scholarly journals A Simplified Model for Predicting Friction Factors of Laminar Blood Flow in Small-Caliber Vessels

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 75 ◽  
Author(s):  
Aikaterini Mouza ◽  
Olga Skordia ◽  
Ioannis Tzouganatos ◽  
Spiros Paras
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Friction Factor ◽  
Small Diameter ◽  
Numerical Data ◽  
Blood Flow Rate ◽  
Vessel Diameter ◽  
Simplified Model ◽  
Glycerol Solution ◽  
Fanning Friction Factor

The aim of this study was to provide scientists with a straightforward correlation that can be applied to the prediction of the Fanning friction factor and consequently the pressure drop that arises during blood flow in small-caliber vessels. Due to the small diameter of the conduit, the Reynolds numbers are low and thus the flow is laminar. This study has been conducted using Computational Fluid Dynamics (CFD) simulations validated with relevant experimental data, acquired using an appropriate experimental setup. The experiments relate to the pressure drop measurement during the flow of a blood analogue that follows the Casson model, i.e., an aqueous Glycerol solution that contains a small amount of Xanthan gum and exhibits similar behavior to blood, in a smooth, stainless steel microtube (L = 50 mm and D = 400 μm). The interpretation of the resulting numerical data led to the proposal of a simplified model that incorporates the effect of the blood flow rate, the hematocrit value (35–55%) and the vessel diameter (300–1800 μm) and predicts, with better than ±10% accuracy, the Fanning friction factor and consequently the pressure drop during laminar blood flow in healthy small-caliber vessels.

scholarly journals A Simplified Model for Predicting Friction Factors of Laminar Blood Flow in Small-Caliber Vessels

2018 ◽  
Author(s):  
Aikaterini Mouza ◽  
Olga Skordia ◽  
Ioannis D Tzouganatos ◽  
Spiros Paras
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Friction Factor ◽  
Small Diameter ◽  
Numerical Data ◽  
Vessel Diameter ◽  
Simplified Model ◽  
Glycerol Solution ◽  
Set Up ◽  
Fanning Friction Factor

The aim of this study is to provide the scientists with a straightforward correlation that can be applied for predicting the Fanning friction factor and consequently the pressure drop during blood flow in small caliber vessels. Due to the small diameter of the conduit, the Reynolds numbers are low and thus the flow is laminar. The study has been conducted using CFD simulations validated with relevant experimental data acquired using an appropriate experimental set-up. The experiments concern pressure drop measurement during the flow of a blood analogue that follows the Casson model, i.e. an aqueous glycerol solution that contains a small amount of xanthan gum and exhibits similar behavior to blood, in a smooth, stainless steel microtube (L=5.6cm and D=400 μm). The interpretation of the resulting numerical data led to the proposal of a simplified model that incorporates the effect of the flow rate, the hematocrit value (35-55%) and the vessel diameter (300-1800 μm) and predicts with better than ±10% the Fanning friction factor and consequently the pressure drop during laminar blood flow in small caliber vessels.

The effect of pressure drop stabilization in arteries during variations in blood flow rate

1993 ◽  
Vol 148 (3) ◽  
pp. 285-294 ◽  
Author(s):  
V. M. KHAYUTIN ◽  
V. P. NIKOLSKY ◽  
A. N. ROGOZA ◽  
E. V. LUKOSHKOVA
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Flow Rate ◽  
Blood Flow Rate ◽  
Effect Of Pressure

scholarly journals Two-compartment model of inner medullary vasculature supports dual modes of vasopressin-regulated inner medullary blood flow

2010 ◽  
Vol 299 (1) ◽  
pp. F273-F279 ◽  
Author(s):  
Julie Kim ◽  
Thomas L. Pannabecker
Keyword(s):  
Blood Flow ◽  
Blood Flow Rate ◽  
Outer Zone ◽  
Compartment Model ◽  
Transverse Dimension ◽  
Vessel Diameter ◽  
Functional Coupling ◽  
Vascular Bundles ◽  
Transport Pathways ◽  
Vasa Recta

