The influence of low-frequency varying magnetic field on the pulsatile flow in a rigid round tube

ProjcctsupportedbytheNatiol1alNaturalScienceFoundatio11ofChinaThemagnatictherapy,asaneffccti\'emedicaltreatment,hasabroadapp1icatiQn.lnrecentyears,plentyofanimalandclinicalresearcheshavebeendoneandprovedthatmagneticfieldhassuchpositivecurativeefttctsasant…     

Effect of Varying Viscosity on Two-Layer Model of Pulsatile Flow through Blood Vessels with Porous Region near Walls

Transport in Porous Media - The present work concerns the effect of hematocrit-dependent viscosity on pulsatile flow of blood through narrow tube with porous walls. Two-fluid model of blood is...     

Dynamic scaling of unsteady shear-thinning non-Newtonian fluid flows in a large-scale model of a distal anastomosis

Dimensional analysis has been applied to an unsteady pulsatile flow of a shear-thinning power-law non-Newtonian liquid. An experiment was then designed in which both Newtonian and non-Newtonian liquids were used to model blood flow through a large-scale (38.5 mm dia.), simplified, rigid arterial junction (a distal anastomosis of a femorodistal bypass). The flow field within the junction was obtained by Particle Imaging Velocimetry and near-wall velocities were used to calculate the wall shear stresses. Dimensionless wall shear stresses were obtained at different points in the cardiac cycle for two different but dynamically similar non-Newtonian fluids; the good agreement between the measured dimensionless wall shear stresses confirm the validity of the dimensional analysis. However, blood exhibits a constant viscosity at high-shear rates and to obtain complete dynamic similarity between large-scale experiments and life-scale flows, the high-shear viscosity also needs to be included in the analysis. How this might be done is discussed in the paper.     

Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel

A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.     

Exact and numerical simulation of peristaltic flow of a non‐Newtonian fluid with inclined magnetic field in an endoscope

In the present article, we have studied the effects of inclined magnetic field on the peristaltic flow of Jeffrey fluid through the gap between two coaxial inclined tubes. The inner tube is rigid, whereas the outer tube has sinusoidal wave traveling down its wall. The governing equations are simplified using long wave length and low Reynolds number approximations. Exact and numerical solutions have been derived for velocity profile. The expressions for pressure rise and friction force are calculated using numerical integration. Graphical results and trapping phenomenon is presented at the end of the article to see the physical behavior of different parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

血液入口段两相流动的层流NS方程数值模拟

本文采用球形刚性颗粒悬浮于牛顿流体的血液模型，基于有相间滑移的两相流动层流Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，采用相间滑移算法（Ｉｎｔｅｒ－ＰｈａｓｅＳｌｉｐＡｌｇｏｒｉｔｈｍ）对圆管内定常轴对称血液入口两相流动问题进行了计算，获得了与实验结果吻合的计算结果，较好地模拟血液流动中红细胞的径向迁移现象，结果表明，采用二相流动模型研究血液流动是一种有前途的方法。     

Simulations of magnetic capturing of drug carriers in the brain vascular system

The present paper reports on numerical simulations of blood flow and magnetic drug carrier distributions in a complex brain vascular system. The blood is represented as a non-Newtonian fluid by the generalised power law. The Lagrangian tracking of the double-layer spherical particles is performed to estimate particle deposition under influence of imposed magnetic field gradients across arterial walls. Two situations are considered: neutral (magnetic field off) and active control (magnetic field on) case. The double-layer spherical particles that mimic a real medical drug are characterised by two characteristic diameters - the outer one and the inner one of the magnetic core. A numerical mesh of the brain vascular system consisting of multi-branching arteries is generated from raw MRI scan images of a patient. The blood is supplied through four main inlet arteries and the entire vascular system includes more than 30 outlets, which are modelled by Murray’s law. The no-slip boundary condition is applied for velocity components along the smooth and rigid arterial walls. Numerical simulations revealed detailed insights into blood flow patterns, wall-shear-stress and local particle deposition efficiency along arterial walls. It is demonstrated that magnetically targeted drug delivery significantly increased the particle capturing efficiency in the pre-defined regions. This feature can be potentially useful for localised, non-invasive treatment of brain tumours.     

