate has not been studied. In this paper, the stress-strain relationship under quasi-static condition was obtained by quasi-static tensile test, and the power law constitutive equation of CGI with a grade of GJV450 under the condition of large strain, high strain rate, and high temperature was built by orthogonal cutting experiments and finite element iteration. The established power law constitutive equation was applied to the finite element simulation of the cutting process of CGI, which improves the accuracy of finite element analysis. The chip morphology of CGI and the distribution of plastic strain and temperature in the cutting process were analyzed by finite element simulation.

Microstructural evolution, flow stress and constitutive modeling of Al−1.88Mg−0.18Sc−0.084Er alloy during hot compression

To explore the hot compression behavior and microstructural evolution, fine-grained Al−1.88Mg−0.18Sc− 0.084Er (wt.%) aluminum alloy wires were fabricated with Castex (continuous casting−extrusion) and ECAP-Conform, and their hot compression behavior was investigated at temperatures of 673−793 K and strain rates of 0.001−10 s−1; the microstructures were characterized by optical microscope, X-ray diffractometer, transmission electron microscope, and electron backscattered diffractometer, and the flow stresses were obtained by thermal compression simulator. Microstructural evolution and flow curves reveal that dynamic recovery is the dominant softening mechanism. Continuous dynamic recrystallization followed by dynamic grain growth takes place at a temperature of 773 K and a strain rate of 0.001 s−1; the yielding drop phenomenon was discovered. Hyperbolic sine constitutive equation incorporating dislocation variables was presented, and a power law constitutive equation was established. The stress exponent is 3.262, and the activation energy for deformation is 154.465 kJ/mol, indicating that dislocation viscous glide is the dominant deformation mechanism.

REFINED ANALYSIS OF STEADY STATE CREEP OF A ROTATING DISK AND A PLATE WITH A CENTRAL HOLE UNDER UNIFORM TENSILE LOAD BY THE QUAZILINEARIZATION METHOD

Refined analysis of the steady state creep of a rotating disk and a plate with a central hole under uniformtensile load by the quasilinearization method is presented. It is shown that the high values of the creepexponent in power law constitutive equations require more iterations in the framework of the quasilinearizationmethod in each problem. The approximation solution of the problem for an infinite plate with the circularhole under creep regime is obtained by the quazilinearization method. Four approximations of the solution ofthe nonlinear problems are found. It is shown that with increasing the number of approximations the solutionconverges to the limit numerical solution. It is worth to note that the tangential stress reaches its maximumvalue not at the circular hole but at the internal point of the plate. It is also shown that quazilinearizationmethod is an effective method for nonlinear problems.

Sedimentation of Fractal Aggregates in Shear-Thinning Fluids

Solid–liquid separation is a key unit operation in the wastewater treatment, generally consisting of coagulation and flocculation steps to promote aggregation and increase the particle size, followed by sedimentation, where the particles settle due to the effect of gravity. The sedimentation efficiency is related to the hydrodynamic behavior of the suspended particles that, in turn, depends on the aggregate morphology. In addition, the non-Newtonian rheology of sludges strongly affects the drag coefficient of the suspended particles, leading to deviations from the known settling behavior in Newtonian fluids. In this work, we use direct numerical simulations to study the hydrodynamic drag of fractal-shaped particles suspended in a shear-thinning fluid modeled by the power-law constitutive equation. The fluid dynamics governing equations are solved for an applied force with different orientations uniformly distributed over the unit sphere. The resulting particle velocities are interpolated to compute the aggregate dynamics and the drag correction coefficient. A remarkable effect of the detailed microstructure of the aggregate on the sedimentation process is observed. The orientational dynamics shows a rich behavior characterized by steady-state, bistable, and periodic regimes. In qualitative agreement with spherical particles, shear-thinning increases the drag correction coefficient. Elongated aggregates sediment more slowly than sphere-like particles, with a lower terminal velocity as the aspect ratio increases.

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids.

The prediction of the viscosity of suspensions is of fundamental importance in several fields. Most of the available studies have been focused on particles with simple shapes, for example, spheres or spheroids. In this work, we study the viscosity of a dilute suspension of fractal-shape aggregates suspended in a shear-thinning fluid by direct numerical simulations. The suspending fluid is modeled by the power-law constitutive equation. For each morphology, a map of particle angular velocities is obtained by solving the governing equations for several particle orientations. The map is used to integrate the kinematic equation for the orientation vectors and reconstruct the aggregate orientational dynamics. The intrinsic viscosity is computed by a homogenization procedure along the particle orbits. In agreement with previous results on Newtonian suspensions, the intrinsic viscosity, averaged over different initial orientations and aggregate morphologies characterized by the same fractal parameters, decreases by increasing the fractal dimension, that is, from rod-like to spherical-like aggregates. Shear-thinning further reduces the intrinsic viscosity showing a linear dependence with the flow index in the investigated range. The intrinsic viscosity can be properly scaled with respect to the number of primary particles and the flow index to obtain a single curve as a function of the fractal dimension.

