Shear-thinning Model Research Articles

Deformation of a macroscopic yield stress hydrogel during the free fall of a sphere

We investigate the deformation of a macroscopic yield stress fluid consisting of a mixture of water and hydrogel (superabsorbent polymer) with high solid volume fractions and different grain size distributions during the settling of a sphere. The fluid's rheology combines viscous, elastic, and plastic behaviors and is described by a shear-thinning yield stress model. Experiments were conducted in two motion regimes: the continuous fall, where the sphere reaches a constant terminal velocity, and the intermittent regime, with alternating periods of motion and no-motion. Particle image velocimetry and spatiotemporal images of laser-illuminated fluid cross sections were used to determine the yield surface and analyze local grain motion dynamics. In both regimes, a yield surface similar to an ovoid spheroid is observed. A scaling law is derived for lateral deformation (perpendicular to the fall direction), dependent on sphere size and Yield number (Y). This scaling law provides reliable estimations of maximum deformation widths, consistent with experiments in the literature using different yield stress fluids. For all fluid samples used, the flow within the yielded region shows a strong fore-aft asymmetry, characterized by a negative wake at the back of the sphere related to the elastic component of the bulk deformation. In the intermittent motion regime, we find that the transition from no-motion to motion is associated with reaching a maximum level of compression or triggering sufficient irreversible plastic events in the region of fluid under compression. This leads to a sudden avalanche-type of event where stresses are relaxed and the sphere starts moving downward again.

Stress boundary layers for the Phan-Thien–Tanner fluid at the static contact line in extrudate swell

The method of matched asymptotic expansions is used to examine the behaviour of the Phan-Thien–Tanner (PTT) fluid in the neighbourhood of the contact line singularity in extrudate swell. The solution structure for this shear-thinning viscoelastic fluid model has solvent stresses that dominate the polymer stresses, but requires stress boundary layers to fully resolve the solution at the die wall and free surface. The sizes and mechanism of the boundary layers at the two surfaces are different. We derive and present a similarity solution for the boundary layer at the die wall and an exact solution for the boundary layer at the free surface. An expression for the local behaviour of the free surface is also derived. The results for the boundary layers completes the preliminary asymptotic results for the PTT model presented in previous work.

Unifying the roll waves.

Free surface flows down a slope occur in various real-life scenarios, such as civil engineering, industry, and natural hazards. Unstable waves can develop at the free surface when inertia is sufficiently strong, indicated by the Reynolds number exceeding a critical value. Although this instability has been investigated for specific fluids with different rheologies, a common framework is still lacking to facilitate comparison among the various models. In this study, we investigate the linear stability of a generalized Newtonian fluid, where the viscosity [Formula: see text] remains unspecified. We meticulously construct new dimensionless quantities to minimize dependence on the rheology, and subsequently derive the Orr-Sommerfeld equation of stability for any generalized Newtonian fluid, which has never been done before. We conduct a long-wave expansion and generate a novel analytical expression for the wave celerity, along with the critical Reynolds number. The originality in this study is that the analytical expressions obtained are valid for any rheology, and are easy to compute from a rheological measurement or from a base flow profile measurement. These results are subsequently scrutinized using various shear-thinning, shear-thickening, and viscoplastic rheology models. They exhibit excellent agreement with experimental or numerical data as well as theoretical findings from existing literature. Furthermore, the novel analytical expressions enable a much more comprehensive investigation into the impact of rheology on stability. While our approach does not encompass singular or non-monotonous rheology, the analytical expressions derived from the long-wave expansion exhibit remarkable resilience and they continue to accurately predict both the wave speed and the instability threshold in such cases.