The outer zone of the renal inner medulla (IM) is spatially partitioned into two distinct interstitial compartments in the transverse dimension. In one compartment (the intercluster region), collecting ducts (CDs) are absent and vascular bundles are present. Ascending vasa recta (AVR) that lie within and ascend through the intercluster region (intercluster AVR are designated AVR2) participate with descending vasa recta (DVR) in classic countercurrent exchange. Direct evidence from former studies suggests that vasopressin binds to V1 receptors on smooth muscle-like pericytes that regulate vessel diameter and blood flow rate in DVR in this compartment. In a second transverse compartment (the intracluster region), DVR are absent and CDs and AVR are present. Many AVR of the intracluster compartment exhibit multiple branching, with formation of many short interconnecting segments (intracluster AVR are designated AVR1). AVR1 are linked together and connect intercluster DVR to AVR2 by way of sparse networks. Vasopressin V2 receptors regulate multiple fluid and solute transport pathways in CDs in the intracluster compartment. Reabsorbate from IMCDs, ascending thin limbs, and prebend segments passes into AVR1 and is conveyed either upward toward DVR and AVR2 of the intercluster region, or is retained within the intracluster region and is conveyed toward higher levels of the intracluster region. Thus variable rates of fluid reabsorption by CDs potentially lead to variable blood flow rates in either compartment. Net flow between the two transverse compartments would be dependent on the degree of structural and functional coupling between intracluster vessels and intercluster vessels. In the outermost IM, AVR1 pass directly from the IM to the outer medulla, bypassing vascular bundles, the primary blood outflow route. Therefore, two defined vascular pathways exist for fluid outflow from the IM. Compartmental partitioning of V1 and V2 receptors may underlie vasopressin-regulated functional compartmentation of IM blood flow.

Development of a 1D Model for Assessing the Aortic Root Pressure Drop With Viscosity and Compliance

2013 ◽  
Author(s):  
Hossein Mohammadi ◽  
Raymond Cartier ◽  
Rosaire Mongrain
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Aortic Valve ◽  
Aortic Stenosis ◽  
Flow Rate ◽  
Aortic Root ◽  
Blood Flow Rate ◽  
Effective Orifice Area ◽  
Valvular Heart Diseases ◽  
1D Model

Aging and some pathologies such as arterial hypertension, diabetes, hyperglycemia, and hyperinsulimenia cause some geometrical and mechanical changes in the aortic valve microstructure. Cupsal thickening and lost of extensibility (increasing stiffness) are the consequences of these changes in the aortic valve which have a negative impact on the function of the valve [1]. The most frequent form of diseases of the aortic valve is the calcific aortic stenosis which is responsible for 80% of the North American deaths due to valvular heart diseases [2]. In this pathology, calcified nodules on the valve leaflets occur which lead to the thickening and stiffening of the leaflets and restricting the natural motion of the valve which presents an increased resistance to forward blood flow during the ejection phase of the cardiac cycle. To reduce the mortality and morbidity from the aortic stenosis, clinical management and proper diagnosis are essential [3]. Tranvalvular pressure gradient (TPG) and the effective orifice area (EOA), the minimum cross sectional area of the blood flow across the stenosis, are the most commonly used indices for assessing the aortic stenosis [4]. Numerous studies have been done to relate the TPG across the stenosis to the blood flow rate and EOA. Gorlin (1951) was the first to establish a relationship between TPG and EOA [5]. Several studies have reported deviations in valve area calculation by using Gorlin formula. This formula was derived based on some assumptions such as rigid circular orifice, non viscous and steady flow, while valvular orifices are compliant and the flow through them is viscous and pulsatile [6]. Several corrections have been proposed. However, even with these improved formula, significant deviations are still reported [7]. Calark (1978), Bermejo et al (2002) and Garcia et al (2006), by presenting a theoretical model, tried to express TPG in terms of the blood flow rate and EOA [8–10]. None of these studies considered the effect of the aortic root compliance on TPG. Nobari et al reported that the stiffening of the aorta changes the pressure drop and affects the leaflets motion [11]. Therefore, the objective of this study is to develop a 1D model for assessing the aortic pressure drop for the transient viscous blood flow across the aortic stenosis, by taking into account the vessel wall compliance. The derived TPG will be expressed in terms of the surrogate variables which are anatomical and hemodynamic data meaningful and accessible for physicians.

