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This study aimed to develop an alternative approach to characterise the linear viscoelastic behaviour of asphalt binders. A rheogram model was firstly proposed based on the Carreau–Yasuda model; its accuracy was substantiated by high R2 values. The dynamic shear modulus master curve model was then obtained using the relationship between the magnitude of complex viscosity and dynamic shear modulus and the two definitions of the time-temperature shift factor. Afterwards, the phase angle master curve model was derived according to the approximate Kramers–Kronig relation. The proposed approach was demonstrated to be capable of accurately characterising the linear viscoelastic behaviour of selected asphalt binders. In addition, the predicted zero shear viscosity (ZSV) could be potentially employed to evaluate the asphalt binder rutting resistance. Compared with the widely-used Christensen-Anderson-Marasteanu (CAM) model, the developed master curves models were better at constructing the phase angle master curves of selected asphalt binders. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a complex cardiovascular condition characterised by the buildup of fatty deposits, known as plaques, on the inner walls of arteries. Stenosis occurs when the narrowing of an artery becomes particularly pronounced due to the accumulation of plaque. This narrowed lumen leads to significant pressure drops during blood flow, which may lead to decreased blood flow to the target tissues. The current study focuses on conducting computational fluid dynamic (CFD) simulations of blood flow within a linear segment of the LAD (Left anterior descending) coronary artery, subject to differing degrees of atherosclerotic stenosis. The simulations are performed using COMSOL Multiphysics 5.6®. The study has computed pressure drops by considering the laminar flow of blood as a two-phase non-Newtonian fluid. The rheological characteristics have been modelled using the Carreau Yasuda model. It considers varying stenosis severities ranging from 10% to 90%, coupled with blood velocities spanning from 0.07 m/s to 0.2 m/s. Additionally, the findings have been compared to results generated using the Power Law model and Casson-Papanastasiou model for blood rheology. The pressure drop within the stenosed section has been correlated with stenosis percentages through power law models. [ABSTRACT FROM AUTHOR]

The flow through a 4:1 planar contraction has been investigated using different rheological models having the same shear viscosity, namely, the inelastic Carreau-Yasuda model (CY), the enhanced Bautista-Manero-Puig (eBMP), and the exponential version of the Phan-Thien/Tanner (PTT). Noticeable discrepancies were observed with the CY model and the eBMP in terms of the velocity profiles along the centerline and in the exit channel (near the end of the geometry) normal to the flow direction. Transient planar extensional viscosity shows a large effect on vortex dynamics although the effect of transient and steady elongation on pressure drop seems negligible. Simulation results allowed gathering that pressure drop is largely influenced by the shear-thinning behavior of the fluid, noticeably affected by elasticity, and less by extensional viscosity. [ABSTRACT FROM AUTHOR]

This work deals with gliding motion of bacteria over a non-Newtonian slime layer attached to a solid substrate. The surface of a glider is approximated with a simple wavy two-dimensional sheet while the sticky slime is modeled as Carreau–Yasuda fluid. The classical Navier–Stokes equations are transformed by using Galilean transformation and dimensionless variables. Flow beneath the organism is creeping and the lubrication assumption is also valid in this scenario, hence the equation is reduced to fourth-order BVP in terms of stream function. The basic purpose is to compute the gliding speed and flow rate of the slime which are present in the boundary conditions. MATLAB built-in bvp5c solver is utilized to calculate the numerical solution of the stream function. Further, unknowns (flow rate and cell speed) are refined by using modified Newton–Raphson method (MNRT). Further, these pairs are employed in the formula of energy expended. Velocity and stream function is also plotted for these computed pairs. This study is motivated by scientific interest and the desire to understand the dynamics of gliding bacteria. The findings of this study are thought to be beneficial in the development of artificial crawlers. [ABSTRACT FROM AUTHOR]

Brownian motions and Thermophoresis are primary sources of nanoparticle diffusion in nanofluids, having substantial implications for the thermo-physical characteristics of nanofluids. With such a high need, the 2D, laminar MHD (Magnetohydrodynamic) quadratic convective stream of Carreau–Yasuda nano liquid across the stretchy sheet has been reported. The flow is caused by surface stretching. The principal purpose of this extensive study is to enhance thermal transmission. The effects of variable thermal conductivity and heat source are considered as well. The governing boundary layer equations are transmuted using similarity parameters into a series of non-linear ODEs (ordinary differential equations). The bvp4c algorithm is adopted to fix the translated system numerically. The effects of prominent similarity variables over the temperature, velocity and concentration field are graphically visualized and verified via tables. It explored that fluid's speed diminishes for the more significant inputs of the magnetic coefficient, Brownian motion coefficient and Prandtl number. The thermal efficiency is improved for larger values of thermophoretic constant, varying thermal conductance and heat-generating parameters. The concentration field has proved to be a decreasing function of nanofluid constants. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we present a non-isothermal study of the wire coating process using the Carreau–Yasuda fluid model. Our aim is to explore how the Carreau–Yasuda fluid model parameters are linked to key operational factors in the wire coating process. These factors encompass the radius of the coated wire, the volumetric flow rate, and the force needed to pull the wire. The equations that depict the flow and heat transfer within the die are solved: (a) analytically using the perturbation method to get the analytical expression for velocity, temperature distribution, and relevant engineering quantities; (b) numerically using shooting method with the “Runge–Kutta–Fehlberg algorithm.” The physical effects of the Weissenberg number (We), power law index (n), pressure gradient (A), and Brinkman number (Br) on the velocity profile, temperature distribution, and engineering quantities are discussed with the help of different graphs. Our findings reveal that, in the case of shear thinning (n < 1) with a constant pressure gradient, as compared to the Newtonian scenario, both the thickness of the coated wire and the force required to pull the wire decrease with an increase in the Weissenberg number (We). Moreover, the force required to pull the wire also decreases with an increase in the values of the pressure gradient parameter. [ABSTRACT FROM AUTHOR]

