Influence of Non-Newtonian Behavior of Blood on Flow in an Elastic Artery Model

1996 ◽  
Vol 118 (1) ◽  
pp. 111-119 ◽  
Author(s):  
A. Dutta ◽  
J. M. Tarbell
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Rate ◽  
Wall Motion ◽  
Flow Simulation ◽  
Shear Thinning ◽  
Power Law Model ◽  
Viscous Shear ◽  
Sinusoidal Flow

Two different non-Newtonian models for blood, one a simple power law model exhibiting shear thinning viscosity, and another a generalized Maxwell model displaying both shear thining viscosity and oscillatory flow viscoelasticity, were used along with a Newtonian model to simulate sinusoidal flow of blood in rigid and elastic straight arteries. When the spring elements were removed from the viscoelastic model resulting in a purely viscous shear thinning fluid, the predictions of flow rate and WSS were virtually unaltered. Hence, elasticity of blood does not appear to influence its flow behavior under physiological conditions in large arteries, and a purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. When a power law model with a high shear rate Newtonian cutoff was used for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to a Newtonian fluid experiencing the same pressure gradient. The wall shear stress was found to be relatively insensitive to fluid rheology but strongly dependent on vessel wall motion for flows driven by the same pressure gradient. The effect of wall motion on wall shear stress could be greatly reduced by matching flow rate rather than pressure gradient. For physiological flow simulation in the aorta, an increase in mean WSS but a reduction in peak WSS were observed for the power law model compared to a Newtonian fluid model for a matched flow rate waveform.

scholarly journals Mathematical Modelling of Pulsatile Flow of Non-Newtonian Fluid Through a Constricted Artery

2021 ◽  
Vol 8 (3) ◽  
pp. 485-491
Author(s):  
Saktipada Nanda ◽  
Biswadip Basu Mallik ◽  
Samarpan Deb Majumder ◽  
Ramesh Kumar Karthick ◽  
Sagar Suman ◽  
...  
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Rate ◽  
Computational Models ◽  
Research Work ◽  
Flow Parameters ◽  
Wall Shear

The research work explores blood flow into a stenosed artery, or one with abnormal growth within it. At the throats and at the critical height of the stenosis, mathematical and computational models have been developed to calculate the various associated parameters such as flow rate, pressure gradient, impedance, and wall shear stress. Modeling blood as a power law fluid showed the dependency of these quantities on temporal and spatial variables, as well as the frequency of the flow oscillation in time and the key parameters of the flow mechanism. The exponential curve is the geometry of the stenosis studied in this analysis. Analytical expressions for axial velocity, volumetric flow rate, pressure gradient, blood flow resistance, and shear stress have been computed and simulated in ANSYS to generate useful results with respect to variation of flow parameters with power law indices and also for comparison between Newtonian and Non- Newtonian models of blood. Upon investigation, it was found that wall shear stress (WSS) increases with stenosis depth and therefore, plays a crucial role in affecting other flow parameters. At power law index 0.6, the highest shear stress and flow velocity were encountered at approximately 7 Pa and 0.5 m/s respectively.

An Improved Mathematical Model for Relating Shear Stress to Shear Rate in Drilling Fluids and Cement Slurries

1976 ◽  
Vol 16 (01) ◽  
pp. 31-36 ◽  
Author(s):  
R.E. Robertson ◽  
H.A. Stiff
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Yield Stress ◽  
Power Law ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Drilling Fluids ◽  
Rate Data ◽  
Power Law Model ◽  
Proposed Model