A study of non-redirection louvre fin-and-tube heat exchangers

1998 ◽  
Vol 212 (1) ◽  
pp. 1-14 ◽  
Author(s):  
C-C Wang ◽  
Y-P Chang ◽  
K-Y Chi ◽  
Y-J Chang
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Wind Tunnel ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Geometrical Parameters ◽  
Tube Size ◽  
Collar Diameter ◽  
Fanning Friction Factor

Extensive experiments on the heat transfer and pressure drop characteristics of louvre finand-tube heat exchangers were carried out. In the present study, 14 samples of non-redirection louvre fin-and-tube heat exchangers with different geometrical parameters, including the number of tube row, fin pitch and tube size, were tested in a wind tunnel. Results are presented as plots of the Fanning friction factor f and the Colburn j factor against Reynolds number based on the tube collar diameter in the range of 300–8000.

Steady laminar flow of blood through successive restrictions in circular conduits of small diameter

2008 ◽  
Vol 222 (8) ◽  
pp. 1557-1573 ◽  
Author(s):  
D Nag ◽  
A Datta
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Small Diameter ◽  
Rigid Wall ◽  
Pressure Loss Coefficient ◽  
Axial Velocity Distribution ◽  
Recirculation Zones ◽  
Flow Through ◽  
Steady Laminar

In this paper, numerical results on steady laminar flow of blood through an artery having two successive identical axisymmetric restrictions are presented, at varying degrees of restrictions. Physically, such a flow has features in common with steady blood flow through an artery with multiple stenoses. Additionally, results are presented for the blood flow through an artery in the presence of a single restriction, for comparison. The artery has been modelled as a tube with a rigid wall. The rheological characteristics of blood have been assumed both as Newtonian and non-Newtonian. Three different non-Newtonian models of blood — power law, Quemada, and Carreau—Yasuda models — have been considered in the analysis. The haemodynamic effects of the restrictions on the axial velocity distribution, recirculation zones formed downstream to the restrictions, the wall shear stress, and the pressure drop in the artery have been analysed. The irreversible pressure loss coefficient is calculated from the pressure drop and its variation with the degree of stenosis is obtained.

scholarly journals The Natural-Mineral-Based Novel Nanomaterial IFMC Increases Intravascular Nitric Oxide without Its Intake: Implications for COVID-19 and beyond

Nanomaterials ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1699
Author(s):  
Tomohiro Akiyama ◽  
Takamichi Hirata ◽  
Takahiro Fujimoto ◽  
Shinnosuke Hatakeyama ◽  
Ryuhei Yamazaki ◽  
...  
Keyword(s):  
Nitric Oxide ◽  
Blood Flow ◽  
Flow Rate ◽  
Vascular System ◽  
Vascular Complications ◽  
Blood Flow Rate ◽  
Vessel Diameter ◽  
Human Hand ◽  
Natural Mineral ◽  
Living Body

There are currently no promising therapy strategies for either the treatment or prevention of novel coronavirus disease 2019 (COVID-19), despite the urgent need. In addition to respiratory diseases, vascular complications are rapidly emerging as a key threat of COVID-19. Existing nitric oxide (NO) therapies have been shown to improve the vascular system; however, they have different limitations in terms of safety, usability and availability. In light of this, we hypothesise that a natural-mineral-based novel nanomaterial, which was developed based on NO therapy, might be a viable strategy for the treatment and prevention of COVID-19. The present study examined if it could induce an increase of intravascular NO, vasodilation and the consequent increase of blood flow rate and temperature in a living body. The intravascular NO concentration in the hepatic portal of rats was increased by 0.17 nM over 35.2 s on average after its application. An ultrasonic Doppler flow meter showed significant increases in the blood flow rate and vessel diameter, but no difference in the blood flow velocity. These were corroborated by measurements of human hand surface temperature. To our knowledge, this result is the first evidence where an increase of intravascular NO and vasodilation were induced by bringing a natural-mineral-based nanomaterial into contact with or close to a living body. The precise mechanisms remain a matter for further investigation; however, we may assume that endothelial NO synthase, haemoglobin and endothelium-derived hyperpolarising factor are deeply involved in the increase of intravascular NO.

scholarly journals Blood Flow Velocity in the Pial Arteries of Cats, with Particular Reference to the Vessel Diameter

1984 ◽  
Vol 4 (1) ◽  
pp. 110-114 ◽  
Author(s):  
Masahiro Kobari ◽  
Fumio Gotoh ◽  
Yasuo Fukuuchi ◽  
Kortaro Tanaka ◽  
Norihiro Suzuki ◽  
...  
Keyword(s):  
Blood Flow ◽  
Flow Velocity ◽  
Flow Rate ◽  
Blood Flow Velocity ◽  
Blood Flow Rate ◽  
Video Camera ◽  
Vessel Diameter ◽  
Pial Arteries ◽  
Cross Sectional ◽  
Pial Artery