The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet's flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger's flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m−2 s−1 to 0.004281 kg m−2 s−1. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints. [ABSTRACT FROM AUTHOR]

Global approval of the use of fluid viscous dampers to control the buildings response against dynamic loadings is growing. The idea behind incorporating additional dampers is that they will reduce most of the energy that is transmitted to the building during shaking event. The objective of this work is to identify and enhance the design parameters that control the nonlinear behaviour of fluid viscous damper subjected to sinusoidal excitation. For this, a numerical model of the flow inside the dissipater has been carried out based on finite volume method. A novel approach has been adopted to simulate elastic behaviour of the fluid, taking into account its compressibility by using the Murnaghan equation of state. A comparison between the calculations of the proposed model and the experimental tests was carried out. The model proved to be sufficiently accurate. A fluid flow analysis was then conducted to fully understand the internal mechanism of the damper. A parametric study was then performed by varying aspects such as dimensions, geometric relationships between components and fluid properties in order to better understand their effect on the non-linear behaviour of the device. The results highlight the relationship between the parameters governing the shear thinning behaviour of the fluid and the non-linearity exponent of the damper. This makes it possible to better control the non-linear behaviour of the device by selecting the appropriate silicone oil and the appropriate geometric dimensions of its components.

Global approval of the use of fluid viscous dampers to control the buildings response against dynamic loadings is growing. The idea behind incorporating additional dampers is that they will reduce most of the energy that is transmitted to the building during shaking event. The objective of this work is to identify and enhance the design parameters that control the nonlinear behaviour of fluid viscous damper subjected to sinusoidal excitation. For this, a numerical model of the flow inside the dissipater has been carried out based on finite volume method. A novel approach has been adopted to simulate elastic behaviour of the fluid, taking into account its compressibility by using the Murnaghan equation of state. A comparison between the calculations of the proposed model and the experimental tests was carried out. The model proved to be sufficiently accurate. A fluid flow analysis was then conducted to fully understand the internal mechanism of the damper. A parametric study was then performed by varying aspects such as dimensions, geometric relationships between components and fluid properties in order to better understand their effect on the non-linear behaviour of the device. The results highlight the relationship between the parameters governing the shear thinning behaviour of the fluid and the nonlinearity exponent of the damper. This makes it possible to better control the non-linear behaviour of the device by selecting the appropriate silicone oil and the appropriate geometric dimensions of its components. [ABSTRACT FROM AUTHOR]

The gliding motility is widely observed in rod-shaped bacteria known as gliding bacteria, which produce waves on their surfaces and leaves a sticky layer of ooze slime. In the current analysis, we utilize a hydrodynamic complex wavy model to analyze the movement of gliding bacteria over a layer of Carreau-Yasuda (C.Y) fluid. After using lubrication and creeping flow assumption, the resultant fourth-order differential equation of the gliding model is solved numerically with two different techniques, i.e., implicit finite difference method (IFDM) and MATLAB's function Bvp-5c. The convergent solution is obtained for appropriate gliding gaits, slime parameters, and certain guesses of flow rate (Q) and glider speed (Vg/c). Unknowns are refined by the modified secant method in such a way that they will satisfy the mechanical equilibrium condition. Excellent agreement between two different computational approaches and outstanding benchmarking is attained. Power required (P), level curves and velocity profiles are plotted for calculated pair from the said procedure. The key verdict of this present examination is that the bacterial speed and slime velocity can be controlled via five different rheological parameters and two gliding gaits. [ABSTRACT FROM AUTHOR]

Adulteration of honey represents an essential quality assurance concern in the utilisation of this natural product. Honey was serially diluted with high fructose corn syrup and analysed for its rheological profiles at 27 °C. Pure honey at ambient temperatures exhibits a peculiar non-Newtonian rheological behaviour while the behaviour of fructose syrup tends towards Newtonian. The adulteration of honey with this material drags its viscosity towards Newtonian flow behaviour. The results show that the Carreau-Yasuda model correlates the rheology of pure honey samples. Parameters of the Carreau-Yasuda model were observed to reflect the quality of the samples and thus aided their classification. Modified with the insertion of the Mark-Houwink's relation, the Carreau-Yasuda model yielded average molecular weight data on the samples. The Structural Kinetic Model was utilised to give rheological structural information and a second independent assessment of average molecular weight from the rheograms. The average molecular weight of 202 g/mol was obtained using the Structural Kinetic model, while 205 g/mol was obtained using the amended Carreau-Yasuda model. [ABSTRACT FROM AUTHOR]

The necessity of using non-Newtonian models for hemodynamics in geometries mimicking large vessels is investigated. Phase-contrast magnetic resonance imaging (PC-MRI) measurements are performed on a specially-designed phantom representing the aorta while using several types of fluids. These measurements are compared against the results of the lattice Boltzmann method (LBM) computational fluid dynamics (CFD) simulator in 3D. On the phantom side, two types of non-Newtonian fluids (water-based solutions of glycerine with xanthan gum and sucrose with xanthan gum) and Newtonian fluid (clear water) are used in the experiments; three different acrylic plates are inserted to represent aortic stenosis of varying degrees; and two constant flow regimes with high and low flow rates are used. The CFD simulations in the geometry and inflow boundary conditions corresponding to each experiment are performed both with non-Newtonian and Newtonian approaches. Additionally, the accuracy of the PC-MRI flow measurements is assessed and discussed with respect to the known PC-MRI flow underestimation due to turbulence. Based on the type of stenosis and inflow rate, the results indicate that the Newtonian models produce comparable results with the experimentally acquired data, which is in favor of overall less expensive Newtonian models. [ABSTRACT FROM AUTHOR]

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The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet’s flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger’s flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m−2 s−1 to 0.004281 kg m−2 s−1. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints.