The influence of non-Newtonian behaviors of blood on the hemodynamics past a bileaflet mechanical heart valve

This study employs extensive three-dimensional direct numerical simulations to investigate the hemodynamics around a bileaflet mechanical heart valve. In particular, this study focuses on assessing whether non-Newtonian rheological behaviors of blood, such as shear-thinning and yield stress behaviors, exert an influence on hemodynamics compared to the simplistic Newtonian behavior under both steady inflow and physiologically realistic pulsatile flow conditions. Under steady inflow conditions, the study reveals that blood rheology impacts velocity and pressure field variations, as well as the values of clinically important surface and time-averaged parameters like wall shear stress (WSS) and pressure recovery. Notably, this influence is most pronounced at low Reynolds numbers, gradually diminishing as the Reynolds number increases. For instance, surface-averaged WSS values obtained with the non-Newtonian shear-thinning power-law model exceed those obtained with the Newtonian model. At Re=750, this difference reaches around 67%, reducing to less than 1% at Re=5000. Correspondingly, pressure recovery downstream of the valve leaflets is lower for the shear-thinning blood than the constant viscosity one, with the difference decreasing as the Reynolds number increases. On the other hand, in pulsatile flow conditions, jets formed between the leaflets and the valve housing wall are shorter than steady inflow conditions. Additionally, surface-averaged wall shear stress and blood damage (BD) parameter values are higher (with differences more than 13% and 47%, respectively) during the peak stage of the cardiac cycle, especially for blood exhibiting non-Newtonian yield stress characteristics compared to the shear-thinning or constant viscosity characteristics. Therefore, blood non-Newtonian behaviors, including shear-thinning and yield stress behaviors, exert a considerable influence on the hemodynamics around a mechanical heart valve. All in all, the findings of this study demonstrate the importance of considering non-Newtonian blood behaviors when designing blood-contacting medical devices, such as mechanical heart valves, to enhance functionality and performance.

Viscosity-model-independent generalized Reynolds number for laminar pipe flow of shear-thinning and viscoplastic fluids

Understanding the flow dynamics of non-Newtonian fluids is crucial in various engineering, industrial, and biomedical applications. However, the existing generalized Reynolds number formulations for non-Newtonian fluids have limited applicability due to their dependencies on their specific viscosity models. In this study, we propose a new viscosity-model-independent generalized Reynolds number formulation for laminar pipe flow. The proposed method is based on the direct adaptation of the measurement principles of rotational viscometers for wall shear rate estimation. We assess the accuracy of this proposed formulation for power-law and Carreau-Yasuda viscosity models through robust friction factor experiments. The experimental results demonstrate the applicability and effectiveness of the proposed viscosity-model-independent Reynolds number, as the measured friction factor data align closely with our Reynolds number predictions. Furthermore, we compare the accuracy of our Reynolds number formulation against established generalized Reynolds formulations for pure shear-thinning (Carreau-Yasuda) and viscoplastic (Herschel-Bulkley-extended) models. The results of the comparative analysis confirm the reliability and robustness of this generalized Reynolds number in characterizing and interpreting flow behavior in systems with visco-inelastic non-Newtonian fluids. This unified generalized Reynolds number formulation presents new and significant opportunities for precise pipe flow characterization and interpretation as it is applicable to any visco-inelastic (time-independent) viscosity model without requiring additional derivations.

Accuracy and temporal analysis of non-Newtonian models of blood in the computational FFR – Numerical implementation

Non-invasive assessment of stenosed coronary is a goal for clinical applications. Thus, engineering aligned with medicine has been the solution to solve this problem. This work, serving as a proof of concept, has the main goal to predict the non-invasive fractional flow reserve (FFR) in an atherosclerotic coronary artery. A 3-element Windkessel and Womersley models were used to model boundary conditions of the patient-specific coronary arteries: the pressure at the outlets of the artery and the velocity at the inlet, respectively. Apart from implementing the previous conditions in the numerical code, the novelty of this work is to implement and use, in numerical simulations, Newtonian and non-Newtonian models for blood such as Carreau, Carreau-Yasuda, Casson and Simplified Phan-Thien/Tanner to analyse the accuracy of the computed FFR and the computational time of the simulations. Results indicate that the non-Newtonian viscoelastic model, Simplified Phan-Thien/Tanner, took the longest time but produced the most accurate results - 8h and 2.7% relative error between invasive and non-invasive FFR. The shear-thinning non-Newtonian models required lower computational times but returned a higher average error (3.9h; 7.6% error) which is considered significant. The Newtonian model required the least time but had the highest error value (2.9h; 7.8% error). Thus, although the computational time considering the non-Newtonian viscoelastic model is the highest, this model must be considered in the numerical simulations to obtain the FFR since it is the most accurate for this patient case. This research is a step forward to numerically quantify the non-invasive FFR of a patient.