The blood flow velocity and diameter of feline pial arteries, ranging in diameter from 20 to 200 μm, were measured simultaneously using a newly developed video camera method under steady-state conditions for all other parameters. There was a linear relationship between blood flow velocity and pial artery diameter ( y = 0.340 x + 0.309), the correlation coefficient being 0.785 (p < 0.001). The average values for blood flow velocity in pial arteries <50 μm, ≧50 but <100 μm, ≧100 but <150 μm, and ≧150 μm in diameter were 12.9 ± 1.3, 24.6 ± 3.4, 42.1 ± 4.7, and 59.9 ± 5.3 mm/s, respectively. Blood flow rate was calculated as a product of the cross-sectional area and the flow velocity. The blood flow rate increased exponentially as the pial artery diameter increased ( y = 2.71 × 10−4 x2.98). The average values for blood flow rate in pial arteries <50 μm, ≧50 but <100 μm, ≧100 but <150 μm, and ≧150 μm in diameter were 12.8 ± 1.5, 122.1 ± 24.8, 510.2 ± 74.8, and 1524.2 ± 174.4 10−3 mm3/s, respectively. Hemorheological parameters such as the wall shear rate and Reynolds' number were also calculated. The data obtained provide a useful basis for further investigations in the field of cerebral circulation.

Measurements of blood flow to individual glomeruli in the ophidian kidney

1990 ◽  
Vol 258 (6) ◽  
pp. R1313-R1319 ◽  
Author(s):  
S. D. Yokota ◽  
W. H. Dantzler
Keyword(s):  
Blood Flow ◽  
Plasma Osmolality ◽  
Blood Flow Rate ◽  
Vessel Diameter ◽  
Intermittent Flow ◽  
Thamnophis Sirtalis ◽  
Instantaneous Rate ◽  
Single Nephron ◽  
The Difference

Continuous measurements of the instantaneous rate of blood flow to individual glomeruli in a normal vertebrate kidney were made in the garter snake Thamnophis sirtalis. Epifluorescence video microscopy was used to visualize and record blood flow in the afferent arterioles of superficial nephrons. The dual-slit method was used for the determination of red blood cell (RBC) velocity from the video replay. Simultaneous measurements of the vessel diameter allowed the continuous determination of the instantaneous rate of blood flow. A total of 100 glomeruli was surveyed in 12 animals. These glomeruli displayed both constant and highly variable rates of blood flow, with 21% of all nephrons displaying intermittent glomerular perfusion. The mean single-nephron blood flow rate (SNBFR) for all individuals was 23.9 +/- 10.3 (SD) nl/min (n = 12). The percentage of nephrons with intermittent flow for an individual animal increased significantly with increasing plasma osmolality. Intermittency was associated with low SNBFR values; SNBFR averaged 13.5 +/- 10.2 (SD) nl/min (n = 21) in intermittent nephrons and 29.2 +/- 19.0 (SD) nl/min (n = 79) in continuous flow nephrons, the difference being significant (P less than 0.001). Nephrons with continuous perfusion displayed a much greater range of SNBFR values than intermittent nephrons. This suggests that, although changes in whole kidney glomerular filtration rate (GFR) in reptiles need not involve glomerular intermittency, intermittency may lower GFR.

Numerical simulation of pressure drop for three-dimensional rectangular microchannels

2018 ◽  
Vol 35 (6) ◽  
pp. 2234-2254 ◽  
Author(s):  
Zhipeng Duan ◽  
Peng Liang ◽  
Hao Ma ◽  
Niya Ma ◽  
Boshu He
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Three Dimensional ◽  
Numerical Data ◽  
Rectangular Microchannels ◽  
Content Type ◽  
Aspect Ratios ◽  
Rectangular Channels

Purpose The purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios. Design/methodology/approach Using a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product fappRe is referenced as a semi-theoretical fundamental analysis for numerical simulations. Findings The accurate and reliable results of fappRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of fappRe are significantly extended to other different aspect ratios and the novel values of fappRe are presented in the tables. The characteristics of fappRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed. Originality/value From the reliable data, it is shown that the values of fappRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

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