High-performance micromixers play a crucial role in diverse industrial applications. Utilizing chaotic advection as a well-established technique improves mixing efficiency due to the induction of strong secondary flows, acting at the microscopic level for homogenization. This study systematically compares the micromixing process of non-Newtonian fluids using different configurations of spiral micromixers, including Simple Spiral Micromixer (SSM), Rectangular Spiral Micromixer (RSM), Variable Radius Spiral Micromixer (VRSM), and Twisted Spiral Micromixer (TSM). The examination is performed by analyzing effective parameters, such as microchannel geometry, inlet configuration, microchannel aspect ratio, Reynolds number (30 < Re 〈110), and non-Newtonian fluid characteristics, i.e., flow index (0.05 < n < 1) and relaxation time (0.007 s < λ < 0.7 s). Non-Newtonian shear-thinning behavior is described by using the Carreau-Yasuda model. The results include velocity profiles, distributions of the mass fraction, overall assessment of micromixers' performance, mixing energy cost (MEC), the ratio of the Poiseuille number to mixing index (P 0 / MI), and figure of merit (FoM). It is revealed that the TSM micromixer exhibits superior mixing with MI > 84% at Re = 110 when n = 0.05 and 0.2128. The value of FoM strongly depends on n, for instance, FoM of the TSM micromixer is 0.00014 and 0.00004 for n = 0.05 and 0.8, respectively when Re = 50. It is revealed that the MEC is enhanced with n for all micromixers for a given Re , for instance, the MEC of RSM micromixer is about 0.05, 0.07, and 0.38 for n = 0.05, 0.5, and 0.8, respectively, when Re = 50. [ABSTRACT FROM AUTHOR]

Atherosclerosis causes blockages to the main arteries such as the aorta preventing blood flow from delivering oxygen to the organs. Non-invasive diagnosis of these blockages is difficult, particularly in primary healthcare. In this paper, the effect of arterial blockage development and growth is investigated at the descending aorta on some possible non-invasive assessment parameters including the blood pressure waveform, wall shear stress (WSS), time-average WSS (TAWSS) and the oscillation shear index (OSI). Blockage severity growth is introduced in a simulation model as 25%, 35%, 50% and 65% stenosis at the descending aorta based on specific healthy control aorta data clinically obtained. A 3D aorta model with invasive pulsatile waveforms (blood flow and pressure) is used in the CFD simulation. Blockage severity is assessed by using blood pressure measurements at the left subclavian artery. An arterial blockage growth more than 35% of the lumen diameter significantly affects the pressure. A strong correlation is also observed between the ascending aorta pressure values, pressure at the left subclavian artery and the relative residence time (RRT). An increase of RRT downstream from the stenosis indicates a 35% stenosis at the descending aorta which results in high systolic and diastolic pressure readings. The findings of this study could be further extended by transferring the waveform reading from the left subclavian artery to the brachial artery. [ABSTRACT FROM AUTHOR]

Polymer flooding effectiveness is hindered by high temperature and high salinity due to polymer degradation. Researchers proposed the addition of nanoparticles to improve polymer stability to withstand reservoir conditions. Therefore, extensive rheological study and flooding test of partially hydrolyzed polyacrylamide (HPAM) solutions with silica dioxide nanoparticles (SiO2 NPs) were carried out under high temperature and high salinity conditions. The shear viscosity of HPAM-SiO2 NPs in the rheological study was measured using a rheometer while apparent viscosity in porous media was calculated from flooding test and modelled using a numerical model. Apparent viscosity includes shear viscosity and elongational viscosity. Shear viscosity was estimated from the Carreau-Yasuda model and elongational viscosity was correlated with Deborah number via relaxation time. At T=80°C the shear viscosity and apparent viscosity in porous media of HPAM-SiO2 NPs are 50% and 64% higher than HPAM. The results further show that HPAM-SiO2 NPs’ shear viscosity and apparent viscosity in porous media at 60,000 ppm of NaCl are 39% and 53% higher than HPAM, respectively. Nevertheless, the enhanced apparent viscosity of HPAM-SiO2 NPs was owed to the formation of stable and dense interwoven HPAM molecules induced from the hydrogen bonds and alkoxysilane (Si-O-Si) crosslinks between SiO2 NPs and HPAM. This study suggested that the addition of SiO2 NPs could significantly improve the HPAM apparent viscosity in porous media under high temperature and high salinity producing an ideal mobility control agent.

In the present study binary formulations of sodium hyaluronate (▪) and hypromellose (▪) were proposed as medical devices in the field of eye surgeries. Viscoelasticity is tested directly on binary solutions while the rheological behavior in the human eye is mimicked by monitoring the viscoelasticity of ternary mixtures ▪/▪/▪. Both binary and ternary formulations were rheologically characterized at 25 ∘C and 37 ∘C by means of measurements in the oscillatory regime. Amplitude sweep tests revealed that the range of linear viscoelasticity is strongly dependent on the concentration of ▪. For the proposed formulations, it was ascertained that the cohesive energy density at 37 ∘C decreases as ▪ concentration surges; in contrast, at 25 ∘C we detected an increase of cohesive energy were detected. At ▪ mass fraction of α 1 , the two obtained values were comparable. Frequency sweep tests revealed the pseudoplastic character of the binary formulations. In order to fit the complex viscosity modules, the Carreau-Yasuda model was modified. Numerical analysis of the results indicates that the best-fit to the model is obtained when the characteristic parameters take constant values, i.e. n = 0 and m = 1 , regardless of the composition of the formulation. This implies that the modulus of complex viscosity decays hyperbolically. Frequency sweep tests on the ternary formulations were analyzed in terms of both the modulus of complex viscosity to confirm the previous scientific evidence together with an investigation of the phase shift angle between the viscous and elastic components. The results indicate that the addition of water has a different impact on the structure and the cohesion of the mixture at different temperatures. These results suggest that the ternary mixture structure can be sensitively modulated by temperature and the content of water. • The network of Sodium Hyaluronate/Hypromellose is probed by cohesive energy density. • Intraocular medical devices properties are tuned by viscoelastic formulations. • Revised Carreau-Yasuda may assist ophthalmic surgeries predicting complex viscosity. [ABSTRACT FROM AUTHOR]

