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Journal ArticleDOI

Flow through a converging-diverging tube and its implications in occlusive vascular disease — II: Theoretical and experimental results and their implications

01 May 1970-Journal of Biomechanics (Elsevier)-Vol. 3, Iss: 3, pp 307-316
TL;DR: An experimental program to study the flow characteristics of an incompressible fluid through an axisymmetric converging-diverging tube is described, the theoretical and experimental results are compared, and some speculations are made on their implications in occlusive vascular disease.
About: This article is published in Journal of Biomechanics.The article was published on 1970-05-01. It has received 92 citations till now. The article focuses on the topics: Pressure drop & Reynolds number.
Citations
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Journal ArticleDOI
TL;DR: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu $ m diameter glass tube.
Abstract: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu$ m diameter glass tube. During a single orbit the measured particle velocities and paths in steady flow were in good agreement with those calculated for the fluid, predicted by theory to circulate in closed orbits. Over longer periods, however, single blood cells and latex spheres $\mu$ m diameter migrated across the streamlines out of the vortex at a rate depending on the Reynolds number whereas spheres and aggregates of red cells > 30 $\mu$ m diameter remained in the vortex at all Reynolds numbers. Similar behaviour was noted in pulsatile flow when the vortex moved in phase with upstream fluid velocity and particles described spiral orbits of continually changing diameter. With red cell suspensions of 15-45% haematocrit in steady flow, migration of the corpuscles was also observed and resulted in the formation of a particle-free vortex. In pulsatile flow, cells were always present in the vortex, but their concentration which varied periodically was lower than that in the mainstream. The formation of aggregates of latex spheres and human platelets through collisions occurring in orbit, and their migration to the vortex centre was also observed.

122 citations

Journal ArticleDOI
TL;DR: The rheologic effects of multiple “non-obstructive” plaques in main coronary arteries of man were examined by numerically solving the fluid dynamic equations of motion for pulsatile viscous flow of blood through an arterial section using the actual variation of flow rate during the cardiac cycle.

122 citations

Journal ArticleDOI
TL;DR: Comparison of results shows that the behaviors of the two flows are similar at some instances of time, however, important observed differences indicate that for thorough understanding of pulsatile flow behavior in stenosed arteries, the actual physiological flow should be simulated.

92 citations

Journal ArticleDOI
TL;DR: Coronary artery lesions at high risk of thrombotic occlusion share common characteristics that favor higher shear stress and flow separation.
Abstract: BACKGROUND Coronary angiography in acute myocardial infarction has revealed complicated atherosclerotic plaque and a high rate of thrombotic occlusion. However, the characteristics of lesions at high risk of subsequent occlusion are not well known. METHODS AND RESULTS In the present study, the qualitative and quantitative angiographic features of 38 coronary artery lesions that occluded within 3 years to cause an acute myocardial infarction were compared with 64 control segments from the same patients that did not occlude. Compared with control lesions, the lesions that occluded were more likely to have a division branch originating within the stenosis (76% versus 52%, p less than 0.05). The percent lumen diameter reduction was more severe (47.5 +/- 17.8% versus 41 +/- 12.5%, p less than 0.05) and the inflow (21 +/- 10 degrees versus 16 +/- 7 degrees, p less than 0.05) and outflow (20 +/- 10 degrees versus 16 +/- 8 degrees, p less than 0.05) angles of the stenosis were steeper. Time to myocardial infarction after the angiogram interacted with the importance of these features (p less than 0.02). Thus, paired analysis of the lesions that occluded within 3 months and of the most severe control lesion from each patient showed percent lumen diameter reduction of 62.1 +/- 11.5% and 46.4 +/- 11.4%, respectively (p less than 0.001). The length of the stenosis, its asymmetry, and the irregularity of the contours did not help differentiate occlusive from control segments. CONCLUSIONS Coronary artery lesions at high risk of thrombotic occlusion share common characteristics that favor higher shear stress and flow separation.

90 citations

Journal ArticleDOI
TL;DR: In this paper, a global Galerkin/spectral method is used in the solution of the Navier-Stokes equation in periodically constricted tubes and the axisymmetric stationary flow field is computed.

