scholarly journals Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries

2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
D. S. Sankar ◽  
Yazariah Yatim
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Flow Rate ◽  
Core Region ◽  
Core Radius ◽  
The Core ◽  
Casson Model ◽  
Longitudinal Impedance ◽  
Two Fluid

Pulsatile flow of blood in narrow tapered arteries with mild overlapping stenosis in the presence of periodic body acceleration is analyzed mathematically, treating it as two-fluid model with the suspension of all the erythrocytes in the core region as non-Newtonian fluid with yield stress and the plasma in the peripheral layer region as Newtonian. The non-Newtonian fluid with yield stress in the core region is assumed as (i) Herschel-Bulkley fluid and (ii) Casson fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress, plug core radius, and longitudinal impedance to flow obtained by Sankar (2010) for two-fluid Herschel-Bulkley model and Sankar and Lee (2011) for two-fluid Casson model are used to compute the data for comparing these fluid models. It is observed that the plug core radius, wall shear stress, and longitudinal impedance to flow are lower for the two-fluid H-B model compared to the corresponding flow quantities of the two-fluid Casson model. It is noted that the plug core radius and longitudinal impedance to flow increases with the increase of the maximum depth of the stenosis. The mean velocity and mean flow rate of two-fluid H-B model are higher than those of the two-fluid Casson model.

Steady motion of Bingham liquid plugs in two-dimensional channels

2011 ◽  
Vol 705 ◽  
pp. 258-279 ◽  
Author(s):  
Parsa Zamankhan ◽  
Brian T. Helenbrook ◽  
Shuichi Takayama ◽  
James B. Grotberg
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Stress Gradient ◽  
Core Region ◽  
Driving Pressure ◽  
Two Dimensional ◽  
Airway Epithelial ◽  
The Core ◽  
Wall Shear

AbstractWe study numerically the steady creeping motion of Bingham liquid plugs in two-dimensional channels as a model of mucus behaviour during airway reopening in pulmonary airways. In addition to flow analysis related to propagation of the plug, the stress distribution on the wall is studied for better understanding of potential airway epithelial cell injury mechanisms. The yield stress behaviour of the fluid was implemented through a regularized constitutive equation. The capillary number, $\mathit{Ca}$, and the Bingham number, $\mathit{Bn}$, which is the ratio of the yield stress to a characteristic viscous stress, varied over the ranges 0.025–0.1 and 0–1.5, respectively. For the range of parameters studied, it was found that, while the yield stress reduces the magnitude of the shearing along the wall, it can magnify the amplitude of the wall shear stress gradient significantly, and also it can elevate the magnitude of the wall shear stress and wall pressure gradient up to 30 % and 15 %, respectively. Therefore, the motion of mucus plugs can be more damaging to the airway epithelial cells due to the yield stress properties of mucus. The yield stress also modifies the profile of the plug where the amplitude of the capillary waves at the leading meniscus decreases with increase in $\mathit{Bn}$. Other findings are that: the thickness of the static film increases with increasing $\mathit{Bn}$; the driving pressure difference increases linearly with $\mathit{Bn}$; and increasing $\mathit{Bn}$ extends any wall stagnation point beneath the leading meniscus to an unyielded line segment beneath the leading meniscus. With an increase in $\mathit{Bn}$, the unyielded areas appear and grow in the adjacent wall film as well as the core region of the plug between the two menisci. The plug length, ${L}_{P} $, mostly modifies the topology of the yield surfaces. It was found that the unyielded area in the core region between the two menisci grows as the plug length decreases. The very short Bingham plug behaves like a solid lamella. In all computed liquid plugs moving steadily, the von Mises stress attains its maximum value near the interface of the leading meniscus in the transition region. For Bingham plugs moving very slowly, $\mathit{Ca}\ensuremath{\rightarrow} 0$, the driving pressure is non-zero.

scholarly journals Pulsatile Flow of a Two-Fluid Model for Blood Flow through Arterial Stenosis

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
D. S. Sankar
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Fluid Model ◽  
Core Radius ◽  
Flow Through ◽  
Wall Shear ◽  
Two Fluid Model ◽  
Two Fluid

Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.

scholarly journals Pulsatile Flow of Two-Fluid Nonlinear Models for Blood Flow through Catheterized Arteries: A Comparative Study

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
D. S. Sankar ◽  
Usik Lee
Keyword(s):  
Newtonian Fluid ◽  
Pulsatile Flow ◽  
Nonlinear Models ◽  
Fluid Model ◽  
Plug Flow ◽  
Casson Fluid ◽  
Core Region ◽  
The Core ◽  
Casson Model ◽  
Two Fluid

