The influence of magnetic field on wall shear stress in power law fluid flow of blood

Abstract The shear rheology of two mechanically manufactured microfibrillated cellulose (MFC) suspensions was studied in a consistency range of 0.2–2.0% with a pipe rheometer combined with ultrasound velocity profiling. The MFC suspensions behaved at all consistencies as shear thinning power law fluids. Despite their significantly different particle size, the viscous behavior of the suspensions was quantitatively similar. For both suspensions, the dependence of yield stress and the consistency index on consistency was a power law with an exponent of 2.4, similar to some pulp suspensions. The dependence of flow index on consistency was also a power law, with an exponent of − 0.36. The slip flow was very strong for both MFCs and contributed up to 95% to the flow rate. When wall shear stress exceeded two times the yield stress, slip flow caused drag reduction with consistencies higher than 0.8%. When inspecting the slip velocities of both suspensions as a function of wall shear stress scaled with the yield stress, a good data collapse was obtained. The observed similarities in the shear rheology of both the MFC suspensions and the similar behavior of some pulp fiber suspensions suggests that the shear rheology of MFC suspensions might be more universal than has previously been realized.

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Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

Applied Bionics and Biomechanics ◽

10.1155/2015/406195 ◽

2015 ◽

Vol 2015 ◽

pp. 1-12 ◽

Cited By ~ 9

Author(s):

S. Priyadharshini ◽

R. Ponalagusamy

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Pressure Gradient ◽

Power Law ◽

Flow Resistance ◽

Velocity Profiles ◽

Arterial Stenosis ◽

Axial Distance ◽

Tapered Artery ◽

Wall Shear

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move fromr/R=0tor/R=1and it follows a concave pattern when we move fromr/R=0tor/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

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Non-Newtonian Flow Behavior in Microchannels for Emulsion Formation

ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels, Parts A and B ◽

10.1115/icnmm2006-96205 ◽

2006 ◽

Author(s):

Ravi Arora ◽

Eric Daymo ◽

Anna Lee Tonkovich ◽

Laura Silva ◽

Rick Stevenson ◽

...

Keyword(s):

Shear Stress ◽

Pressure Drop ◽

Wall Shear Stress ◽

Power Law ◽

Flow Behavior ◽

Scale Up ◽

High Wall Shear Stress ◽

Shear Rates ◽

Wall Shear ◽

Low Shear

Emulsion formation within microchannels enables smaller mean droplet sizes for new commercial applications such as personal care, medical, and food products among others. When operated at a high flow rate per channel, the resulting emulsion mixture creates a high wall shear stress along the walls of the narrow microchannel. This high fluid-wall shear stress of continuous phase material past a dispersed phase, introduced through a permeable wall, enables the formation of small emulsion droplets — one drop at a time. A challenge to the scale-up of this technology has been to understand the behavior of non-Newtonian fluids under high wall shear stress. A further complication has been the change in fluid properties with composition along the length of the microchannel as the emulsion is formed. Many of the predictive models for non-Newtonian emulsion fluids were derived at low shear rates and have shown excellent agreement between predictions and experiments. The power law relationship for non-Newtonian emulsions obtained at low shear rates breaks down under the high shear environment created by high throughputs in small microchannels. The small dimensions create higher velocity gradients at the wall, resulting in larger apparent viscosity. Extrapolation of the power law obtained in low shear environment may lead to under-predictions of pressure drop in microchannels. This work describes the results of a shear-thinning fluid that generates larger pressure drop in a high-wall shear stress microchannel environment than predicted from traditional correlations.

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Computational fluid dynamics simulations of cerebral aneurysm using Newtonian, power-law and quasi-mechanistic blood viscosity models

Proceedings of the Institution of Mechanical Engineers Part H Journal of Engineering in Medicine ◽

10.1177/0954411920917531 ◽

2020 ◽

Vol 234 (7) ◽

pp. 711-719 ◽

Cited By ~ 1

Author(s):

Khalid M Saqr

Keyword(s):

Fluid Dynamics ◽

Computational Fluid Dynamics ◽

Shear Stress ◽

Wall Shear Stress ◽

Power Law ◽

The Other ◽

Lower Wall ◽

Computational Fluid Dynamics Simulations ◽

Wall Shear ◽

Dynamics Simulations

Cerebral aneurysm is a fatal neurovascular disorder. Computational fluid dynamics simulation of aneurysm haemodynamics is one of the most important research tools which provide increasing potential for clinical applications. However, computational fluid dynamics modelling of such delicate neurovascular disorder involves physical complexities that cannot be easily simplified. Recently, it was shown that the Newtonian simplification used to close the shear stress tensor of the Navier–Stokes equation is not sufficient to explore aneurysm haemodynamics. This article explores the differences between the latter simplification, non-Newtonian power-law model and a newly proposed quasi-mechanistic model. The modified Krieger model, which treats blood as a suspension of plasma and particles, was implemented in computational fluid dynamics context here for the first time and is made available to the readers in a C# code in the supplementary material of this article. Two middle-cerebral artery and two anterior-communicating artery aneurysms, all ruptured, were utilized here as case studies. It was shown that the modified Krieger model had higher sensitivity for wall shear stress calculations in comparison with the other two models. The modified Krieger model yielded lower wall shear stress values consistently in comparison with the other two models. Moreover, the modified Krieger model has generally predicted higher pressure in the aneurysm models. Based on published aneurysm rupture studies, it is believed that ruptured aneurysms are usually correlated with lower wall shear stress values than unruptured ones. Therefore, this work concludes that the modified Krieger model is a potential candidate for providing better clinical relevance to aneurysm computational fluid dynamics simulations.