Numerical calculation of two-dimensional flow in the channel with a partially compliant wall

The present paper is concerned with the flow in a two-dimensional channel whose wall is partially compliant. The flow field is calculated by the finite-difference method. Results are as follows: (1) When the upstream condition is given by steady flow (Reynolds number Re = 50), a compliant part of the wall oscillates with a frequency nearly equal to the characteristic frequency of the elastic wall. Absolute values of the pressure drop across the compliant part become small compared with those of the plane Poiseuille flow with wholly rigid walls. This ensures under physiological conditions that the blood can be transported more easily toward distal parts due to the compliance of vessel walls. (2) When the upstream condition is given by a pulsatile flow (Womersley number α = 8), interaction arises between characteristic frequency of the wall and basic frequency of the main stream near the compliant wall. As the basic frequency of pulsatile flow decreases, absolute values of mean pressure, which drop across the compliant wall, also become small compared with those of pulsatile flow between wholly rigid walls.     

动脉狭窄对血液流速的影响

为了定量计算动脉局部狭窄对动脉管中血液流动速度的影响，本文分别对狭窄区域内定常流和非定常流动进行了求解，得出了狭窄区域内定常流和脉动流的速度表达式。本文将均匀段的流速形经Ｆｏｕｒｉｅｒ分解成定常和脉动两部分，然后分别计算出狭窄区域内对应的定常和脉动流速，经Ｆｏｕｒｉｅｒ合成还原成流速时域波形，同时针对各种情况将不同狭窄对不同的流速波形的作了分析比较。     

用流体双折射方法研究人工心脏瓣膜的脉动流场

本文选用1.5%的MillingYellow溶液,在对二维心瓣低频脉动流场的分析中,仍采用稳态流场的线性光-力学关系。通过摄象机记录下了一个脉动周期内脉动流量Q从36升/小时至55升/小时流场的变化情况,直观地看到主动脉瓣流场中最大切变率的瞬态分布。记录了同一模型在相同条件下稳态流场流量Q为50升/小时的流场,对两种流场下几个典型截面处的最大切变率的数值做了比较。通过对图线的分析,表明在稳态流量与脉动流量相同的情况下,脉动流场的最大切变率数值高于稳态流场,这就说明脉动使流场的剪切作用增强。     

The steady/pulsatile flow and macromolecular transport in T-bifurcation blood vessels

IntroductionThefluiddynamicsofbloodcyclesystemplayanimportantroleinthepathogenesisofatherosclerosis.ThephysiologicalanatomyfoundthattheatherosclerosisappearsoftenatthebifurcationorcurvedflowareatoallkindsofRefs.[1 ,2 ] .Theshearstressvariesgreatlyinthoseareaandinfluencesthemacromoleculartransportacrossthebloodwall[3,4].Thus ,theinvestigationoftheflowandmacromoleculartransportinthesecomplexbloodvesselaandthecorrelationbetweenthemareinterestingtoresearchers.Intheseaspect,Liepschstudiedtheflowi…     

局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。     

Thin film flow of non‐Newtonian MHD fluid on a vertically moving belt

Thin film flow of an Oldroyd 6‐constant fluid on a vertical moving belt is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one‐dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equations are solved analytically and the exact solution is obtained in an elegant way. Numerical solutions are also obtained using higher‐order Chebyshev spectral methods. The influence of various non‐Newtonian parameters, gravitational force and applied magnetic field is investigated. The results showing the effect of gravity, magnetic field and material constants α₁ and α₂ are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical and analytical solutions of an Oldroyd 8‐constant MHD fluid with nonlinear slip conditions

The flow of an Oldroyd 8‐constant non‐Newtonian MHD fluid is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one‐dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equation along with nonlinear boundary conditions is solved analytically and the solution is obtained in an elegant way. Numerical solutions are also obtained using higher order Chebyshev spectral methods. The influence of various non‐Newtonian parameters and applied magnetic field is investigated. Results showing the effect of various physical parameters of the flow are presented and investigated. Copyright © 2010 John Wiley & Sons, Ltd.     

