Non-axisymmetric Homann stagnation-point flows

2012 ◽  
Vol 702 ◽  
pp. 460-469 ◽  
Author(s):  
P. D. Weidman
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Strain Rate ◽  
Stagnation Point ◽  
Rate Ratio ◽  
Numerical Solutions ◽  
New Family ◽  
Outer Potential ◽  
Asymptotic Behaviours ◽  
Stress Parameters

AbstractA modification of Homann’s axisymmetric outer potential stagnation-point flow of strain rate $a$ is obtained by adding periodic radial and azimuthal velocities of the form $b\hspace{0.167em} r\sin 2\theta $ and $b\hspace{0.167em} r\cos 2\theta $, respectively, where $b$ is a shear rate. This leads to the discovery of a new family of asymmetric viscous stagnation-point flows depending on the shear-to-strain-rate ratio $\gamma = b/ a$ that exist over the range $\ensuremath{-} \infty \lt \gamma \lt \infty $. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-$\gamma $ asymptotic behaviours. Sample similarity velocity profiles are also presented.

Mixed convection non-axisymmetric Homann stagnation-point flow

2017 ◽  
Vol 812 ◽  
pp. 418-434 ◽  
Author(s):  
Y. Y. Lok ◽  
J. H. Merkin ◽  
I. Pop
Keyword(s):  
Mixed Convection ◽  
Incompressible Fluid ◽  
Strain Rate ◽  
Stagnation Point ◽  
Similarity Solution ◽  
Rate Ratio ◽  
Numerical Solutions ◽  
Stagnation Point Flow ◽  
Asymptotic Results ◽  
Convection Parameter

The steady mixed convection non-axisymmetric (Homann, Z. Angew. Math. Mech., vol. 16, 1936, pp. 153–164) stagnation-point flow over a vertical flat wall placed in a viscous and incompressible fluid is considered. A similarity solution is derived which involves the dimensionless parameters $\unicode[STIX]{x1D6FE}$, representing the shear-to-strain-rate ratio, and $\unicode[STIX]{x1D706}$, a mixed convection parameter. Forced convection, $\unicode[STIX]{x1D706}=0$, is treated first where solutions additional to those given previously by Weidman (J. Fluid Mech., vol. 702, 2012, pp. 460–469) are found arising from singularities as $\unicode[STIX]{x1D6FE}\rightarrow \pm 1$. Numerical solutions are obtained for representative values of both $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D706}$. Critical values $\unicode[STIX]{x1D706}_{c}$ of $\unicode[STIX]{x1D706}$ are seen in opposing flow and these are treated in detail. Asymptotic results for large $\unicode[STIX]{x1D706}$ and $\unicode[STIX]{x1D6FE}$ are derived.

scholarly journals The elastics – viscosity propertis of printing role offset inks according to relacxation rheometry

2021 ◽  
pp. 37-48
Author(s):  
A.K. Dorosh ◽  
A.V. Shevchuk
Keyword(s):  
Shear Stress ◽  
Elastic Modulus ◽  
Shear Rate ◽  
Strain Rate ◽  
Loss Modulus ◽  
Complex Viscosity ◽  
Shear Strain Rate ◽  
Loss Angle ◽  
Flow Curves ◽  
Quantitative Measurements

Dire relacxation rheometry methods carried out quantitative measurements and established quvalitative patterns of the dependencies of the main elastic-viscous characteristics for the Cybo black ink system in the temperature range of ( 293-333)°K of its technological resistence, namely : the equilibrium elastic modulus and the angle loss modulus and loss angle tangent; complex viscosity and full reological flow curves of the first shear rate and second (viscosity) of the species; degree of destraction of elastic and viscous properties depending on the value: shear stress; shear strain rate ; relative or absolute deformation on the sample and its temperature.

scholarly journals Safety of Five Tuina Manipulations in Rats with Deep Vein Thrombosis