The apparent viscosity to model the behaviour of liquefied sands

The liquefaction induced loss of soil strength and stiffness marks a change of soil state, that switches from solid to liquid. Recently, the research has revealed that when liquefaction is attained, the soil behaves as a non-Newtonian fluid. Therefore, the framework of soil mechanics cannot be adopted and then the soil behaviour should be studied using a fluid mechanic approach. Several research works highlighted the large potentiality of the apparent viscosity () as the parameter ruling both the liquefaction triggering and the behaviour of liquefied sands. Mele (2022) showed that liquefied sands exhibit a shear-thinning behavior (i.e. decreasing viscosity with increasing shear strain rate), highlighting the direct link between k and n (parameters of shear-thinning model) to the soil demand (CSR). This paper aims to confirm the proposed correlations of Mele (2022) passing from small to full scale. To do that, the results of 1D non-linear site response analysis of the well-known case study of Treasure Island (California), affected by extensive liquefaction phenomena during the 1989, have been studied and interpreted with a “viscous perspective”. The good agreement of the calibrated pseudo-plastic law with the results of the dynamic analysis confirms, the relevance of as physically based parameter for the correct modeling of the behaviour of liquefied sandy soils.

Data-driven rheological characterization of stress buildup and relaxation in thermal greases

Thermal greases, often used as thermal interface materials, are complex paste-like mixtures composed of a base polymer in which dense metallic (or ceramic) filler particles are dispersed to improve the heat transfer properties of the material. They have complex rheological properties that impact the performance of the thermal interface material over its lifetime. We perform rheological experiments on thermal greases and observe both stress relaxation and stress buildup regimes. This time-dependent rheological behavior of such complex fluid-like materials is not captured by steady shear-thinning models often used to describe these materials. We find that thixo-elasto-visco-plastic (TEVP) and nonlinear-elasto-visco-plastic (NEVP) constitutive models characterize the observed stress relaxation and buildup regimes, respectively. Specifically, we use the models within a data-driven approach based on physics-informed neural networks (PINNs). PINNs are used to solve the inverse problem of determining the rheological model parameters from the dynamic response in experiments. These training data are generated by startup flow experiments at different (constant) shear rates using a shear rheometer. We validate the “learned” models by comparing their predicted shear stress evolution to experiments under shear rates not used in the training datasets. We further validate the learned TEVP model by solving a forward problem numerically to determine the shear stress evolution for an input step-strain profile. Meanwhile, the NEVP model is further validated by comparison to a steady Herschel–Bulkley fit of the material’s flow curve.

Comment on Neupert, T.; Bartel, D. Evaluation of Various Shear-Thinning Models for Squalane Using Traction Measurements, TEHD and NEMD Simulations. Lubricants 2023, 11, 178

The field of EHL (elastohydrodynamic lubrication) may be the only one in science in which a model for shear-dependent viscosity would be evaluated by means other than viscometer measurements [...]

Reply to Bair, S. Comment on “Neupert, T.; Bartel, D. Evaluation of Various Shear-Thinning Models for Squalane Using Traction Measurements, TEHD and NEMD Simulations. Lubricants 2023, 11, 178”

After the publication of our paper, we received a comment [...]

