Analysis of Flow of Shear Thinning Colloidal and Polymeric Systems Which Exhibit Elastic Recovery or Rigidity

1967 ◽  
Vol 40 (5) ◽  
pp. 1505-1515
Author(s):  
T. Gillespie
Keyword(s):  
Experimental Data ◽  
Relaxation Time ◽  
Shear Rate ◽  
Elastic Recovery ◽  
Relaxation Times ◽  
Shear Thinning ◽  
Structural Theory ◽  
Polymeric Systems ◽  
New Equation

Abstract The hydrodynamic-structural theory of viscosity is extended to take into account the possibility of a distribution of relaxation times. A new equation is presented which is easily applied to experimental data. The effect of a distribution of lifetimes is to extend the range of shear rate over which shear thinning occurs. When the ratio of the largest relaxation time to the smallest relaxation time is greater than 1 but less than 10 the new equation gives results in agreement with the Willamson equation. When this ratio of maximum relaxation time to minimum relaxation time is 300 ± 100 the new equation agrees with an equation recently suggested by Cross. The utility of the new equation is discussed and is illustrated by using it to determine the relaxation time spectra in polystyrene melts.

Numerical Simulation of the Effect of Rheological Parameters on Shear-Thinning Droplet Formation

2014 ◽  
Author(s):  
Voon-Loong Wong ◽  
Katerina Loizou ◽  
Phei-Li Lau ◽  
Richard S. Graham ◽  
Buddhika N. Hewakandamby
Keyword(s):  
Relaxation Time ◽  
Steady State ◽  
Shear Rate ◽  
Level Set ◽  
Droplet Diameter ◽  
Shear Thinning ◽  
Droplet Formation ◽  
Droplet Breakup ◽  
Rheological Parameters ◽  
Characteristic Relaxation Time

Immiscible non-Newtonian-Newtonian fluid systems in microfluidics constitute an essential study as non-Newtonian fluids consistently met in medical and biological systems. Although a large number of experimental investigations have been reported in this area, attempts to develop predictive models appear to be limited. This paper is an attempt to incorporate a non-Newtonian stress model together with front-tracking scheme used in computational fluid dynamics. A conservative two-phase level set method (LSM) was applied for capturing the droplet breakup dynamics and relevant hydrodynamics of shear-thinning carboxymethylcellulose (CMC) droplets. Our droplets comprise of 0.02wt% to 1.2wt% CMC solutions in a Newtonian continuous fluids system (olive oil) employed in a T-shaped microfluidic cell. A Carreau-Yasuda viscosity model for shear-thinning CMC droplets has been implemented. This shear-dependent constitutive model fitted well to our steady state non-linear shear measurements for polymeric CMC solutions, with asymptotic viscosities at zero and infinite shear rates, and with different degrees of shear thinning (η0/η∞) in steady state. The particular focus of this study was to systematically undergo parametric studies on the influence of rheological parameters of the specified model such as zero (η0) and infinite shear viscosity (η∞), and relaxation time (λ) on the droplet formation processes. The level set simulation predicted that the droplet diameter increases with increasing η0/η∞. The effect of η0/η∞ has been found to have more prominent impact on droplet diameter for higher CMC concentrations. The variation in droplet diameter becomes less significant at the higher degrees of shear-thinning for all concentrations of CMC dispersed solutions. In the limit of zero shear-thinning effect, the droplet diameter increases when the dispersed phase viscosity decreases. Additionally, the effect of λ on the droplet diameter is also discussed. The reciprocal of the characteristic relaxation time (1/λ) corresponds to a critical shear rate that indicates the onset shear rate for shear-thinning. As λ increases, the numerical studies clearly reveal that the droplet diameter is increasing until it reaches a plateau for larger values of λ. The influence of λ leads to a more significant impact on droplet diameter for higher CMC concentration. These findings will ultimately help in understanding the sensitivity of rheological parameters to the microdroplet formation.

Full EHL Simulations Using the Actual Ree–Eyring Model for Shear-Thinning Lubricants

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Punit Kumar ◽  
M. M. Khonsari ◽  
Scott Bair
Keyword(s):  
Experimental Data ◽  
Relaxation Times ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Shear Thinning ◽  
Flow Curves ◽  
Shear Thinning Fluids ◽  
Flow Units ◽  
Eyring Model ◽  
Measured Flow

The Eyring sinh law, which is the most widely used model to describe the shear-thinning behavior of elastohydrodynamic lubrication (EHL) lubricants, fails to replicate the experimentally measured flow curves for shear-thinning lubricants. Interestingly, this law was rejected by Eyring for shear-thinning fluids and, in fact, it was found useful only for fluids thought to exhibit thixotropy. The “actual Ree–Eyring model” for shear-thinning involves multiple flow units with appropriate relaxation times. This paper presents an extensive set of full EHL line and point contact simulations to investigate the usefulness of the actual Ree–Eyring model in EHL applications with shear-thinning lubricants. Comparisons with published experimental data establish the validity of the actual Ree–Eyring model. Also presented is the application of an appropriate shifting rule expected to improve the agreement between simulations and experiments.