During surgeries, blood often oozes out of the operated tissue and this has to be sucked out by the S–I device. Blood is more viscous than saline, the cleaning fluid is used in the S–I process. Therefore, for a more comprehensive CFD flow analysis of the improved forceps is simulated in the present work for different driving pressures. The resulting flow rate of blood is compared among the prospective designs and the S–I device currently in use. The new surgical forceps eliminates re-insertion of dissector with suction-irrigator and is reusable, multi-functional, non-toxic, corrosion resistant, toughened, and cost-effective. [ABSTRACT FROM AUTHOR]

In the current study, non-Newtonian flow pattern and heat transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and heat transfer have been successfully verified with the previous studies. Several parameters such as Nusselt number, Drag coefficient, and Carreau number are investigated in details. Considering the temperature-dependent viscosity, it is seen that with increasing thetemperature-thinning index, the drag coefficient increases, but the Nusselt number decreases. By rotating the square obstacle, the results display that increasing the angle of inclination from zero to 45 degrees, increases both the drag coefficient and the Nusselt number. Also, the highest rate of heat transfer occur at the angle of 45 degrees (diamond); however it has a negative impact on the Drag coefficient.

In this work, the effect of cellulose filaments (CFs) dispersion on the relaxation behavior of thermoplastics matrices was studied. The dispersion state of polystyrene/CF composites produced by two different processing methods, leading to two different dispersion qualities, was assessed using scanning electron microscopy (SEM), transmission electron microscopy, and small amplitude oscillatory shear (SAOS). Instead of the generally used plateau value of G′, the melt yield stress of the modified Carreau–Yasuda model was used to find an accurate value of the percolation threshold concentration. It was concluded that in this case, the process involving a solution mixing step led to a better dispersion than the process involving only melt mixing. Then, using the weighted relaxation spectra calculated using the Honerkamp and Weese method on SAOS results, it was shown that the better the dispersion, the more delayed the relaxation process of the polymer matrix. Finally, by studying the relaxation spectra as well as the melt yield stress of polypropylene/CF composites, it was possible to understand the evolution of their morphology upon CF concentration. It was shown that below 5 wt. %, a well dispersed network of CF was obtained, whereas from 5 to 15 wt. % CFs were agglomerating, then leading to a network of agglomerated fibers for concentrations above 15 wt. %. Those assessments done using SAOS results were confirmed by SEM. [ABSTRACT FROM AUTHOR]

PLA/regenerated cellulose (RC) nanocomposites containing 0.5, 1.0, 1.5, 2.0, 3.0 and 5.0 wt% cellulose were prepared by the Pickering emulsion process. The structure and the rheological properties of the composites were characterized by microscopy, the measurement of melt flow rate and oscillatory rheometry. Viscosity was modelled with the modified Carreau-Yasuda and the modified Cross models, and a new model was proposed as well. The results show that RC is a suitable reinforcement for PLA and the Pickering emulsion process produces homogeneous material. Good dispersion and the relatively large aspect ratio of the cellulose nanofiller leads to the formation of a network structure already at small cellulose content. Viscosity increases rapidly with increasing cellulose concentration and a yield stress appears already at 0.5 wt% RC content. Modeling helps the quantitative analysis of the experimental results and offers additional information about the structure and properties of the composites studied. All three models predict yield stress well, but only the new model gives reasonable values for the power law exponent. Other parameters and their composition dependence are difficult to interpret.

Flow bifurcation transitions of shear-thinning fluid and Newtonian fluid, flow through a two-dimensional rectangular channel in presence of intermediate steps have been considered in this manuscript. Employing SIMPLE algorithm, the governing equations have been solved numerically and using FLUENT software to visualize the simulation results for convenience. The Rheological properties of shear-thinning and Newtonian fluids are described in the light of Carreau-Yasuda model. The result of this formulation has been validated with those of an earlier work. The motivation of this work is to study the bifurcation characteristics for different values of Reynolds numbers in presence of multiple steps in a rectangular channel. Pressure drop characteristic has also been studied for different values of expansion ratio and intermediate steps. For some particular value of expansion ratio (ER), a linear relation between 𝑅𝑒𝑐𝑟𝑖𝑡 and the value of 𝑛 of Carreau- Yasuda model has been shown. [ABSTRACT FROM AUTHOR]