A numerical study on the impact of lubricant rheology and surface topography on heavily loaded non-conformal contacts

The increasing requirement of high-power density (power throughput/ weight) in modern day machines lead to thin film lubrication condition in various machine components (rolling element bearings, gears, cams, etc,) due to severe loading conditions. Surface roughness features and lubricant rheology plays a vital role in thin film lubrication, and significantly affects the lubrication performance and lifetime of machine components. The present work demonstrates surface topography and lubricant rheology effects on the traction coefficient for heavily loaded non-conformal contacts. The load-sharing concept considering elastic-plastic deformation of asperities, and Carreau shear-thinning rheological model is employed to describe the dry rough contacts and non-Newtonian behavior of lubricant. An influence of surface topography parameters such as roughness, skewness, kurtosis, and pattern ratio on the traction coefficient is discussed. From results, it is found that among different surface topographies, negatively skewed surfaces having isotropic surface pattern exhibit minimum traction coefficient. The load share function and the critical rolling speed are determined for various surface topographies which provides further insights into the surface topography effect on traction coefficient. The findings of present study are noteworthy as they provide a theoretical basis for an assessment of the lubrication performance of heavily loaded non-conformal contacts.

Integrating shape and performance control in polycrystalline cubic boron nitride fabricated using powder extrusion printing

Polycrystalline Cubic Boron Nitride (PcBN) is widely utilized due to its remarkable wear resistance and high hardness. In this report, we employ powder extrusion 3D printing (PEP) combined with high temperature and high-pressure method (HTHP). The study investigates the rheological properties of multi-material feedstocks, shape-performance control, and densification mechanism in printing and sintering processes. The findings reveal that the PcBN feedstocks conform to the shear thinning model. The porosity of green parts amounts to 2.43%. The expansion rates of the debinded cuboid sample in length, width, and height were 0.15%, 0.46%, and 2.32%, respectively, while the expansion rates of the debinded cylindrical sample in the radial direction and the height direction were 0.41% and 0.85%, respectively, at 50 °C for 20 h. The flexural strength and hardness of the PcBN increase with the increase of sintering temperature, reaching the maximum of 1000.1 MPa and 4221.5 HV, respectively, at 1500 °C.

Evaluation of Various Shear-Thinning Models for Squalane Using Traction Measurements, TEHD and NEMD Simulations

The accurate prediction of friction in highly loaded concentrated contacts is one of the most challenging aspects of thermal elastohydrodynamic (TEHD) simulation. The correct modelling of fluid behaviour on the macroscale, in particular non-Newtonian flow behaviour, is an essential prerequisite. For many years, shear-thinning models have been developed and validated with different approaches and controversially discussed. In basic research, model fluids are often used in this context, which have a similar behaviour to practical lubricants. Accompanied by earlier research results, this paper carries out comprehensive investigations on the rheometric behaviour of the model fluid squalane. Based on traction measurements at four different tribometers, an overall parameter optimisation and performance evaluation of three different shear-thinning models is performed using numerical TEHD simulations. In order to additionally validate the theoretical viscosity behaviour, the optimised shear-thinning curves are then compared with comprehensive non-equilibrium molecular dynamics (NEMD) simulations. The key aspect of this paper is the simultaneous consideration of the shear-thinning models in terms of rheometric, experimental, and simulative investigations without changing the parameters. All investigations show that the Eyring model, despite its simplicity, provides the best agreement in both the numerical contact simulation and the NEMD simulations.

Sensitivity of TEHL Simulations to the Use of Different Models for the Constitutive Behaviour of Lubricants

This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consists of the Tait equation of state, the Doolittle Newtonian viscosity model, and the Carreau shear thinning model. The second group includes the Dowson equation of state, the Roelands–Houpert Newtonian viscosity model, and the Eyring shear thinning model. The simulations were conducted using a Computational Fluid Dynamic and Fluid-Structure Interaction (CFD-FSI) approach, which employs a homogeneous equilibrium model for the flow simulation along with a linear elastic solver to describe the deformation of the solid materials. The simulations were conducted under a load range of 100 kN/m to 200 kN/m and a slide-to-roll-ratio (SRR) range between 0 and 2 using Squalane lubricant. The results show up to a 10% deviation in central film thickness, a 31% deviation in coefficient of friction (CoF), and a 38% deviation in maximum lubricant temperature when using the different constitutive models. This study highlights the sensitivity of TEHL simulation results to the choice of constitutive models for lubricants and the importance of carefully selecting the appropriate models for specific applications.