scholarly journals Analysis of Power Input of an In-Line Rotor-Stator Mixer for Viscoplastic Fluids

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 916
Author(s):  
Mehmet Ayas ◽  
Jan Skocilas ◽  
Tomas Jirout
Keyword(s):  
Experimental Data ◽  
Shear Rate ◽  
Shear Thinning ◽  
Power Input ◽  
Rotor Speed ◽  
Shear Thinning Fluids ◽  
Power Draw ◽  
Rate Profile ◽  
Shear Thinning Fluid

In this work, the power draw and shear profile of a novel in-line rotor-stator mixer were studied experimentally and the laminar flow regime was simulated. The power draw of the rotor-stator mixer was investigated experimentally using viscoplastic shear-thinning fluid and the results of the obtained power consumptions were verified through simulations. The power draw constant and Otto-Metzner coefficient were determined from the result of experimental data and through simulations. A new method is suggested for the determination of the Otto-Metzner coefficient for the Herschel–Bulkley model and the term efficiency is introduced. It was shown that the proposed method can be applied successfully for the prediction of the Otto-Metzner coefficient for the mixing of viscoplastic shear-thinning fluids. The effect of geometry and rotor speed on power consumption and shear rate profile in the investigated mixer is discussed from the results of the simulations. It was found that numerical methods are a convenient tool and can predict the power draw of the in-line rotor-stator mixer successfully.

scholarly journals Active Brownian Filamentous Polymers under Shear Flow

Polymers ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 837 ◽  
Author(s):  
Aitor Martín-Gómez ◽  
Gerhard Gompper ◽  
Roland Winkler
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Persistence Length ◽  
Relaxation Times ◽  
Shear Thinning ◽  
Weissenberg Number ◽  
Flexible Polymers ◽  
Orientation Relaxation ◽  
Independent Behavior ◽  
Analytical Expressions

The conformational and rheological properties of active filaments/polymers exposed to shear flow are studied analytically. Using the continuous Gaussian semiflexible polymer model extended by the activity, we derive analytical expressions for the dependence of the deformation, orientation, relaxation times, and viscosity on the persistence length, shear rate, and activity. The model yields a Weissenberg-number dependent shear-induced deformation, alignment, and shear thinning behavior, similarly to the passive counterpart. Thereby, the model shows an intimate coupling between activity and shear flow. As a consequence, activity enhances the shear-induced polymer deformation for flexible polymers. For semiflexible polymers/filaments, a nonmonotonic deformation is obtained because of the activity-induced shrinkage at moderate and swelling at large activities. Independent of stiffness, activity-induced swelling facilitates and enhances alignment and shear thinning compared to a passive polymer. In the asymptotic limit of large activities, a polymer length- and stiffness-independent behavior is obtained, with universal shear-rate dependencies for the conformations, dynamics, and rheology.

scholarly journals T2 mapping of the peritumoral infiltration zone of glioblastoma and anaplastic astrocytoma

2021 ◽  
pp. 197140092198932
Author(s):  
Timo Alexander Auer ◽  
Maike Kern ◽  
Uli Fehrenbach ◽  
Yasemin Tanyldizi ◽  
Martin Misch ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Isocitrate Dehydrogenase ◽  
Anaplastic Astrocytoma ◽  
T2 Mapping ◽  
Relaxation Times ◽  
Region Of Interest ◽  
World Health ◽  
High Grade ◽  
High Grade Gliomas ◽  
Health Organization

Purpose To characterise peritumoral zones in glioblastoma and anaplastic astrocytoma evaluating T2 values using T2 mapping sequences. Materials and methods In this study, 41 patients with histopathologically confirmed World Health Organization high grade gliomas and preoperative magnetic resonance imaging examinations were retrospectively identified and enrolled. High grade gliomas were differentiated: (a) by grade, glioblastoma versus anaplastic astrocytoma; and (b) by isocitrate dehydrogenase mutational state, mutated versus wildtype. T2 map relaxation times were assessed from the tumour centre to peritumoral zones by means of a region of interest and calculated pixelwise by using a fit model. Results Significant differences between T2 values evaluated from the tumour centre to the peritumoral zone were found between glioblastoma and anaplastic astrocytoma, showing a higher decrease in signal intensity (T2 value) from tumour centre to periphery for glioblastoma ( P = 0.0049 – fit-model: glioblastoma –25.02± 19.89 (–54–10); anaplastic astrocytoma –5.57±22.94 (–51–47)). Similar results were found when the cohort was subdivided by their isocitrate dehydrogenase profile, showing an increased drawdown from tumour centre to periphery for wildtype in comparison to mutated isocitrate dehydrogenase ( P = 0.0430 – fit model: isocitrate dehydrogenase wildtype –10.35±16.20 (–51) – 0; isocitrate dehydrogenase mutated 12.14±21.24 (–15–47)). A strong statistical proof for both subgroup analyses ( P = 0.9987 – glioblastoma R2 0.93±0.08; anaplastic astrocytoma R2 0.94±0.15) was found. Conclusion Peritumoral T2 mapping relaxation time tissue behaviour of glioblastoma differs from anaplastic astrocytoma. Significant differences in T2 values, using T2 mapping relaxation time, were found between glioblastoma and anaplastic astrocytoma, capturing the tumour centre to the peritumoral zone. A similar curve progression from tumour centre to peritumoral zone was found for isocitrate dehydrogenase wildtype high grade gliomas in comparison to isocitrate dehydrogenase mutated high grade gliomas. This finding is in accordance with the biologically more aggressive behaviour of isocitrate dehydrogenase wildtype in comparison to isocitrate dehydrogenase mutated high grade gliomas. These results emphasize the potential of mapping techniques to reflect the tissue composition of high grade gliomas.