Sodium hyaluronate and hydroxypropyl methylcellulose (hypromellose) have proven to be highly useful, finding application in ophthalmic areas as viscosity enhancer agent in eye drops, gelling agent in injections and polymeric matrix in film, filaments and inserts. In this study, the viscosities of binary mixtures to be used as medical devices in microsurgery are analyzed and their pseudoplastic behavior under varying mixing conditions is monitored. All the way such polymers are used to solve extreme surgical situations leaving intermediate situations uncovered because viscosity data of their different combinations are lacking. In this paper, the viscosities of binary mixtures of medical devices used in microsurgery are analyzed and their pseudoplastic behavior under varying mixing conditions is monitored. The zero-shear viscosities, i.e., the maximum viscosity acquired by the system, are described in terms of two "hypothetical" fluids and the experimental results are in agreement with R 2 = 0.98. This provides a useful and immediately used tool for predicting the viscosity of different binary mixtures between medical devices. An extrapolative technique is used to determine the viscosity at infinity γ ˙. Non-Newtonian behavior is well-described by the Carreau-Yasuda model whose parameters were calculated. The model provides a useful analytical basis for predicting the behavior of different possible mixtures. The effect that prepared gels undergo in the human eye is mimicked by following the viscosimetric behavior along a dilution line where the mass(hypromellose)/mass(hyaluronate) ratio is constant. A complex rheological behavior emerges from the results due to the interaction of water molecules that make the 3D structure of hyaluronate brittle and reduce viscosity. At high dilutions, however, there is evidence of structure strengthening due to hydrophobic interactions between the polymer chains and an inversion of the viscosimetric curves at 25 ∘C and 37 ∘C is recorded. • Medical devices sodium hyaluronate/Hypromellose based are used to lubricate the eye. • Preparation of a formulation having predetermined viscosity to use in surgeon plan. • The dynamic behavior in the eye is mimicked by hyaluronate/hypromellose/water system. [ABSTRACT FROM AUTHOR]

A mixed least‐squares finite element model with spectral/hp approximations was developed to analyze a three‐dimensional natural convection of non‐Newtonian fluid, which obeys the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, stress, temperature, and heat flux as the field variables. The least‐squares formulation provides a variational framework for the Navier–Stokes equations and no compatibility of the approximation spaces for field variables is imposed. Also, the use of spectral/hp elements in conjunction with the least‐squares formulation alleviates various forms of locking which often appear in low‐order least‐squares finite element models for incompressible viscous flows and yields accurate results with exponential convergence. To verify and validate the code for Newtonian fluids, the current results are compared with the numerical and experimental results in the literature. Then, the parametric effects of the Carreau–Yasuda model on the flow characteristics are studied. [ABSTRACT FROM AUTHOR]

Mixing at microscales is purely governed by the diffusion mass transport phenomenon, which is a time‐consuming process requiring a prolonged length of the microchannel to obtain desired results. The present study proposes a novel three‐dimensional helical micromixer (TDHM) with a rectangular cross‐section to achieve splendid mixing performance within a short distance contrary to the simple T‐micromixer (STM). A thorough numerical investigation of mixing performance and fluid flow patterns has been conducted using the continuity, species transport, and the Navier–Stokes equations with Newtonian and non‐Newtonian fluid at a wide range of Reynolds number (0.2–320) and mass flow rate (0.00005–0.091 kg/h), respectively. Blood is selected as the non‐Newtonian fluid, and its rheological characteristics are numerically captured by implementing the Carreau–Yasuda model, whereas water is used to study mixing with the Newtonian fluid. At Re = 2, the mixing index of TDHM is 40. 5% more than that of the STM with water as the working fluid, whereas for blood, it is 34.3%, and thus, it was concluded that the TDHM gives much better performance at much less axial distance than that of the STM at all values of the Reynolds number and flow rates considered in the study. Therefore, TDHM can be utilized for various biomedical, chemical, and biochemical applications. [ABSTRACT FROM AUTHOR]

This paper is devoted to analytical solutions for the base flow and temporal stability of a liquid film driven by gravity over an inclined plane when the fluid rheology is given by the Carreau–Yasuda model, a general description that applies to different types of fluids. In order to obtain the base state and critical conditions for the onset of instabilities, two sets of asymptotic expansions are proposed, from which it is possible to find four new equations describing the reference flow and the phase speed and growth rate of instabilities. These results lead to an equation for the critical Reynolds number, which dictates the conditions for the onset of the instabilities of a falling film. Different from previous works, this paper presents asymptotic solutions for the growth rate, wavelength and celerity of instabilities obtained without supposing a priori the exact fluid rheology, being, therefore, valid for different kinds of fluids. Our findings represent a significant step toward understanding the stability of gravitational flows of non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

This study aimed to determine the bromatological composition and the behavior of rheological parameters on the pulp eggplant (Solanum melongena). Bromatological analyzes were performed according to the reference methods, in which a percentage of moisture 90.98%, total carbohydrates 6.86%, crude fiber 1.94%, crude protein 1.19%, Fat 0.31% and 0.49% of ash has been obtained. Viscous flow curves were calculated in the steady state over a temperature range of 10-80°C, and the rheological properties of the pulp were evaluated as a function of temperature. The pulp showed pseudoplastic behavior (shear thinning type) at all temperatures, and the relationship between viscosity and the Carreau-Yasuda model (R2>0.99). The Arrhenius equation was fitted to the data for the apparent viscosity of the pulp with respect to temperature, with activation energy E=1081.61 J/mol. The results provide information on bromatological composition and the rheological behavior of eggplant pulp and may have applications in the design of processes using this raw material. [ABSTRACT FROM AUTHOR]