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ying Zhou ◽  
Yumo Zhang ◽  
Xiaoyan Zhang ◽  
Zhuo Chen ◽  
Jian Dong ◽  
...  
Keyword(s):  
Deep Vein Thrombosis ◽  
Shear Rate ◽  
Strain Rate ◽  
Rate Ratio ◽  
Plasma Viscosity ◽  
High Shear Rate ◽  
High Shear ◽  
Vein Thrombosis ◽  
Deep Vein ◽  
Low Shear

Objective. To study the effects of five tuina manipulations in rats with deep vein thrombosis (DVT) and to explore how to safely perform tuina in the treatment of thrombotic diseases. Methods. Seventy-two male Sprague-Dawley (SD) rats were randomly divided into the model, pointing manipulation, plucking manipulation, kneading manipulation, pushing manipulation, and pulling manipulation groups (n = 12). DVT model was established by incomplete ligation. The tuina intervention was started on the next day after modeling and applied once a day 10 times by the manipulation simulators. On the 3rd and 10th days after intervention, respectively, the effects of tuina on thrombosis were evaluated based on thrombus elasticity, blood coagulation, fibrinolytic function and blood rheology with the ultrasound elastography, four coagulation tests, enzyme linked immunosorbent assay (ELISA), and hemorheology tests. Results. In the pointing manipulation group, the strain rate ratio, 6-ketoprostaglandin F1α (6-Keto-PGF1α), and high shear rate were decreased, and the thromboxane B2 (TXB2) content was increased ( P < 0.05 ). In the plucking manipulation group, the D-dimer and 6-Keto-PGF1α contents were increased, prothrombin time (PT) was shortened, and activated partial thromboplastin time (APTT) was activated, and the high shear rate and plasma viscosity were decreased ( P < 0.05 ). In the kneading manipulation group, APTT was shortened, and 6-Keto-PGF1α, high shear rate, and plasma viscosity were decreased ( P < 0.05 ). In the pushing manipulation group, the strain rate ratio, low shear rate, and high shear rate were all decreased ( P < 0.05 ). In the pulling manipulation group, both the strain rate ratio and the low shear rate were decreased ( P < 0.05 ). The 6-Keto-PGF1α changes on the 3rd and 10th days after intervention were opposite in the pushing manipulation group and the pulling manipulation group ( P < 0.05 ). Conclusion. The pointing, pushing, and pulling manipulations seem to be safe in the early period of thrombosis, but the risk is likely to be elevated as the treatment course of intervention increases. The plucking and kneading manipulations potentially have certain risks in the treatment of DVT in rats.

Two-dimensional generalized non-Newtonian EHL lubrication: Shear rate-based solution versus shear stress-based solution

2021 ◽  
pp. 135065012110504
Author(s):  
Hai Chao Liu ◽  
Bin Bin Zhang ◽  
Volker Schneider ◽  
C.H. Venner ◽  
G. Poll
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Point Contact ◽  
Shear Thinning ◽  
High Shear ◽  
Two Dimensional ◽  
Ehl Lubrication ◽  
Ehl Contact

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

scholarly journals Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

2021 ◽  
Author(s):  
Patrick Wilms ◽  
Jan Wieringa ◽  
Theo Blijdenstein ◽  
Kees van Malssen ◽  
Reinhard Kohlus
Keyword(s):  
Shear Stress ◽  
Liquid Phase ◽  
Shear Rate ◽  
Shear Viscosity ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Wall Slip ◽  
Flow Index ◽  
Concentrated Suspensions

AbstractThe rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

Investigation on the Rheological Behavior of Polyamide6/Montmorillonite Nanocomposites by Reactive Extrusion

2011 ◽  
Vol 233-235 ◽  
pp. 1998-2001 ◽  
Author(s):  
Ming Zhao ◽  
Xiao Zhong Lu ◽  
Kai Gu ◽  
Xiao Min Sun ◽  
Chang Qing Ji
Keyword(s):  
Activation Energy ◽  
Shear Stress ◽  
Shear Rate ◽  
Rheological Behavior ◽  
Reactive Extrusion ◽  
Shear Thinning ◽  
Experimental Results ◽  
Montmorillonite Nanocomposites

The rheological behavior of PA6/montmorillonite(MMT) by reactive extrusion was investigated using cone-and-plate rheometer. The experimental results indicated that PA6/MMT exhibited shear-thinning behavior. The shear stress of both neat PA6 and PA6/MMT increased with the increase in the shear rate. The reduction of the viscous activation energy with the increase of shear stress reflected PA6/MMT can be processed over a wider temperature.