74 citations

References
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Book
01 Jun 1974

1,455 citations


"Flow through a converging-diverging..." refers background in this paper

  • ...McDonald (10) states that if the parameter (w/v) is less than one, then the flow may be treated as quasisteady, where is the radius of the artery, w is the...

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Book
01 Jan 1963

1,314 citations

Journal ArticleDOI
TL;DR: The purpose of this study is to quantify the acute changes in endothelial histology that are associated with an induced increase in blood velocity and to establish the “normal” endothelial cell population density as a function of stress exposure.
Abstract: The purpose of this study is to quantify the acute changes in endothelial histology that are associated with an induced increase in blood velocity A nontraumatic intra-aortic device was designed to produce a rapid convergence of the aortic blood stream into a narrow channel along the ventral aspect of the thoracic aorta in dogs The endothelial surface overlying this channel was exposed to a broad range of surface shearing stress by the accelerated blood flow Techniques were developed to quantify the resulting distribution of shearing stress so that the stress to which the endothelial surface was exposed at every point along the channel could be determined Special histologic techniques were developed using formalin fixation and gelatin embedding of the tissue so that endothelial cytology could be studied and criteria for normal cells established Using these criteria, cell counts were done to establish the "normal" endothelial cell population density as a function of stress exposure The stress corresponding to the mode of these cell density distribution curves was defined as the acute yield stress (τ c ) The acute yield stress for endothelial cells was found to be 379±85 (SD) dynes/cm 2 Exposure to stress in excess of this value for periods as short as one hour resulted in marked deterioration of the endothelial surface consisting of endothelial cytoplasmic swelling, cell deformation, cell disintegration, and finally dissolution and erosion of cell substance The relationship of these events to cellular rheology and interfacial chemistry is discussed

1,249 citations


"Flow through a converging-diverging..." refers background in this paper

  • ...endothelial changes associated with large velocity gradients (32)....

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  • ...If the constriction is severe so that true turbulence is generated, then it is quite likely that the fluctuating stress (due to fluctuating pressures and velocity gradients) on the endothelial lining causes a deterioration of the endothelial cells, as envisioned by Fry (32)....

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  • ...Further, since an increased concen­ tration of fibrinogen may occur in the interfacial region between the arterial wall and the blood (32), it is possible that a fibrin network may develop in the stagnant blood near the separation and reattachment points....

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  • ...§ - = f # 5 ' ^ ) + o R̂ , J l + 2 (̂ —) [1 " -̂ ] (32)...

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  • ...Fry (32) states that under normal conditions a molecule such as fibrinogen is competing for water, but its affinity for water is lower than that of other substances in the blood....

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Book
01 Jan 1934

550 citations


"Flow through a converging-diverging..." refers background in this paper

  • ...somewhat flatter than the parabolic distribution, and the slight convergence has a tendency to stabilize the laminar mode of flow (16)....

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  • ...g = A(Ç) + B(̂ ) + C(̂ )̂ + D(̂ )̂ + E (16)...

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Book
01 Jan 1964
TL;DR: The second edition of this book as mentioned in this paper is the most complete and complete version of the first edition of the paper, with a much richer coverage of theoretical hydrodynamics, including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.
Abstract: Leonardo wrote, Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics; replace Mechanics by Fluid mechanics and here we are.- From the Preface to the Second EditionAlthough the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena.Much progress has occurred in the half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity and surface tension cannot be ignored. The advent of nanotechnology has broadened interest in the hydrodynamics of thin films, and hydromagnetic effects and radiative heat transfer are routinely encountered in materials processing. This monograph develops the basic equations, in the three most important coordinate systems, in a way that makes it easy to incorporate these phenomena into the theory.The book originally described by Prof. Langlois as "a monograph on theoretical hydrodynamics, written in the language of applied mathematics" offers much new coverage including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.

370 citations


"Flow through a converging-diverging..." refers background in this paper

  • ...However, Langlois (26) states that re­ searchers have been unsuccessful in trying to find an exact solution to the axisymmetric problem....

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