The pulsatile flow of blood through catheterized arteries is analyzed by treating the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is represented by (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for the flow quantities obtained by Sankar (2008) for the two-fluid Casson model and Sankar and Lee (2008) for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is noted that the plug-flow velocity, velocity distribution, and flow rate of the two-fluid H-B model are considerably higher than those of the two-fluid Casson model for a given set of values of the parameters. Further, it is found that the wall shear stress and longitudinal impedance are significantly lower for the two-fluid H-B model than those of the two-fluid Casson model.

scholarly journals Induction of aneurysmogenic high positive wall shear stress gradient by wide angle at cerebral bifurcations, independent of flow rate

2019 ◽  
Vol 131 (2) ◽  
pp. 442-452 ◽  
Author(s):  
Alexandra Lauric ◽  
James E. Hippelheuser ◽  
Adel M. Malek
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Rate ◽  
Stress Gradient ◽  
Dependent Manner ◽  
Parent Vessel ◽  
Spatial Gradients ◽  
Bifurcation Angle ◽  
Wall Shear ◽  
Dynamics Simulations

OBJECTIVEEndothelium adapts to wall shear stress (WSS) and is functionally sensitive to positive (aneurysmogenic) and negative (protective) spatial WSS gradients (WSSG) in regions of accelerating and decelerating flow, respectively. Positive WSSG causes endothelial migration, apoptosis, and aneurysmal extracellular remodeling. Given the association of wide branching angles with aneurysm presence, the authors evaluated the effect of bifurcation geometry on local apical hemodynamics.METHODSComputational fluid dynamics simulations were performed on parametric bifurcation models with increasing angles having: 1) symmetrical geometry (bifurcation angle 60°–180°), 2) asymmetrical geometry (daughter angles 30°/60° and 30°/90°), and 3) curved parent vessel (bifurcation angles 60°–120°), all at baseline and double flow rate. Time-dependent and time-averaged apical WSS and WSSG were analyzed. Results were validated on patient-derived models.RESULTSNarrow symmetrical bifurcations are characterized by protective negative apical WSSG, with a switch to aneurysmogenic WSSG occurring at angles ≥ 85°. Asymmetrical bifurcations develop positive WSSG on the more obtuse daughter branch. A curved parent vessel leads to positive apical WSSG on the side corresponding to the outer curve. All simulations revealed wider apical area coverage by higher WSS and positive WSSG magnitudes, with increased bifurcation angle and higher flow rate. Flow rate did not affect the angle threshold of 85°, past which positive WSSG occurs. In curved models, high flow displaced the impingement area away from the apex, in a dynamic fashion and in an angle-dependent manner.CONCLUSIONSApical shear forces and spatial gradients are highly dependent on bifurcation and inflow vessel geometry. The development of aneurysmogenic positive WSSG as a function of angular geometry provides a mechanotransductive link for the association of wide bifurcations and aneurysm development. These results suggest therapeutic strategies aimed at altering underlying unfavorable geometry and deciphering the molecular endothelial response to shear gradients in a bid to disrupt the associated aneurysmal degeneration.

scholarly journals Pipe rheology of microfibrillated cellulose suspensions

Cellulose ◽  
2019 ◽  
Vol 27 (1) ◽  
pp. 141-156 ◽  
Author(s):  
Tuomas Turpeinen ◽  
Ari Jäsberg ◽  
Sanna Haavisto ◽  
Johanna Liukkonen ◽  
Juha Salmela ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Power Law ◽  
Slip Flow ◽  
Microfibrillated Cellulose ◽  
Flow Index ◽  
Shear Rheology ◽  
Power Law Fluids ◽  
Wall Shear

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.

Development of a Transient Mechanistic Two-Phase Flow Model for Wellbores

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 942-955 ◽  
Author(s):  
Mahdy Shirdel ◽  
Kamy Sepehrnoori
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase ◽  
Wall Shear ◽  
Two Fluid Model ◽  
Two Fluid

Summary A great deal of research has been focused on transient two-phase flow in wellbores. However, there is lack of a comprehensive two-fluid model in the literature. In this paper, we present an implementation of a pseudo-compositional, thermal, fully implicit, transient two-fluid model for two-phase flow in wellbores. In this model, we solve gas/liquid mass balance, gas/liquid momentum balance, and two-phase energy balance equations to obtain five primary variables: liquid velocity, gas velocity, pressure, holdup, and temperature. This simulator can be used as a stand-alone code or can be used in conjunction with a reservoir simulator to mimic wellbore/reservoir dynamic interactions. In our model, we consider stratified, bubbly, intermittent, and annular flow regimes using appropriate closure relations for interphase and wall-shear stress terms in the momentum equations. In our simulation, we found that the interphase and wall-shear stress terms for different flow regimes can significantly affect the model's results. In addition, the interphase momentum transfer terms mainly influence the holdup value. The outcome of this research leads to a more accurate simulation of multiphase flow in the wellbore and pipes, which can be applied to the surface facility design, well-performance optimization, and wellbore damage estimation.