The performance of fluid devices, such as channels, valves, nozzles, and pumps, may be improved by designing them through the topology optimization method. There are various fluid flow problems that can be elaborated in order to design fluid devices and among them there is a specific type which comprises axisymmetric flow with a rotation (swirl flow) around an axis. This specific type of problem allows the simplification of the computationally more expensive 3D fluid flow model to a computationally less expensive 2D swirl flow model. The topology optimization method applied to a Newtonian fluid in 2D swirl flow has already been analyzed before, however not all fluids feature Newtonian (linear) properties, and can exhibit non-Newtonian (nonlinear) effects, such as shear-thinning, which means that the fluid should feature a higher viscosity when under lower shear stresses. Some fluids that exhibit such behavior are, for example, blood, activated sludge, and ketchup. In this work, the effect of a non-Newtonian fluid flow is considered for the design of 2D swirl flow devices by using the topology optimization method. The non-Newtonian fluid is modeled by the Carreau-Yasuda model, which is known to be able to accurately predict velocity distributions for blood flow. The design comprises the minimization of the relative energy dissipation considering the viscous, porous, and inertial effects, and is solved by using the finite element method. The traditional pseudo-density material model for topology optimization is adopted with a nodal design variable. A penalization scheme is introduced for 2D swirl flow in order to enforce the low shear stress behavior of the non-Newtonian viscosity inside the modeled solid material. The optimization is performed with IPOPT (Interior Point Optimization algorithm). Numerical examples are presented for some 2D swirl flow problems, comparing the non-Newtonian with the Newtonian fluid designs. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of non-Newtonian two-phase fluid-flow through a channel with a cavity was studied. Carreau-Yasuda non-Newtonian model which represents well the dependence of stress on shear rate was used and the effect of n index of the model and the effect of input Reynolds on the attribution of flow were considered. Governing equations were discretized using the finite volume method on staggered grid and the form of allocating flow parameters on staggered grid is based on marker and cell method. The QUICK scheme is employed for the convection terms in the momentum equations, also the convection term is discretized by using the hybrid upwind-central scheme. In order to increase the accuracy of making discrete, second order Van Leer accuracy method was used. For mixed solution of velocity-pressure field SIMPLEC algorithm was used and for pressure correction equation iteratively line-by-line TDMA solution procedure and the strongly implicit procedure was used. As the results show, by increasing Reynolds number, the time of sweeping the non-Newtonian fluid inside the cavity decreases, the velocity of Newtonian fluid increases and the pressure decreases. In the second section, by increasing n index, the velocity increases and the volume fraction of non-Newtonian fluid after cavity increases and by increasing velocity, the pressure decreases. Also changes in the velocity, pressure and volume fraction of fluids inside the channel and cavity are more sensible to changing the Reynolds number instead of changing n index. [ABSTRACT FROM AUTHOR]

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular characteristics. In this paper, we analyze numerically the temporal stability of films of non-Newtonian liquids falling by gravity, on the onset of instability. The liquid flows over an incline, where surface waves appear under certain conditions, and we do not fix a priori its rheological behavior. For that, we made used of the Carreau–Yasuda model without assigning specific values to its constants, and we compute general stability solutions. The numerical strategy is based on expansions of Chebyshev polynomials for discretizing the Orr–Sommerfeld equation and boundary conditions, and a Galerkin method for solving the generalized eigenvalue problem. In addition, an Inverse Iteration method was implemented to increase accuracy and improve computational time. The result is a robust and light numerical tool capable of finding the critical conditions for different types of fluids, which we use to analyze some key fluids. We show that the outputs of the general code match previous solutions obtained for specific computations. Besides increasing our knowledge on surface-wave instabilities in non-Newtonian liquids, our findings provide a new tool for obtaining comprehensive solutions on the onset of instability. • The stability of gravity-driven flows of non-Newtonian films is analyzed. • Equations based on the Carreau–Yasuda model are discretized with a Galerkin method. • A comprehensive code, that is valid for different kinds of fluids, is proposed. • Outputs of the comprehensive code match previous solutions of dedicated codes. • The code is robust, light and capable of accurately finding the critical conditions. [ABSTRACT FROM AUTHOR]

Highlights • Development of the least-squares finite element model to study non-Newtonian fluids in three dimensions. • Use of the spectral approximation functions and associated finite elements in three dimensions. • Parametric study of the Carreau–Yasuda viscosity model for three-dimensional backward-facing step and lid-driven cavity problems. • Both verification (with manufactured solutions) and validation (against available experimental data) results are presented. Abstract A mixed least-squares finite element model with spectral/ hp approximations was developed to analyze three-dimensional, steady, and incompressible flows of generalized Newtonian fluids. The Carreau–Yasuda constitutive model was used for viscosity model. Velocity, pressure, and stress are the field variables of the finite element model (hence, called a mixed model). The least-squares formulation offers a variational setting for the Navier–Stokes equations; hence no compatibility of the approximation spaces used for the velocity, pressure, and stress fields is imposed if the polynomial order is sufficiently high. Also, using high-order spectral/ hp elements in the least-squares formulation for the Navier–Stokes equations alleviates various forms of locking and accurate results can be obtained with exponential convergence. To verify the present formulation and computational module, the method of manufactured solutions and two different benchmark problems (namely, lid-driven cavity flow and backward-facing step flow) are used. Then the effect of different parameters of the Carreau–Yasuda model on the flow behavior is studied. [ABSTRACT FROM AUTHOR]

Inelasticity effects on the migration of a drop and pairwise interaction of drops in a simple shear flow are studied using a finite-difference front-tracking method. The Carreau-Yasuda model is used to adjust the shear-thinning behavior of fluids. Results showed that drop deformation and migration rate of drops in an inelastic system are smaller than those in a Newtonian one. It was revealed that inelasticity has larger effects for the case in which Newtonian drops suspended in a non-Newtonian phase. The time of collision process is shorter for an inelastic system in comparison with the Newtonian one. For two Newtonian drops in an elastic matrix, the results demonstrated that the drops exhibit reversible cross-flow migration at high inelasticity. [ABSTRACT FROM AUTHOR]

A mixed least-squares finite element model (LSFEM) with spectral/hp approximations is developed for the analysis of steady, two-dimensional flows of generalized Newtonian fluids obeying the Carreau-Yasuda constitutive model. The finite element model (FEM) is composed of velocity, pressure, and stress fields as independent variables (therefore, called a mixed model). FEMs based on least-squares formulations are considered an alternative variational setting to the conventional weak-form Galerkin models for the Navier-Stokes equations, and no compatibility conditions on the approximation spaces are needed for the velocity, pressure, and stress fields if the polynomial order (p) is sufficiently high (say, p > 3, as determined numerically). In addition, applying high-order spectral/hp approximation functions to the least-squares formulation avoids various forms of locking that often occur in low-order LSFEMs for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. The benchmark problem of the flow past a circular cylinder is solved to verify and validate the model. Then, a parametric study is performed to examine the effect of change in parameters of the Carreau-Yasuda model on the flow past a circular cylinder. [ABSTRACT FROM AUTHOR]

