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

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

Bifurcation of flow and mass transport in a curved blood vessel

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis. The project supported by National Natural Science Foundation of China (10002003), JSPS Postdoctoral Fellowship for Foreign Researcher and Foundation for University Teachers, the Ministry of Education     

Rational structure of blood vessels

The issue of the optimal (from the viewpoint of strength) structure of blood vessels of a living organism is considered. It is shown that the angle of packing of muscular fibers in vessels is optimal in terms of strength of arteries. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 24–30, May–June, 2006.     

Non-isothermal flow of polymer melts in a curved tube

The results of a numerical study (using finite differences) of heat transfer in polymer melt flow is presented. The rheological behaviour of the melt is described by a temperature-dependent power-law model. The curved tube wall is assumed to be at constant temperature. Convective and viscous dissipation terms are included in the energy equation. Velocity, temperature and viscosity profiles, Nusselt numbers, bulk temperatures, etc. are presented for a variety of flow conditions. Br — Brinkman number - c specific heat, J/kg K - De — Dean number - E dimensionless apparent viscosity, eq. (14d) - G dimensionless shear rate, eq. (19) - k parameter of the power-law model, °C^–1, eq. (7) - mass flow rate, kg/s - m ₀ parameter of the power-law model, Pa · s ⁿ , eq. (7) - n parameter of the power-law model, eq. (7) - Nu 2r _p/ — Nusselt number, eqs. (28,31) - p pressure, Pa - Pe — Péclet number - P —(p/)/r _c — pressure gradient, Pa/m - dissipated energy, W, eq. (29) - total energy, W, eq. (30) - r radial coordinate, m - r _c radius of tube-curvature, m, fig. 1 - r _p radius of tube, m, fig. 1 - r _t variable, m, eq. (6) - R dimensionless radial coordinate, eq. (14a) - R _c dimensionlessr _c, eq. (14a) - R _t dimensionlessr _t, eq. (14a) - t temperature, °C - bulk temperature, °C, eq. (27) - t ₀ inlet temperature of the melt, °C - t _w tube wall temperature, °C - T dimensionless temperature, eq. (14c) - T _w dimensionless tube wall temperature - T dimensionless bulk temperature - u ₁ variable, s^–1, eq. (4) - u ₂ variable, s^–1, eq. (5) - U ₁ dimensionlessu ₁, eq. (18) - U ₂ dimensionlessu ₂, eq. (18) - v velocity in-direction, m/s - average velocity of the melt, m/s - V dimensionlessv, eq. (14b) - dimensionless , eq. (15) - z r _c — centre length of the tube, m - Z dimensionlessz, eq. (14e) - heat transfer coefficient, W/m² K - shear rate, s^–1, eq. (8) - — shear rate, s^–1 - apparent viscosity, Pa · s, eq. (7) - ₀ — apparent viscosity, Pa · s - angular coordinate, rad, fig. 1 - thermal conductivity, W/m K - melt density, kg/m³ - axial coordinate, rad, fig. 1 - rate of strain tensor, s^–1, eq. (8) - (—p) pressure drop, Pa     

Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic(EMHD)flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflo...     

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

Combined free and forced convection for developed flow in curved pipes with finite curvature ratio

Combined free and forced convection for developed flow in a curved pipe with arbitrary curvature ratio is studied numerically. The curved pipe is heated with axially uniform heat flux, while the wall temperature is maintained peripherally uniform. The buoyancy force is accounted by the Boussinesq approximation. The effects of the Dean, Prandtl, and Rayleigh numbers and especially of a wide range of curvature ratios on the flow resistance and the average heat transfer rate are presented. The significant distortion of the dividing streamline and the appearance of the secondary flow with one dominant cell for pipe flow with higher buoyancy force and curvature ratio are also discussed.     

Dynamics of the blood flow in the curved artery with the rolling massage

Arterial wall shear stress and flow velocity are important factors in the development of some arterial diseases. Here, we aim to investigate the dynamic effect of the rolling massage on the property of the blood flow in the curved artery. The distributions of flow velocity and shear stress for the blood flow are computed by the lattice Boltzmann method, and the dynamic factors under different rolling techniques are studied numerically. The study is helpful to understand the mechanism of the massage and develop the massage techniques.     

Electrokinetic flow and energy conversion in a curved microtube

Curved channels are ubiquitous in microfluidic systems. The pressuredriven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number. The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer (EDL) potential. The EDL potential at the outer side of the bend is larger than that at the inner side of the bend. The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow. Since the spanwise pressure gradient is dominant over the inertial force, the resulting axial velocity profile is skewed into the inner region of the curved channel. Furthermore, the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section. The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows. Remarkably, the curved geometry could be beneficial to improving the electrokinetic energy conversion (EKEC) efficiency.     

INTEGRAL INVARIANT IN NONCONSERVATIVE SYSTEMS AND ITS APPLICATION IN MODERN PHYSICS

In this paper,the Poincaré and Poincaré-Cartan integral invariants in nonconservativesystems are established.According to the integral invariant,he non-linear oscillation ofparticles in 3-folded symmetry spiral sector cyclotron is investigated.It turns out that themethod is successful.     