An experimental investigation of pulsatile flow through a smooth constriction

Measurements of flow disturbances in the downstream region of modeled stenoses in a rigid tube, with upstream pulsatile flow are reported. Experiments were conducted over physiologically relevant mean Reynolds numbers of 600; based on the tube diameter and the time-averaged value of upstream centerline velocity. Contoured constrictions with 25%, 50% and 75% area reductions were investigated and velocity data were obtained from ensemble averaging techniques (phase-locked waveform). Experimental data over extensive spatial regions of poststenotic fields were taken, employing a two-component laser Doppler velocimeter LDV. Constant time sampling techniques for performing data or frequency analyses were used to avoid velocity bias and to study the evolution of poststenotic flow disturbances. It is found that different types of flow disturbances exist downstream of the constriction. Data analysis methods with the aid of flow visualization allow accurate classification of the disturbances which are sensitive indicators of mild to moderate constrictions. Although the present study was motivated by a biological situation, sufficient data were reported in detail that they may also be used by investigators working in computational fluid dynamics.     

动脉瘤内流场以及瘤体尺寸的影响的数值研究

采用计算流体动力学(CFD)数值模拟的方法,在周期性脉动速度入流条件下,建立刚性动脉瘤模型并研究了动脉瘤模型中流场的特征(速度、压力、壁面剪切应力)。得到了脉动入流一个周期内流场特征的变化规律,发现动脉瘤的后端有相当高的压力和壁面剪切应力,而且高压力和壁面剪切应力分布的位置几乎是固定的。探讨了不同动脉瘤尺寸对内部流场的影响,动脉瘤的直径与瘤体长度之比越大,瘤壁承受的剪切应力就越大,动脉瘤破裂的危险性就越高。     

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied. Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid. An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress. Finite difference method is employed to solve the momentum equation for the core region. The numerical solutions for velocity, flow rate and flow resistance are computed. The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated. It is observed that the velocity increases with the increase of plasma layer thickness. An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t. An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number. The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature.     

Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring‐type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flows through a rigid pipe in the vicinity of a sharp‐edged mechanical ring‐type constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10⁴, Womersley number (Nw) of the order of 50 with a corresponding Strouhal number (St) of the order of 0.04. The pulsatile flow considered is a sinusoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transitional laminar and turbulent flow characteristics in an alternative manner within the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streamlines, vorticity, shear stress and isobars. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when compared with those during deceleration period. Various parametric equations within a pulsatile cycle have also been formulated through numerical experimentations with different pulsatile amplitudes. In the vicinity of constrictions, the empirical relationships were obtained for the instantaneous flow rate (Q), the pressure gradient (dp/dz), the pressure loss (P_loss), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max). Elliptic relation was observed between flow rate and pressure gradient. Quadratic relations were observed between flow rate and the pressure loss, the maximum values of shear stress, wall shear stress, turbulent kinematic energy and the turbulent viscosity. Linear relationships exist between the instantaneous flow rate and the maximum values of vorticity, wall vorticity and velocity. The time‐average axial pressure gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright © 1999 John Wiley & Sons, Ltd.     

Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. For an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop taking into account of the rotational non-axisymmetric stationary conducting flow.Making use of the analytic solution, exact formulas for the angular velocity components as well as for the wall shear stresses are extracted. It is proved analytically that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. According to Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though decreases for small magnetic fields because of the dominance of Joule heating, it eventually increases for growing magnetic field parameters.     

An analysis model of pulsatile blood flow in arteries

IntroductionTheperiodicallypulsatilebloodflowinthearterycausesthecircumferentialandaxialmotionoftheelasticbloodvesselandinturntheoscillationofthevesselaffectsthatofthebloodflow .Womersley[1]resolvedsuccessfullythisfluid_solidcouplingproblembysolvingbothlinearNavier_Stokesequationsandthemotionequationsofthethin_walledelastictubeandgainedtheexpressionsofthebloodflowvelocitiesandthevasculardisplacements.Histheoryhasbeenthebasisforthequantitativeanalysisoftherelationshipofthearterialstructureandi…