scholarly journals Effects of Surface Tension and Yield Stress on Mucus Plug Rupture: A Numerical Study

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Yingying Hu ◽  
Francesco Romanò ◽  
James B. Grotberg
Keyword(s):  
Surface Tension ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Pressure Difference ◽  
Rupture Process ◽  
Viscoplastic Fluid ◽  
Air Interface ◽  
Mucus Plug ◽  
Wall Shear

Abstract We study the effects of surface tension and yield stress on mucus plug rupture. A three-dimensional simplified configuration is employed to simulate mucus plug rupture in a collapsed lung airway of the tenth generation. The Herschel–Bulkley model is used to take into account the non-Newtonian viscoplastic fluid properties of mucus. Results show that the maximum wall shear stress greatly changes right prior to the rupture of the mucus plug. The surface tension influences mainly the late stage of the rupture process when the plug deforms greatly and the curvature of the mucus–air interface becomes significant. High surface tension increases the wall shear stress and the time needed to rupture since it produces a resistance to the rupture, as well as strong stress and velocity gradients across the mucus–air interface. The yield stress effects are pronounced mainly at the beginning. High yield stress makes the plug take a long time to yield and slows down the whole rupture process. When the effects induced by the surface tension and yield forces are comparable, dynamical quantities strongly depend on the ratio of the two forces. The pressure difference (the only driving in the study) contributes to wall shear stress much more than yield stress and surface tension per unit length. Wall shear stress is less sensitive to the variation in yield stress than that in surface tension. In general, wall shear stress can be effectively reduced by the smaller pressure difference and surface tension.

Coating of Electronic Components by the RTV Dispersion—Part I: Physical Model of the Deposition Process Determined by Drop Tests

1993 ◽  
Vol 115 (3) ◽  
pp. 233-239
Author(s):  
J. A. Owczarek
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Yield Stress ◽  
Physical Model ◽  
Volumetric Flow Rate ◽  
Deposition Process ◽  
Test Method ◽  
Electronic Components ◽  
Drop Tests ◽  
Dispersion Part

This paper describes a study of the process of deposition of RTV dispersion on electronic components placed on substrates. The objective was to develop a technique for the consistent manufacture of encapsulant coating of a desired thickness and extent. In addition, it was desired to obtain an understanding of the phenomenon of run-over, or wicking, of the RTV dispersion onto external leads of circuits being encapsulated, and of means to control it. In this paper physical properties of the RTV dispersion which influence the deposition process were determined using a novel drop test method. These properties allow building of a physical model of the deposition process, and its analysis. The results of drop tests show that the RTV dispersion behaves like a plastic “false body” material which possesses yield stress after a long rest, and which retains residual yield stress after shearing. Part I of this paper is concerned with building of the physical model of the encapsulant deposition process. It also deals with the derivation of an equation relating the wall shear stress to the encapsulant volumetric flow rate.

Wall Shear Stress in Development Process of Aneurysm Around Anterior Communicating Artery

2004 ◽  
Author(s):  
Kenichi Umezawa ◽  
Akihiro Torisu ◽  
Susumu Kudo ◽  
Ryuhei Yamaguchi
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Steady Flow ◽  
Flow Rate ◽  
Development Process ◽  
Anterior Cerebral Artery ◽  
High Flow ◽  
Anterior Communicating Artery ◽  
Wall Shear ◽  
Small Aneurysm

In the present paper, the distribution of the wall shear stress around the apex of the anterior communicating artery (ACoA) in the development process of aneurysm has been studied in laminar steady flow. The anterior communicating artery composing the circle of Willis is one of the predilection sites where the cerebral aneurysm occurs frequently. Once the small aneurysm initiates around the apex in one anterior cerebral artery (ACA) with high flow rate, the distribution of the wall shear stress abruptly changes around the initial aneurysm. With the development of the aneurysm, the wall shear stress distinctly changes along the concaved surface of the aneurysm. The distribution of the wall shear stress in the development process of the aneurysm is physiologically discussed from the viewpoint of hemodynamics.

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