Flow through a converging-diverging tube and its implications in occlusive vascular disease — II

Forrester, John H.; Young, Donald F.

doi:10.1016/0021-9290(70)90032-1

Cited by 73 publications

(32 citation statements)

References 9 publications

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“…Flows through constrictions are popular in blood flow studies, and the analytical method used in this paper is an extension of the pioneering analysis carried out in [1][2][3]. The method used is called the Karman-Pohlhausen method, which essentially leads to the determination of the axial velocity profile.…”

Section: Introductionmentioning

confidence: 99%

“…The method used is called the Karman-Pohlhausen method, which essentially leads to the determination of the axial velocity profile. In [1][2][3], the fluid is considered to be Newtonian and incompressible, and the no-slip assumption is used, as would be common for blood flow applications. A more accurate pressure distribution was later developed for the same flow problem and presented in [4].…”

Section: Introductionmentioning

confidence: 99%

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Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Akhter

Rohlf

2014

Entropy

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The flow of a compressible fluid with slip through a cylinder with an asymmetric local constriction has been considered both numerically, as well as analytically. For the numerical work, a particle-based method whose dynamics is governed by the multiparticle collision (MPC) rule has been used together with a generalized boundary condition that allows for slip at the wall. Since it is well known that an MPC system corresponds to an ideal gas and behaves like a compressible, viscous flow on average, an approximate analytical solution has been derived from the compressible Navier-Stokes equations of motion coupled to an ideal gas equation of state using the Karman-Pohlhausen method. The constriction is assumed to have a polynomial form, and the location of maximum constriction is varied throughout the constricted portion of the cylinder. Results for centerline densities and centerline velocities have been compared for various Reynolds numbers, Mach numbers, wall slip values and flow geometries.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Akhter

Rohlf

2014

Entropy

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“…This includes, but is not limited to micro fluidic systems, 2, 3 nutrient transport in bloodflow, 4,5 single and multiphase transport in porous media, [6][7][8][9][10][11][12] and transport in groundwater systems. [13][14][15][16] The basic idea behind Taylor dispersion is simple.…”

Section: Introductionmentioning

confidence: 99%

The impact of inertial effects on solute dispersion in a channel with periodically varying aperture

et al. 2012

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We investigate solute transport in channels with a periodically varying aperture, when the flow is still laminar but sufficiently fast for inertial effects to be nonnegligible. The flow field is computed for a two-dimensional setup using a finite element analysis, while transport is modeled using a random walk particle tracking method. Recirculation zones are observed when the aspect ratio of the unit cell and the relative aperture fluctuations are sufficiently large; under non-Stokes flow conditions, the flow in non-reversible, which is clearly noticeable by the horizontal asymmetry in the recirculation zones. After characterizing the size and position of the recirculation zones as a function of the geometry and Reynolds number, we investigate the corresponding behavior of the longitudinal effective diffusion coefficient. We characterize its dependence on the molecular diffusion coefficient D m , the Péclet number, the Reynolds number, and the geometry. The proposed relation is a generalization of the well-known Taylor-Aris relationship relating the longitudinal dispersion coefficient to D m and the Péclet number for a channel of constant aperture at sufficiently low Reynolds number. Inertial effects impact the exponent of the Péclet number in this relationship; the exponent is controlled by the relative amplitude of aperture fluctuations. For the range of parameters investigated, the measured dispersion coefficient always exceeds that corresponding to the parallel plate geometry under Stokes conditions; in other words, boundary fluctuations always result in increased dispersion. The transient approach to the asymptotic regime is also studied and characterized quantitatively. We show that the measured characteristic time to attain asymptotic conditions is controlled by two competing effects: (i) the trapping of particles in the near-immobile zone and, (ii) the enhanced mixing in the central zone where most of the flow takes place (mainstream), due to its thinning. C 2012 American Institute of Physics. [http://dx