scholarly journals Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

1966 ◽  
Vol 49 (5) ◽  
pp. 989-1005 ◽  
Author(s):  
Richard Fitzhugh
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Giant Axon ◽  
Temperature Curve ◽  
Effect Of Temperature ◽  
Threshold Temperature ◽  
Ionic Conductances ◽  
And Shifts ◽  
The Right ◽  
Increasing Temperature

In the squid giant axon, Sjodin and Mullins (1958), using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman (1962), using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold vs. temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has two effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) factor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 µsec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.

scholarly journals Effect of Surfactants on Gas Holdup in Shear-Thinning Fluids

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Shaobai Li ◽  
Siyuan Huang ◽  
Jungeng Fan
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Sodium Dodecyl ◽  
Shear Thinning ◽  
Gas Holdup ◽  
Bubble Columns ◽  
Gas Velocity ◽  
Shear Thinning Fluids ◽  
Liquid Surface Tension ◽  
Superficial Gas Velocity

In this study, the gas holdup of bubble swarms in shear-thinning fluids was experimentally studied at superficial gas velocities ranging from 0.001 to 0.02 m·s−1. Carboxylmethyl cellulose (CMC) solutions of 0.2 wt%, 0.6 wt%, and 1.0 wt% with sodium dodecyl sulfate (SDS) as the surfactant were used as the power-law (liquid phase), and nitrogen was used as the gas phase. Effects of SDS concentration, rheological behavior, and physical properties of the liquid phase and superficial gas velocity on gas holdup were investigated. Results indicated that gas holdup increases with increasing superficial gas velocity and decreasing CMC concentration. Moreover, the addition of SDS in CMC solutions increased gas holdup, and the degree increased with the surfactant concentration. An empirical correlation was proposed for evaluating gas holdup as a function of liquid surface tension, density, effective viscosity, rheological property, superficial gas velocity, and geometric characteristics of bubble columns using the experimental data obtained for the different superficial gas velocities and CMC solution concentrations with different surfactant solutions. These proposed correlations reasonably fitted the experimental data obtained for gas holdup in this system.

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.

scholarly journals Longer T2relaxation time is a marker of hypothalamic gliosis in mice with diet-induced obesity

2013 ◽  
Vol 304 (11) ◽  
pp. E1245-E1250 ◽  
Author(s):  
Donghoon Lee ◽  
Joshua P. Thaler ◽  
Kathryn E. Berkseth ◽  
Susan J. Melhorn ◽  
Michael W. Schwartz ◽  
...  
Keyword(s):  
Relaxation Time ◽  
High Field ◽  
Relaxation Times ◽  
Quantitative Mri ◽  
Human Studies ◽  
Mri Findings ◽  
Diet Induced Obesity ◽  
Magnetic Resonance Imaging Mri ◽  
The Right ◽  
Mr Brain

A hallmark of brain injury from infection, vascular, neurodegenerative, and other disorders is the development of gliosis, which can be detected by magnetic resonance imaging (MRI). In rodent models of diet-induced obesity (DIO), high-fat diet (HFD) consumption rapidly induces inflammation and gliosis in energy-regulating regions of the mediobasal hypothalamus (MBH), and recently we reported MRI findings suggestive of MBH gliosis in obese humans. Thus, noninvasive imaging may obviate the need to assess MBH gliosis using histopathological end points, an obvious limitation to human studies. To investigate whether quantitative MRI is a valid tool with which to measure MBH gliosis, we performed analyses, including measurement of T2relaxation time from high-field MR brain imaging of mice fed HFD and chow-fed controls. Mean bilateral T2relaxation time was prolonged significantly in the MBH, but not in the thalamus or cortex, of HFD-fed mice compared with chow-fed controls. Histological analysis confirmed evidence of increased astrocytosis and microglial accumulation in the MBH of HFD-fed mice compared with controls, and T2relaxation times in the right MBH correlated positively with mean intensity of glial fibrillary acidic protein staining (a marker of astrocytes) in HFD-fed animals. Our findings indicate that T2relaxation time obtained from high-field MRI is a useful noninvasive measurement of HFD-induced gliosis in the mouse hypothalamus with potential for translation to human studies.

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