Effects of Partial Substitution of Sprouted Buckwheat (Fagopyrum Esculentum) and Chickpea (Cicer arietinum) Flours on its Functional Properties

This study was conducted to investigate the effects of sprouting buckwheat and chickpeas on their nutritional and physicochemical properties. Lipid content decreased significantly (P<0.05) after buckwheat germination but increased significantly (P<0.05) after chickpea germination. Protein, vitamin B₆ total phenols, and total flavonoid content increased significantly (P<0.05) in sprouted treatments compared to non-sprouted treatments. Water holding capacity was significantly (P<0.05) greater for sprouted treatments which could be related to the greater number of proteins after germination. Otherwise, water holding capacity decreased at 55oC for sprouted treatments, which could be due to decreased swelling power at higher temperatures. A shear-thinning model fitted the flow behavior index of sprouted and non-sprouted treatments. Moreover, sprouting also contributed to the decrease in pasting viscosities, except for breakdown viscosity. The use of sprouted buckwheat and chickpea to replace fractions of wheat flour resulted in a significant (p<0.05) increase in syneresis during the freeze-thaw cycle of flour, cooked pasta water uptake and solid leaching out due to increasing soluble sugars after germination and a weaker gluten network because of adding gluten-free ingredients.

A Comparison of the High-Pressure Viscometry and Optical Inference Methods Used to Determine the Pressure-Viscosity Coefficient

Abstract Pressure-viscosity coefficients (PVC) are used in the predictions of elastohydrodynamic lubricated (EHL) componentry. These coefficients are obtained by either viscometry or optical EHL inference. The literature indicates that each method differs in its conclusion. Those who favor viscometry believe optical methods yield a misleading coefficient. Those who favor optical methods suggest low shear viscometric results over-predict the high shear-influenced film thickness. This work compares each method relative to di-(ethylhexyl) sebacate (DEHS), and five MIL and DOD spec lubricants. PVC results from viscometry and two optical methods are presented. Comparisons are made relative to other published measurements. Conclusions show PVCs inferred from optical film thickness measurements, differ from those obtained by viscometry. Viscometry methods are demonstrated as being consistent. Optically inferred results have uncertainty and require ample data to align with classical dimensionless speed exponents. While the optical measurements are truly EHL, the test conditions fall outside the fitted window of classical algebraic film equations, like that of Hamrock and Dowson. The PVC discrepancies, between optical inference and viscometry and for the studied fluids, cannot be explained by the proper account of the refractive index, shear thinning models, and/or film thickness correction models.

Rheological measurement of untreated sewage by straight tube

Sewage contains abundant low-grade heat energy, and recycling it using a heat pump system is an effective way to reduce carbon emissions. The particles in sewage will cause untreated sewage to exhibit non-Newtonian characteristics, and accurate rheological measurement is important for sewage transmission and distribution system design. The traditional rotary rheometer deforms, agglomerates, or breaks the solid particles in sewage, which affects the measurement results. Therefore, in this study, a horizontal tube rheological test bench was built for urban sewage. Constitutive equations and viscosity expressions of untreated and prepared urban sewage at different temperatures and particle concentrations were tested. The results show that untreated and prepared sewage conforms to the shear-thinning model of power-law fluids in non-Newtonian fluids even at particle wet mass concentration as low as 0.103%. The flow characteristic index n of sewage is unrelated to temperature, and its influence is mainly reflected in the consistency coefficient k. However, the sewage flow characteristic index n increases with a decrease in particle concentration. In the laminar flow range of 0.02–0.2 m/s, the flow resistance obtained by treating untreated sewage as a Newtonian fluid was approximately 1.36–1.99 times that of the non-Newtonian fluid model, which will result in a larger power system design and higher energy consumption. Under turbulent flow conditions, the drag coefficient of the Newtonian model was approximately 1.13 times that of the non-Newtonian model. This shows that when designing a sewage source heat pump system, the power-law fluid shear-thinning characteristics of untreated sewage must be fully considered, which helps reduce the calculated energy consumption of transportation.