Theoretical study on the bifurcation of vortexes structure for flow in curved tube

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｕｒｖｅｄｔｕｂｅｉｓｎｏｔｏｎｌｙｃｏｍｍｏｎｉｎｉｎｄｕｓｔｒｙ ,ｂｕｔａｌｓｏａｔｔｒａｃｔｓｓｐｅｃｉａｌａｔｔｅｎｔｉｏｎｏｆｒｅｓｅａｒｃｈｅｒｓｉｎｂｉｏｍｅｃｈａｎｉｃｓｂｅｃａｕｓｅａｏｒｔｉｃａｒｃｈｉｓｔｈｅｐｌａｃｅｗｈｅｒｅａｔｈｅｒｏｓｃｌｅｒｏｓｉｓｈａｐｐｅｎｓｍｏｓｔｆｒｅｑｕｅｎｔｌｙ[1～ 3].Ｓｉｎｃｅｔｈｅｐｈｙｓｉｏｌｏｇｉｃａｌｆｅａｔｕｒｅｏｆｒｅａｌｂｌｏｏｄｖｅｓｓｅｌｉｓｖｅｒｙｃｏｍｐｌｉｃａｔｅｄ ,ｔｈｅｆｌｏ…     

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.     

Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.     

Computational technique for flow in blood vessels with porous effects

IntroductionThehemodynamicsofflowsthroughbloodvesselsisofgreatinterest,becausethesevesselspresentasubstantialhealthriskandareamajorcauseofmortalityandmorbidityintheindustrializedworld .Researchpapersonthebloodflowhaveappearedbutmostofthemhaveneglectedtheporosityeffectsduetovesselwalls.Inthisstudyweareinterestedintheflowthroughabloodvesseltakingintoaccounttheporosityeffectsofthevessels.Fluidflowthroughaporousmediumisoffundamentalimportancetowiderangeofdisciplinesinthevariousbranchesofnaturalsci…     

弯曲动脉的血流动力学数值分析

利用计算流体力学的理论和方法对弯曲动脉中的血流动力学进行数值分析，是研究心血管疾病流体动力学机理的一种行之有效的方法。本文将升主动脉、主动脉弓和降主动脉联系起来作为弯曲动脉几何模型，给出了血液流动的边界条件以及计算条件。根据生理脉动流条件，对狗的弯曲动脉几何模型内发展中的血液流动进行了有限元数值模拟，并利用可视化方法对血液流动的轴向速度、二次流、壁面切应力等计算结果进行了分析。研究结果表明，在弯管内侧壁处，同时存在主流方向和二次流方向的回流，此处容易形成涡流。弯管内侧壁比外侧壁的壁面切应力具有更强的脉动性。     

Experimental determination of the flow transport coefficients in the coupled equations of two-phase flow in porous media

The transport coefficients in the coupled equations of two-phase flow are defined if the pressure gradient in one of the two flowing fluids is equal to zero. This definition has been used in experiments with oil and water in a sandpack and the four transport coefficients have been measured over wide water saturation ranges. The values of the cross coefficients were found to be significant as they ranged from 10 to 35% of the value of the effective permeability to water and from 5 to 15% of the effective permeability to oil, respectively.     

Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe

This paper presents a model for the evolution of a transversal concentration profile of a macromolecular solution (PEO) injected into a cylindrical pipe at turbulent flow conditions (R 40000). This model, based on the diffusion of a scalar quantity emitted by two diametrically opposed point sinks, proves to be in good agreement with the experimental data. C concentration - C _w wall concentration - C _i initial concentration before injection - x downstream distance from the slot - y normal distance from the wall - characteristic height of diffusion, i.e. the value ofg at whichC/C _w = 0.5 - n characteristic exponent - R radius of pipe - D diameter of pipe - a, b constants - L _m mixing length, i.e. the value ofx at whichC _w /C _i =Q _i /Q _T - Q _i flow rate of injection - Q _T flow rate - f, g annex functions - n ₀ maximal value ofn     

Boundary layer development of pulsatile blood flow in a tapered vessel

Assuming that the tapered angle is small,the problems of developing flow under unsteady oscillatory condition are studied in this paper.The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length,and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.     

Numerical modelling of shear-dependent mass transfer in large arteries

A numerical scheme for the simulation of blood flow and transport processes in large arteries is presented. Blood flow is described by the unsteady 3D incompressible Navier–Stokes equations for Newtonian fluids; solute transport is modelled by the advection–diffusion equation. The resistance of the arterial wall to transmural transport is described by a shear-dependent wall permeability model. The finite element formulation of the Navier–Stokes equations is based on an operator-splitting method and implicit time discretization. The streamline upwind/Petrov–Galerkin (SUPG) method is applied for stabilization of the advective terms in the transport equation and in the flow equations. A numerical simulation is carried out for pulsatile mass transport in a 3D arterial bend to demonstrate the influence of arterial flow patterns on wall permeability characteristics and transmural mass transfer. The main result is a substantial wall flux reduction at the inner side of the curved region. © 1997 John Wiley & Sons, Ltd.