Abstract The Newtonian, Bingham, and power law models previously have been used to approximate the previously have been used to approximate the rheology of drilling fluids and cements. The proposed yield-pseudoplastic model provides more consistently accurate descriptions of the rheology of such fluids. Simple explicit relationships between the wall shear rate and the volumetric flow rate in both pipe and annular flow have been derived from this model for use in engineering calculations. Introduction Two mathematical models have been widely used with drilling fluids and cement slurries for relating shear stress to shear rate. The most popular is that of Bingham,.T = Ty + ny, .............................(1) which describes this relationship as linear after an initial yield. Very few, if any, drilling fluids or cement slurries conform to this model, and no explicit relationship can be derived between the shear rate and the volumetric flow rate in a pipe or an annulus. In recent years, the Ostwald-de Waele or "power law" model,.T = K yn,...................................(2) has gained popularity. Eq. 2 describes a fluid with no yield stress and a constant ratio between the logarithms of the shear stress and the shear rate over a workable range. Simple explicit relationships between the shear rate and the volumetric flow rate in a pipe and an annulus can be derived from the equation, but the model often does not fit actual shear stress and shear rate data. Actual shear stress/shear rate data for many fluids place them in the category of yield-pseudoplastics, fluids that exhibit a yield stress as well as a nonlinear relationship between shear stress and shear rate once flow is initiated. A three-parameter model for such fluids, proposed by Herschel and Bulkley, combines the characteristics of the Bingham and power law models:.T = Ty + K yn ..............................(3) Eq. 3 describes the behavior of yield-pseudoplastics reasonably well, but again, no explicit relationship can be derived between the shear rate and the volumetric flow rate in a pipe or an annulus. Thus, the need exists for a model that will adequately describe yield-pseudoplastics, such as drilling fluids and cement slurries, and that has the analytical utility of the power law model for engineering calculations. PROPOSED MODEL PROPOSED MODEL The proposed model takes the form.T = A (y + C)B,.............................(4) It adequately describes the relationship between shear rate and shear stress for most drilling fluids and cement slurries. A simple explicit equation replacing shear rate to the volumetric flow rate in a pipe or annulus can be derived from Eq. 4. As an pipe or annulus can be derived from Eq. 4. As an added feature, the values of the constants characterize the fluid. Thus, it can be seen that when B = 1.0 and C = 0, Eq. 4 becomes.T = A y, ...................................(5) which describes the flow properties of a Newtonian fluid. When B = 1.0 and C 0, the fluid is a Bingham plastic, as described in Eq. 1. When B 1.0 and plastic, as described in Eq. 1. When B 1.0 and C = 0, the fluid follows the power law model, as shown in Eq. 2. The parameters A and B can be considered similarly to the parameters of the power law model. However, the third parameter, C, has a somewhat different connotation than the yield stress of the Bingham model. SPEJ P. 31

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
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.

scholarly journals On the convergence rate of the Kačanov scheme for shear-thinning fluids

CALCOLO ◽  
2021 ◽  
Vol 59 (1) ◽  
Author(s):  
Pascal Heid ◽  
Endre Süli
Keyword(s):  
Convergence Rate ◽  
Power Law ◽  
Shear Thinning ◽  
Energy Difference ◽  
Iteration Scheme ◽  
Power Law Model ◽  
A Posteriori ◽  
Shear Thinning Fluids ◽  
Finite Dimensional ◽  
Contraction Factor

AbstractWe explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the contraction factor in the context of the power-law model. Significantly, this factor is shown to be independent of the choice of the cut-off parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.

Laminar Forced Convection in Viscous Shear-Thinning Liquid Flows Inside Circular Pipes: Case for a Modified Power-Law Rheology

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
J. Subedi ◽  
S. Rajendran ◽  
R. M. Manglik
Keyword(s):  
Heat Transfer ◽  
Shear Rate ◽  
Convective Heat Transfer ◽  
Power Law ◽  
Shear Thinning ◽  
Frictional Loss ◽  
Viscous Shear ◽  
Laminar Forced Convection ◽  
Rheology Model ◽  
Low Shear

Abstract Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.

A CFD Study of the Flow of a Power-Law Fluid in Annuli With Variable Eccentricity

2006 ◽  
Author(s):  
Oswaldo Nun˜ez ◽  
Armando J. Blanco
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Pattern ◽  
Power Law ◽  
Numerical Solutions ◽  
Oil Industry ◽  
Flow Patterns ◽  
Rheological Parameters ◽  
Annular Space ◽  
Industrial Processing