Effect of Coriolis and buoyancy forces on three-dimensional flow of chemically reactive tangent hyperbolic fluid subject to variable viscosity

Thermophoresis effect has wide range of applications in electro-static precipitators and in biology for calculating single biological macro molecules, such as genomic-length DNA and HIV virus in the micro channels. Current study deal with effects of Coriolis and buoyancy forces on the three-dimensional boundary layer flow of tangent hyperbolic fluid with thermo-migration and haphazard motion of nano-sized particles. Arrhenius kind of chemical reaction is taken along an exponentially stretchable surface. The main focus of current exploration is to execute shear thinning nano-liquid flow past an exponentially rotating stretchable surface under the influence of variable viscosity, mixed convection and activation energy. We are motivated to explore the features of three-dimensional shear thinning model combined under the features of mixed convention, variable viscosity, and activation energy. The mathematical model is designed to generate PDEs and converted them into ODEs by employing fractious transformation. The numerical outcomes are exhibited via graphs by employing Bvp4c numerical technique whereas the values of skin friction coefficient are calculated by monopolizing shooting method. Characteristics of the parameters appearing in modeling like the viscosity parameter, power-law index, local Weissenberg number, mix convection parameter, rotation parameter, Prandtl number and chemical reaction parameter are comprehensively analyzed through graphical behavior. The impact of governing parameters on skin friction, heat and mass transfer rates is illustrated through tables. The detail analysis anticipates that the elevation in Weissenberg number and porosity caused decline in velocity. Further, the temperature behaves doppositely analogous to development Prandtl besides the thermophoresis parameter.

Optimal Design of Hydraulic Disc Brake for Magnetorheological (MR) Application

This paper aims to provide a new design considering compressive force application in the MR fluid andimprove its braking torque by optimizing it. According to the current study, compressing the MR region will increase braking torque compared to no compression. The area covered by an existing model of the conventional disc brake is taken into consideration for the unique design of the MR brake to operate in shear and compression mode, and the required compression given by the hydraulic pressure similar to a conventional disc brake. The suggested MR brake’s structural layout is presented. The Herschel-Bulkley shear thinning model’s mathematical expression for the torque equation for the compression and shear modes is provided. An analytical magnetic circuit is done for the proposed design for determining the relationship between applied current and magnetic field strength as a function of the geometrical and material attributes of the MR brake. Simulation is done on COMSOL software with the help of an AC/DC module, considering the non-linear relationship between the magnetic field and magnetic flux. Simulation results of braking torque achieved with the varying current are determined. The graph displays the braking torque for current in the compression plus shear mode as well as shear mode. After that, optimization is done on the proposed model for optimal design parameters. For optimization, we adopt the most popular Genetic Algorithm (GA) method. Optimization aims to increase the braking torque capacity of the MR brake for the given volume.

Fluid-structure interaction model of blood flow in abdominal aortic aneurysms with thermic treatment

Hyperthermia is one of the non-invasive therapy of an Abdominal Aortic Aneurysm (AAA), which is achieved by applying a heat source upon the AAA without surgical operation. This research paper considers laminar flow and heat transfer in a heated abdominal aortic aneurysm using an isothermal boundary condition. Heat is added to explicate the thermal treatment of a diseased artery. The blood is assumed as a non-Newtonian fluid based on the shear-thinning Carreau model. Two unequal aneurysms are assumed in the lower wall to simulate bulges or a disordered artery. Flexible wall segments are assumed in the upper wall and opposing to each aneurysm. The transient momentum and energy equations are solved based on the fluid–structure interaction (FSI) using the Arbitrary-Lagrangian–Eulerian (ALE) method. It is found that the shear stress is much higher for a higher index of the power-law fluid governing the blood viscosity and hence, it is strictly recommended to reduce the viscous nature of the blood in diseased vessels. It is found also that the thermal energy can be greatly transported across the blood at a higher Reynolds number, this means that the hyperthermia therapy becomes effective when blood flows violently through the aortic.