Are the dynamic response characteristics of brachial artery flow-mediated dilation sensitive to the magnitude of increase in shear stimulus?

2008 ◽  
Vol 105 (1) ◽  
pp. 282-292 ◽  
Author(s):  
K. E. Pyke ◽  
J. A. Hartnett ◽  
M. E. Tschakovsky
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Dynamic Response ◽  
Phase I ◽  
Brachial Artery ◽  
Flow Mediated Dilation ◽  
Final Phase ◽  
Stimulus Magnitude ◽  
Brachial Artery Diameter ◽  
Response Characteristics

The purpose of this study was to determine the dynamic characteristics of brachial artery dilation in response to step increases in shear stress [flow-mediated dilation (FMD)]. Brachial artery diameter (BAD) and mean blood velocity (MBV) (Doppler ultrasound) were obtained in 15 healthy subjects. Step increases in MBV at two shear stimulus magnitudes were investigated: large (L; maximal MBV attainable), and small (S; MBV at 50% of the large step). Increase in shear rate (estimate of shear stress: MBV/BAD) was 76.8 ± 15.6 s−1 for L and 41.4 ± 8.7 s−1 for S. The peak %FMD was 14.5 ± 3.8% for L and 5.7 ± 2.1% for S ( P < 0.001). Both the L (all subjects) and the S step trials (12 of 15 subjects) elicited a biphasic diameter response with a fast initial phase (phase I) followed by a slower final phase. Relative contribution of phase I to total FMD when two phases occurred was not sensitive to shear rate magnitude ( r2 = 0.003, slope P = 0.775). Parameters quantifying the dynamics of the FMD response [time delay (TD), time constant (τ)] were also not sensitive to shear rate magnitude for both phases (phase I: TD r2 = 0.03, slope P = 0.376, τ r2 = 0.04, slope P = 0.261; final phase: TD r2 = 0.07, slope P = 0.169, τ r2 = 0.07, slope P = 0.996). These data support the existence of two distinct mechanisms, or sets of mechanisms, in the human conduit artery FMD response that are proportionally sensitive to shear stimulus magnitude and whose dynamic response is not sensitive to shear stimulus magnitude.

Effect of Shear Surface Boundaries on Stress for Shearing Flow of Dry Metal Powders—An Experimental Study

1987 ◽  
Vol 109 (2) ◽  
pp. 232-237 ◽  
Author(s):  
K. Craig ◽  
R. H. Buckholz ◽  
G. Domoto
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Normal Stress ◽  
Particle Diameter ◽  
Surface Boundary ◽  
Metal Powders ◽  
Shear Surface ◽  
Shear Cell ◽  
Shearing Flow ◽  
Solids Content

This paper studies the rapid simple shearing flow of dry cohesionless metal powders contained between parallel rotating plates. In this study, an annular shear cell test apparatus was used; the dry metal powders are rapidly sheared by rotating one of the shear surfaces while the other shear surface remains fixed. Such a flow geometry is of interest to tribologists working in the area of dry or powder lubrication. The shear stress and normal stress on the stationary surface are measured as a function of the following parameters: shear surface boundary material and roughness, the shear-cell gap thickness, the shear-rate and the fractional solids content. Both the fractional solids content and the gap thickness are kept at prescribed values during stress measurements. In this experiment the metal powder tested is different from the shear transmission surface material; the effect on the measured normal and shear stress data are reported. The results show the dependence of the normal stress and the shear stress on the shear-rate, particle density and particle diameter. Likewise, a significant stress dependence on both the fractional solids content and the shear-cell gap thickness was observed.