• The extended Carreau-Yasuda model coupled with temperature is used. • Bubble dynamics in high-viscosity gelled propellants is studied in detail. • The effect of parameters in Carreau-Yasuda model on the bubble dynamics is studied. • The effect of surface tension on the high-liquid-viscosity two-phase flow is studied. Gelled propellants are a new type of propellant whose rheological properties are altered by adding gelling agents to the liquid propellants. Due to their complicated rheological properties, air bubbles can easily be mixed with the propellants and their removal in the manufacturing and casting processes is a challenging task. This can also cause irregular burning or even result in catastrophic failure. To understand the bubble dynamics in gelled propellants, we study the motion of a single bubble rising in a quiescent water-gel with a temperature and shear dependent viscosity. We use the Volume of Fluid (VOF) method where the continuous surface tension model is used to calculate the surface tension. The extended Carreau-Yasuda model coupled with temperature variation is used for the viscosity, and the parameters in the constitutive model are fitted to the experimental data. The effects of temperature, surface tension, and the other parameters in the constitutive model on the motion of a single bubble rising in the gel fuel are studied numerically. The results show that the deformation, the shear-thinning effect, and the terminal speed of the bubble increase with increasing the temperature. We also notice that it is difficult for the vortex inside the bubble to break through the boundary of the bubble with such a high liquid viscosity even when the surface tension is decreased significantly. In addition, it is found that the bubble can maintain its basic shape, with only an upward concavity at the bottom center of the bubble, and even with a very small surface tension, the terminal speed of the bubble does not show a significant change. Moreover, both the rheological index and the characteristic time in the constitutive model have some influence on the motion of the bubble, but the characteristic time seems to have a greater influence. [ABSTRACT FROM AUTHOR]

• 'Rheological behavior of wormlike reverse micellar solutions loaded and unloaded fit well Carreau-Yasuda Model. • The presence of P. guajava leaves extracts into the wormlike reverse micelles modifies its behavior. • OH groups in aqueous extracts of P. guajava increase the size of wormlike reverse micellar systems. Phenolic compounds are molecules that provide health benefits. However, they present problems for their use. The use of wormlike reverse micelles to load aqueous extracts of Psidium guajava (guava) was carried out. Different solutions (i.e., content variation of canola oil, oleic acid, soy lecithin; stirring time, stirring speed) were obtained by incorporation of water by ultrasound and centrifugation. The behavior of the wormlike micelles was evaluated with optical microscopy, simple shear tests, and Raman microscopy with and without aqueous extract of guava leaves. The wormlike reverse micelles solution were adjusted to the Carreau-Yasuda model. Influence of the aqueous extracts of guava leaves were observed in the parameters of Carreau-Yasuda model, related with changes in the packing of the hydroxyl groups and high order of packing in wormlike reverse micellar system. [ABSTRACT FROM AUTHOR]

The ability of a gel to act like a solid-like material at rest and flow like a liquid when sheared can be very useful in propulsion system. Numerical simulation of the flow of gel fuels can be used as a reference to assist experimental studies and applications of these materials. Non-linear rheological effects such as shear thinning, yield stress, thixotropy and viscoelasticity can create difficulties in the formulation and in the numerical investigations. This paper uses a thixotropic shear-thinning constitutive relationship while using a second-order kinetic equation for the structural parameter, where the Carreau–Yasuda model is used for a 5% organic kerosene gel. We study the simple shear flow to verify the accuracy of the numerical method, and the impact of the constitutive parameters on the apparent viscosity as a function of shear rate. To look at the thixotropic flow in more complex flows, we initially study the pipe flow of an organic kerosene gel for different pumping conditions. After performing a parametric study, we find that the thixotropy of the gel strongly affects the shear history, that is, the nonuniform aging distribution. The destruction of the microstructure can be accelerated by adjusting the flow intensity and the model parameters, but it seems that it is difficult to arrive at the equilibrium state within the time scale of the propulsion system; this poses a challenge to the design of the system. • A second-order kinetic equation for the structural parameter and the Carreau–Yasuda model are used for kerosene gel. • After performing a parametric study, we find that the thixotropy of the gel strongly affects the shear history. • The destruction of the microstructure can be accelerated by adjusting the flow intensity and the model parameters. [ABSTRACT FROM AUTHOR]

Gelled fuels combine the main advantages of liquid fuels (throttle ability) and solid fuels (easy handling, etc.) due to their non-Newtonian characteristics. In this paper, we study the flow characteristics of water-hydroxypropylcellulose (HPC) gel in converging tubes and tapered injectors which mimic the flow and injection of kerosene gel in typical geometries of propulsion systems. The water-HPC gel is modeled as a non-linear fluid, where the shear viscosity is assumed to depend on the local shear rate and modeled by the Carreau−Yasuda model; the model parameters are fitted with our experimental measurements done by a rotational rheometer. The numerical simulations indicate that for the converging tubes, increasing the convergence angle, causes the mean apparent viscosity at tube exit to decrease while the mass flow rate reduces at a constant pressure drop. Therefore, there is a balance between the lowering of the pressure loss and reducing mean apparent viscosity. In the tapered injectors, the straight pipe after the converging part has a detrimental effect on the viscosity reduction.