Experimental and numerical characterisation of rheological properties of a drop test response of a ballistic plastilina

Plastilina is often used as a ballistic witness material (BWM) behind the armour to evaluate the backface signature (BFS). Indeed, it is cheap, reusable and it keeps its deformation after being impacted. Moreover, while it aims at evaluating the performance of ballistic protections when no perforation occurs, it can be subjected to a very wide range of strain/shear rates during a ballistic impact. Therefore, there is a need to improve the knowledge about the mechanical/rheological response of such a material. This paper proposes both experimental and modelling approaches to determine the response of the specific ballistic plastilina red Weible® over a wide range of shear/strain rate. A capillary rheometry analysis with control of temperature was performed up to 8.104 s−1. The corrections of Rabinowitsch and Bagley were applied and an attempt of the analysis of Mooney was considered. From the rheology of plasticine, a two-parameters based power-law constitutive equation was deduced. An experimental drop test was carried out using a specific standard setup. A high-speed camera was used for measuring the penetration depth of a steel ball into the plastilina. A numerical simulation of the drop test was performed by taking into account the mechanical properties of the plastilina. A good correlation was observed between the experimental and numerical results in terms of indentation depth evolution.

Regional Segregation With Spatial Considerations-Based Analytical Filling Time Model for Non-Newtonian Power-Law Underfill Fluid in Flip-Chip Encapsulation

Abstract This paper presents a new analytical filling time model to predict the flow of non-Newtonian underfill fluid during flip-chip encapsulation process. The current model is formulated based on the regional segregation approach, instead of the conventional porous media approximation. In this approach, the filling times were computed separately at different filling stages, before being summed up till the required filling distance. The non-Newtonian property of underfill fluid is modeled using the conventional power-law constitutive equation. Additionally, the spatial aspects of the underfill flow were incorporated into the present analysis. For instance, the evolution of underfill menisci from convex to concave was analytically developed and the contact line jump (CLJ) criterion was improved using minimal flow assumption. Upon validated with three distinct past underfill experiments, the current analytical model is found to have the best performance as it predicted the filling times with the least discrepancy among other existing filling time models. Quantitatively, the discrepancies were averagely reduced by an absolute value of at least 8.68% and 4.90%, respectively, for the first two set of validation studies. Generally, this model is particularly useful in manufacturing lines to estimate the process time of flip-chip underfill, as well as for the optimizations of process and package design.

Elastic waves in a circular cylinder and cylindrical annulus for a subclass of implicit constitutive equations

The propagation of elastic waves in a circular cylinder and cylindrical annulus for two types of power-law constitutive equations is investigated. These power-law constitutive equations can describe elastic responses where the linearised strain and stress are nonlinearly related. These constitutive equations are a subclass of the more general class of implicit constitutive equations and are characterised by expressing the strain as a non-invertible function of the stress. Pseudo-solitary stress wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are derived. We find that for the power-law constitutive equation of Type I, a shock front will develop at the back of the wave while for the power-law constitutive equation of Type II, a shock front will develop at the front of the wave. Estimates of the times at which the shock front will develop are given. Standing wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are also obtained and the periods of oscillation are compared.

Experimental and numerical study of erosion in a non-Newtonian hydraulic fracturing fluid

Erosion in hydraulic fracturing fluid is investigated utilizing Computational Fluid Dynamics (CFD) and with comparison to new experimental data for sand in shear thinning non-Newtonian fluids. A grid optimized CFD-based erosion prediction procedure is applied utilizing Dense Discrete Phase Model (DDPM) and one-way coupling model. The effect of different turbulence models on flow modeling, sand particle transport and impact characteristics are also examined. Constant viscosity fluid and power law constitutive equations are implemented and their capability in predicting erosion is examined by comparison to experimental data gathered in this investigation. This investigation has shown that significant error can arise from utilizing constant viscosity model to predict erosion resulting from particles entrained in non-Newtonian fluids. Thus, this investigation has resulted in selecting the best CFD approach and model combination for predicting erosion in this hydraulic fracturing non-Newtonian fluid.