Some industrials processes are associated with flow of non-Newtonian fluids in annular spaces. Examples are found in oil industry and food industrial processing. In some cases, gravitational forces cause internal pipe deflection and, consequently, the eccentricity changes along of axis of the annular space. So, flow patterns are modified respect to those found in constant eccentricity annular spaces. Current industrial practice consists on extrapolate predictions based on flow patterns from the constant eccentricity critical scenario, corresponding to the critical region where both boundaries are closer, to the variable eccentricity actual scenario. In practice, using this approach, flow pattern predictions could significantly deviate from the actual profile, and variables such as shear stress at walls or pressure gradient could not be estimated with adequate accuracy. This work consists of a Computational Fluid Dynamics study, aimed to state the implications of evaluating flow patterns, assuming constant eccentricity, in opposition to a more realistic scenario, considering deflection path along the annular space, using a commercial code. A particular application is made to mud removal during well cementing operations in oil industry. For the casing in the hole, the deflection equation is solved and eccentricity along of the system axis is found. Flow of a non-Newtonian fluid described by Power Law model is considered. Oil industry typical conditions are considered for fluid density, rheological parameters, flow rates, casing and hole sizes, and annulus eccentricity. The flow regime was considered laminar. Numerical model capability to reproduce accurately flow patterns in these conditions was assured by comparison with others analytical-numerical solutions for concentric systems. Results show that local Reynolds number Re, shear stress τw and pressure gradient predictions G, under local eccentricity variations, differ from those under constant eccentricity. Differences in Re and τw show a maximum for eccentricity ranging from 60% to 80%, for all flow conditions whereas for G, this difference increases as casing deflection does it. When variable eccentricity models are compared to constant eccentricity one, the latter approach underestimates Re and τw along the narrowest section of the annuli, whereas overestimates the same features along the widest clearance. Additionally, considerably higher variations between these two models are taking place along the narrowest section compared to the variations arising on the widest annular section. When applied to well cementing processes, these results show that considering the most realistic scenario may impact significantly the flow pattern prediction on the annulus during primary cementing operations. Therefore, the quality of the cement job may be greatly compromised.

scholarly journals Direct numerical simulations of ripples in an oscillatory flow

2019 ◽  
Vol 863 ◽  
pp. 572-600 ◽  
Author(s):  
Marco Mazzuoli ◽  
Aman G. Kidanemariam ◽  
Markus Uhlmann
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Oscillatory Flow ◽  
Oscillation Period ◽  
Small Scale ◽  
Bed Shear Stress ◽  
Sediment Bed ◽  
Ripple Formation ◽  
Sediment Flow

Sea ripples are small-scale bedforms which originate from the interaction of an oscillatory flow with an erodible sand bed. The phenomenon of sea ripple formation is investigated by means of direct numerical simulation in which the sediment bed is represented by a large number of fully resolved spherical grains (i.e. the flow around each individual particle is accounted for). Two sets of parameter values (differing in the amplitude and frequency of fluid oscillations, among other quantities) are adopted which are motivated by laboratory experiments on the formation of laminar rolling-grain ripples. The knowledge of the origin of ripples is presently enriched by insights and by providing fluid- and sediment-related quantities that are difficult to obtain in the laboratory (e.g. particle forces, statistics of particle motion, bed shear stress). In particular, detailed analysis of flow and sediment bed evolution has confirmed that ripple wavelength is determined by the action of steady recirculating cells which tend to accumulate sediment grains into ripple crests. The ripple amplitude is observed to grow exponentially, consistent with established linear stability analysis theories. Particles at the bed surface exhibit two kinds of motion depending on their position with respect to the recirculating cells: particles at ripple crests are significantly faster and show larger excursions than those lying in ripple troughs. In analogy with the segregation phenomenon of polydisperse sediments, the non-uniform distribution of the velocity field promotes the formation of ripples. The wider the gap between the excursion of fast and slow particles, the larger the resulting growth rate of the ripples. Finally, it is revealed that, in the absence of turbulence, the sediment flow rate is driven by both the bed shear stress and the wave-induced pressure gradient, the dominance of each depending on the phase of the oscillation period. In phases of maximum bed shear stress, the sediment flow rate correlates more with the Shields number while the pressure gradient tends to drive sediment bed motion during phases of minimum bed shear stress.

scholarly journals Treatment of Shear Stress versus Shear Rate Data for Natural Fiber Reinforced Polymer Composites: A Discussion

2019 ◽  
Vol 11 (1) ◽  
pp. 89-100
Author(s):  
K. Begum ◽  
M. A. Islam
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Power Law ◽  
Flow Index ◽  
Rate Data ◽  
Power Law Model ◽  
Fiber Reinforced ◽  
Melt Viscosity ◽  
Fiber Loading ◽  
Stress Dependent

The rheological properties of melt jute fiber reinforced polypropylene (PP) composites were conducted at constant shear stress. The measured shear stress and shear rate data are fitted to a power law model for measuring stress-independent melt viscosity of the composites. The viscosity increased with the increase of fiber loading and decreased with the rise of temperature. The flow behavior index, n was found to decrease with the increase of fiber loading and increase with the rise of temperature. The shear stress and shear rate data collected from different specialized research journals have also been fitted to the power law model to measure the stress-independent melt viscosity and flow index as in all the previous literatures viscosity is treated as stress dependent parameter. It was found that the dependence of the viscosity and the flow index observed from previous literature data with fiber loading and temperature was quite consistent with the present study.

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