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“…In contrast, mild, hemodynamically insignificant narrowings interact with Reynolds numbers in excess of 100 to 200 to create more subtle changes in blood flow, so-called disturbed laminar flow (Figure 1). [17][18][19][20] In the present study, we have demonstrated that the Reynolds numbers at the inlet and the throat of a residual lesion frequently exceeded the threshold for the development of disturbed laminar flow and then predicted adverse clinical outcome.…”

Section: Kinlay Et Al Coronary Flow and Clinical Outcomementioning

confidence: 51%

“…[17][18][19][20] In the present study, the Reynolds numbers (Reynolds numberϭvelocityϫ diameterϫdensity/viscosity) at the inlet and within the throat of the lesion were calculated by using the velocity and luminal diameters at these sites, assuming a density of blood of 1.05 g/cm 3 and a viscosity of 1/30 poise. 14 …”

Section: Blood Flow Parameters and Reynolds Numbersmentioning

confidence: 99%

Coronary Flow Velocity and Disturbed Flow Predict Adverse Clinical Outcome After Coronary Angioplasty

Kinlay

Grewal

Manuelin

et al. 2002

ATVB

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Objective-Laminar flow becomes disturbed at high velocities, reducing shear stress and augmenting vascular inflammation and proliferation, processes that are pivotal in restenosis and atherogenesis. We hypothesized that disturbed blood flow after coronary angioplasty is associated with adverse long-term clinical outcome. Methods and Results-The cineangiograms from 97 patients undergoing laser-assisted coronary angioplasty were analyzed. Coronary blood flow velocity, the residual lesion dimensions, and the Reynolds number (an index of disturbed flow) were measured by using a frame-counting technique and quantitative coronary angiography. Cox proportional hazards were used to assess the relative risk of adverse events (target-vessel revascularization, myocardial infarction, or death) over a mean 2.5 years after the index procedure. There were 41 adverse events during 245 patient years of follow-up (17% per year of follow-up). The risk of an adverse event was increased for patients with a high flow velocity (Ͼ250 mm/s; relative risk 2.5, 95% CI 1.3 to 4.7) or a high Reynolds number (Ͼ200) at the stenosis inlet (relative risk 2.1, 95% CI 1.1 to 4.1) at the end of the procedure. Adjustment for other factors did not alter these results. Key Words: disturbed coronary flow Ⅲ Reynolds number Ⅲ outcomes Ⅲ angioplasty T he clinical outcome after percutaneous coronary interventions is related to the risk of restenosis, which is related to the postprocedural minimal luminal diameter, [1][2][3][4] and to disease progression. These events could also be determined by disturbed laminar blood flow at residual stenoses, which creates shear stresses that adversely affect the biology of the arterial wall. [5][6][7][8][9][10][11][12][13] Normal laminar blood flow acts on endothelial cells to generate molecules that promote a vasodilatory, anticoagulant, anti-inflammatory, and growthinhibitory surface. [5][6][7][8][9][10][11][12][13] Disturbed laminar blood flow is more likely to occur at higher flow velocities and creates sites of abnormally low and high shear stress, and these are sensed by the endothelium. Abnormally low shear stress in particular activates endothelial cell genes and their products to stimulate vascular inflammation, smooth muscle cell proliferation, and a procoagulant surface. [5][6][7][8][9][10][11][12][13] Disturbed laminar blood flow is prone to occur in vascular segments with high Reynolds numbers (calculated as velocityϫdiameterϫdensity/viscosity), 14 especially at sites of mild luminal narrowing (Figure 1). Percutaneous coronary interventions aim to favorably alter stenosis severity but may not restore normal laminar flow. The present study examines the hypothesis that coronary flow velocity and disturbed laminar blood flow at a residual coronary lesion after successful laser-assisted coronary intervention are associated with adverse long-term clinical outcomes. We studied this cohort because this ablative technique creates a lumen that is relatively free of dissections (avoiding complex flow patterns and ma...

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Flow through a converging-diverging tube and its implications in occlusive vascular disease — II

Cited by 73 publications

References 9 publications

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

The impact of inertial effects on solute dispersion in a channel with periodically varying aperture

Coronary Flow Velocity and Disturbed Flow Predict Adverse Clinical Outcome After Coronary Angioplasty

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