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Lymphatic endothelial cell calcium pulses are sensitive to spatial gradients in wall shear stress

Molecular Biology of the Cell ◽

10.1091/mbc.e18-10-0618 ◽

2019 ◽

Vol 30 (7) ◽

pp. 923-931

Author(s):

Vinay N. Surya ◽

Eleftheria Michalaki ◽

Gerald G. Fuller ◽

Alexander R. Dunn

Keyword(s):

Shear Stress ◽

Fluid Flow ◽

Wall Shear Stress ◽

Cell Types ◽

General Question ◽

Pulse Dynamics ◽

Spatial Gradients ◽

Wall Shear ◽

Valve Formation

Cytosolic calcium (Ca2+) is a ubiquitous second messenger that influences numerous aspects of cellular function. In many cell types, cytosolic Ca2+ concentrations are characterized by periodic pulses, whose dynamics can influence downstream signal transduction. Here, we examine the general question of how cells use Ca2+ pulses to encode input stimuli in the context of the response of lymphatic endothelial cells (LECs) to fluid flow. Previous work shows that fluid flow regulates Ca2+ dynamics in LECs and that Ca2+-dependent signaling plays a key role in regulating lymphatic valve formation during embryonic development. However, how fluid flow might influence the Ca2+ pulse dynamics of individual LECs has remained, to our knowledge, little explored. We used live-cell imaging to characterize Ca2+ pulse dynamics in LECs exposed to fluid flow in an in vitro flow device that generates spatial gradients in wall shear stress (WSS), such as are found at sites of valve formation. We found that the frequency of Ca2+ pulses was sensitive to the magnitude of WSS, while the duration of individual Ca2+ pulses increased in the presence of spatial gradients in WSS. These observations provide an example of how cells can separately modulate Ca2+ pulse frequency and duration to encode distinct forms of information, a phenomenon that could extend to other cell types.

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Induction of NO and prostaglandin E2 in osteoblasts by wall-shear stress but not mechanical strain

AJP Endocrinology and Metabolism ◽

10.1152/ajpendo.1997.273.4.e751 ◽

1997 ◽

Vol 273 (4) ◽

pp. E751-E758 ◽

Cited By ~ 44

Author(s):

R. Smalt ◽

F. T. Mitchell ◽

R. L. Howard ◽

T. J. Chambers

Keyword(s):

Shear Stress ◽

Fluid Flow ◽

Wall Shear Stress ◽

Bone Cells ◽

Mechanical Strain ◽

Osteoblastic Cells ◽

Long Bone ◽

Shear Stresses ◽

No Production ◽

Wall Shear

The nature of the stimulus sensed by bone cells during mechanical usage has not yet been determined. Because nitric oxide (NO) and prostaglandin (PG) production appear to be essential early responses to mechanical stimulation in vivo, we used their production to compare the responsiveness of bone cells to strain and fluid flow in vitro. Cells were incubated on polystyrene film and subjected to unidirectional linear strains in the range 500–5,000 microstrain (με). We found no increase in NO or PGE2 production after loading of rat calvarial or long bone cells, MC3T3-E1, UMR-106–01, or ROS 17/2.8 cells. In contrast, exposure of osteoblastic cells to increased fluid flow induced both PGE2 and NO production. Production was rapidly induced by wall-shear stresses of 148 dyn/cm2 and was observed in all the osteoblastic populations used but not in rat skin fibroblasts. Fluid flow appeared to act through an increase in wall-shear stress. These data suggest that mechanical loading of bone is sensed by osteoblastic cells through fluid flow-mediated wall-shear stress rather than by mechanical strain.

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Analysis of Flow Characteristics of the Blood Flowing through an Inclined Tapered Porous Artery with Mild Stenosis under the Influence of an Inclined Magnetic Field

Journal of Biophysics ◽

10.1155/2014/797142 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Neetu Srivastava

Keyword(s):

Magnetic Field ◽

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Flow Rate ◽

Flow Characteristics ◽

Volumetric Flow Rate ◽

Mhd Equations ◽

Inclined Magnetic Field ◽

Wall Shear

Analytical investigation of MHD blood flow in a porous inclined stenotic artery under the influence of the inclined magnetic field has been done. Blood is considered as an electrically conducting Newtonian fluid. The physics of the problem is described by the usual MHD equations along with appropriate boundary conditions. The flow governing equations are finally transformed to nonhomogeneous second-order ordinary differential equations. This model is consistent with the principles of magnetohydrodynamics. Analytical expressions for the velocity profile, volumetric flow rate, wall shear stress, and pressure gradient have been derived. Blood flow characteristics are computed for a specific set of values of the different parameters involved in the model analysis and are presented graphically. Some of the obtained results show that the flow patterns in converging region (ξ<0), diverging region (ξ>0), and nontapered region (ξ=0) are effectively influenced by the presence of magnetic field and change in inclination of artery as well as magnetic field. There is also a significant effect of permeability on the wall shear stress as well as volumetric flow rate.

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Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Open Physics ◽

10.2478/s11534-011-0034-3 ◽

2011 ◽

Vol 9 (5) ◽

Cited By ~ 6

Author(s):

Kuppalapalle Vajravelu ◽

Sreedharamalle Sreenadh ◽

Palluru Devaki ◽

Kerehalli Prasad

Keyword(s):

Shear Stress ◽

Fluid Flow ◽

Wall Shear Stress ◽

Yield Stress ◽

Newtonian Fluid ◽

Power Law ◽

Fluid Model ◽

Elastic Tube ◽

Yield Stress Fluid ◽

Power Law Index

AbstractThe constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t 1 and t 2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

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