Numerical simulation is carried out to study forced convection in non-Newtonian fluids flowing through sandstones. Simulation is carried out using lattice Boltzmann method (LBM) for both shear-thinning and shear-thickening, by varying the power law index from 0.5 to 1.5 in Carreau–Yasuda model. Parameters involved in LBM and Carreau model are identified to achieve numerical convergence. Permeability and porosity are varied in the range of 10−10–10−6and 0.1–0.7, respectively, to match actual geometrical properties of sandstone. Numerical technology is validated by establishing Darcy's law by plotting the graph between velocity and pressure gradient. Consequently, investigation is carried out to study the influence of material properties of porous media on flow properties such as velocity profiles, temperature profiles, and Nusselt number. [ABSTRACT FROM PUBLISHER]

The objective of this work was the analysis of the temperature effect on the rheological behavior of papaya pulp (Carica papaya). Viscous flow curves at steady state were experimentally determined at 5, 15, 25, 40, 60 and 80°C evaluating the influence of temperatures on the rheological parameters. The tests show the pulps presented non-Newtonian shear thinning behavior, adjusted to the Carreau-Yasuda model. The influence of temperature on the viscosity of the pulp was modeled using an Arrhenius type equation, showing a decrease in viscosity with increasing temperature. The results contribute new information for on the rheological behavior of papaya pulp for the application in the design of processes to manufacture of foods products from this raw material. [ABSTRACT FROM AUTHOR]

Various greases are often used for lubrication of various roller bearing and more seldom for slide bearings operating under rather lower speed values, when the mixed or boundary friction occur, for example, during operation in the start-stop regime. Three various commercial greases were tested, differing in the value of the kinematic viscosity of the base oils used in them, measured at temperature 40 °C and 100 °C, and the resulting different dropping point temperature. The rheological properties of such greases have been determined using the rotary rheometer. Based on the resulted dependencies of the apparent viscosity on the shear rate the parameters of the Carreau-Yasuda rheological model chosen, have been estimated. The prediction of rheological parameters for three plastic greases studied obtained with particularly good accuracy. Among the tested greases, the grease with the highest drop point temperature turned out to be a mechanically stable grease. The differences in parameters values could be affected by differences in the compounds of the greases studied. [ABSTRACT FROM AUTHOR]

• 3D DNS of inertial lift forces on a particle in a straight rectangular microchannel. • Shear gradient and wall-induced lift in Newtonian fluids and xanthan gum solutions. • Variable viscosity for controlling the particle migration in different Re numbers. • Inconsistent lift and equilibrium position in power-law and Carreau-Yasuda models. • Shear-thinning viscosity pushes the equilibrium positions to the microchannel walls. Direct three-dimensional Numerical Simulations (DNS) are performed to calculate the inertial lift forces on a single particle in a straight rectangular microchannel of Newtonian fluid and xanthan gum solutions. The shear-thinning behavior of xanthan gum solutions is demonstrated experimentally and represented mathematically using the power-law and Carreau-Yasuda models. Similar to Newtonian fluids, our simulations delineate the dominant region of shear gradient and wall-induced lift forces for power-law and Carreau-Yasuda fluids. The variable viscosity of non-Newtonian fluids allows us to better control the particle motion which seems promising in the inertial focusing method. Owing to their different formulations, power-law and Carreau-Yasuda models result in inconsistent lift forces. This incompatibility appears to intensify at higher concentrations of xanthan gum (higher shear-thinning characteristics) solutions and stems from the fact that the power-law viscosity considerably diverges from the experimental and Carreau-Yasuda viscosity in both low and high shear-rate regions. The power-law model is more sensitive to the Re number compared to the Carreau-Yasuda model, especially for high concentrations of xanthan gum solutions. Furthermore, the results indicate the presence of two equilibrium positions for both Newtonian fluid and xanthan gum solutions in the microchannel cross-section. By increasing the Re number, the Newtonian and Carreau-Yasuda fluids push the particle equilibrium positions toward the center of the microchannel while the power-law model pushes the equilibrium positions toward the microchannel wall. Furthermore, both power-law and Carreau-Yasuda models indicate the shift of equilibrium positions to the microchannel wall by increasing the shear-thinning characteristics. [ABSTRACT FROM AUTHOR]

This paper reports a numerical study of natural convection in a vertical enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the vertical walls of the enclosure while the horizontal ones are assumed adiabatic. A Carreau–Yasuda model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the shear thinning fluids. The governing parameters for the problem are the thermal Rayleigh number Ra , Prandtl number Pr , power-law index n , aspect ratio A and parameters of non–Newtonian fluid model. A semi-analytical solution, valid for an infinite layer ( A ≫ 1), is derived on the basis of the parallel flow approximation. The influence of the constitutive Carreau–Yasuda equation parameters on the fluid flow, temperature field and heat transfer is discussed in detail. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations. The results reveal the strong influence of the pseudoplastic behavior of a non-Newtonian fluid on its natural convection heat transfer within the enclosure. Results are also obtained by considering the same phenomenon on the basis of the power law model. A comparison is made between the predictions of the two rheological models. [ABSTRACT FROM AUTHOR]

Abstract: A new algorithm to recover centroidal velocities from face-normal data on two-dimensional unstructured staggered meshes is presented. The proposed approach uses iterative defect correction in conjunction with a lower-order accurate Gauss reconstruction to obtain second-order accurate centroidal velocities. We derive the conditions that guarantee the second-order accuracy of the velocity reconstruction and demonstrate its efficacy on arbitrary polygonal mesh topologies. The necessity of the proposed algorithm for non-Newtonian flow simulations is elucidated through numerical simulations of channel flow, driven cavity and backward facing step problems with power-law and Carreau fluids. Numerical investigations show that second-order accuracy of the reconstructed velocity field is critical to obtaining physically consistent solutions of vorticity-dominated flows on non-orthogonal meshes. It is demonstrated that the spurious solutions are not linked to discrete conservation and arise solely due to the lower order accuracy of velocity reconstruction. The importance of the proposed algorithm for hemodynamic simulations is highlighted through studies of laminar flow in an idealized stenosed artery using different blood models. [Copyright &y& Elsevier]