Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries

Sankar, D. S.; Lee, Usik

doi:10.1016/j.cnsns.2008.10.015

Cited by 82 publications

(31 citation statements)

References 19 publications

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“…Recently, Vajravelu et al [19] studied the peristaltic pumping of a Herschel-Bulkley fluid in an inclined tube. Available literature on non-Newtonain fluid model namely, HerschelBulkley fluid model with low shear rates [20][21][22][23][24][25] under different physical situations shows that not much work has been carried out with elastic tubes.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2011

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Abstract:The 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 = 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 ( 1 and 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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Section: Introductionmentioning

confidence: 99%

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

et al. 2011

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“…Although the effect of sheardependent viscosity and also the effect of fluid's elasticity have already been investigated in constricted channels under pulsatile conditions [14][15][16][17][18][19][20][21][22] , there appears to be no published work addressing pulsatile flow of fluids having time-dependent viscosity, i.e., thixotropic fluids. This is quite surprising realizing the fact that such fluids (i.e., fluids for which viscosity decreases by the progress of time, even at a constant shear rate) are quite common in the real world.…”

Section: Most Industrial Fluids and Virtually All Physiological Fluidsmentioning

confidence: 99%

“…( 1 9 ) rz w(r, z, t) (r, z, t) u(r, z, t) 0, 0, 0, 0 on r 0 r r (20) u(r, z,0) 0, w(r, z,0) 0, (r, z,0) 1. …”

Section: Mathematical Formulationmentioning

confidence: 99%

Pulsatile Flow of Thixotropic Fluids through a Partially-Constricted Tube

Nezamidoost

Sadeghy

Askari

2013

J. Soc. Rheol., Jpn

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Pulsatile flow of thixotropic fluids is investigated numerically in a partially-constricted tube assuming that the fluid obeys Moore's structural model as is constitutive equation. Assuming that the flow is laminar, incompressible, two-dimensional and axisymmetric, the equations of motion are simplified using lubrication theory. The simplified equations are then solved numerically using the finite difference method. A suitable coordinate transformation is used to immobilize the boundary of the tube. The effect of the structure breakdown/reformation parameters is investigated on the velocity field and wall shear stress distribution. The importance of the geometrical parameters of the constriction is also investigated on the flow characteristics.

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“…14) In recent years, the literature has witnessed several publications demonstrating that the non-Newtonian behavior of the blood can dramatically affect its flow through local constrictions. [15][16][17][18][19][20] In the present study, we are going to study constriction flow of a purely-viscous non-Newtonian fluid having a sheardependent viscosity. An objective of the present study is to see how flow irregularities (i.e., separation) downstream of the constriction are affected when the degree of shear-thinning or shear-thickening behavior of the blood is manipulated either deliberately (say, through the use of appropriate injections into the blood) or inadvertently (say, by a typical disease).…”

Section: Introductionmentioning

confidence: 99%

MHD Flow of Power-Law Fluids in Locally-Constricted Channels

Esmaeili

Sadeghy

2009

J. Soc. Rheol., Jpn

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In the present study, the effect of a transverse magnetic field is investigated on the flow separation phenomenon at the lee of a single, two-dimensional symmetric constriction assuming that the fluid of interest is of the power-law type. For steady, two-dimensional, and incompressible flow, the equations of motion will be solved using the finite volume formulation based on a staggered grid. Numerical results obtained for the velocity and pressure fields suggest that flow separation occurring downstream the constriction can be controlled by manipulating the degree of the shear-thinning behavior of the fluid and/or by applying an external magnetic field. That is, the size of the separation bubble formed in flow through constrictions is predicted to decrease by an increase in the power-law exponent and/or the strength of the externally imposed magnetic field. The wall shear stress is also predicted to increase by an increase in the strength of the magnetic field.

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Mathematical modeling of pulsatile flow of non-Newtonian fluid in stenosed arteries

Cited by 82 publications

References 19 publications

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

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

Pulsatile Flow of Thixotropic Fluids through a Partially-Constricted Tube

MHD Flow of Power-Law Fluids in Locally-Constricted Channels

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