scholarly journals Investigation of the Sedimentation Property of Backfill Material on the Basis of Rheological Test: A Case Study of Iron Tailings

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yong Wang ◽  
Aixiang Wu ◽  
Lianfu Zhang ◽  
Hongjiang Wang ◽  
Fei Jin
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Mass Concentration ◽  
Filling Material ◽  
Quantitative Characterization ◽  
Filling Materials ◽  
Characterization Studies ◽  
Rheological Test ◽  
Sedimentation Property

Sedimentation of filling materials could cause pipe blocking accident in mines. However, few quantitative characterization studies have investigated the sedimentation characteristics of filling materials. In this study, the sedimentation property of iron tailings with a cement-sand ratio of 1 : 4 and mass concentration of 73%∼82% was investigated based on rheology measurements. Results showed that shear stress increased as shear rate rose from 0 s−1to 120 s−1. The shear stress increased as the filling material concentration increased as well. However, when the shear rate was reversed from 120 s−1to 0 s−1, the shear stress presented an increase-constant-decrease change pattern as the mass concentration increases in the rheological curve. Accordingly, the sedimentation performance of iron tailings filling material was divided into three types: intense sedimentation (the ascending rheological curve) in the mass concentration range of 73%∼76%, slight sedimentation (the constant rheological curve) in the mass concentration range of 77%∼79%, and almost no sedimentation (the descending rheological curve) in the mass concentration range of 80%∼82%. The associated mechanism involving slurry mass concentration-rheological curves-sedimentation performance was illustrated. A correlation between the pipeline rheology and filling material sedimentation performance was established, which provides a practical guide to avoid pipeline blocking while transporting the filling material.

ENTROPY INFLUENCE ON THE DEPENDENCE OF THE NANOFLUIDS VISCOSITY ON TEMPERATURE AND SHEAR RATE

2021 ◽  
Vol 7 (3) ◽  
pp. 89-105
Author(s):  
Lyudmila P. SEMIKHINA ◽  
Daniil D. Korovin
Keyword(s):  
Activation Energy ◽  
Shear Stress ◽  
Shear Rate ◽  
Viscous Flow ◽  
High Reliability ◽  
Narrow Particle Size Distribution ◽  
Disperse Systems ◽  
Rotational Viscometer ◽  
Surfactant Micelles ◽  
Dispersed Systems

A Brookfield DV-II + Pro rotational viscometer was used to study the viscosity of 7 samples of concentrated nanodispersed systems (nanofluids) with a similar viscosity (6-22 mPa ∙ s), the particles of the dispersed phase in which are nanosized surfactant micelles and conglomerates from them. It was found that for 5 out of 7 studied reagents, there is a decrease in viscosity typical for dispersed systems with an increase in the shear rate, and their flow curves, that is, the dependence of the shear stress on the shear rate, correspond to the ideal plastic flow of non-Newtonian fluids. Moreover, with high reliability, R2 ≥ 0.999 is described by the Bingham equation with a small value of the limiting shear stress (less than 0.2 Pa). It is shown that all the studied reagents are also characterized by an increase in the activation energy of a viscous flow Е with an increase in the shear rate. As a result, a decrease in viscosity with an increase in shear rate, typical for disperse systems, including nanofluids, is provided by a more significant increase in entropy changes ΔS compared to Е. It has been substantiated that, depending on the ratio between the activation energy of viscous flow Е and the change in entropy ΔS, the viscosity of concentrated micellar dispersed systems with an increase in the shear rate can decrease, remain unchanged, and increase. The last two cases, not typical for disperse systems and nanofluids, were identified and studied using the example of two demulsifiers, RIK-1 and RIK-2, with a maximum of a very narrow particle size distribution at 160 ± 5 nm, corresponding to the size of a special type of very stable micelles Surfactant — vesicle.

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