BLOOD FLOW AND MACROMOLECULAR TRANSPORT IN CURVED BLOOD VESSELS

A numerical analysis of the steady/pulsatile flow and macromolecular (such as LDL and Albumin) transport in curved blood vessels was carried out. The computational results predict that the vortex of the secondary flow is time-dependent in the aortic arch. The concentration of macromolecule concentrates at the region of sharp curve, and the wall concentration at the outer part is higher than that at the inner part. Atherosclerosis and thrombosis are prone to develop in such regions with sharp flow.     

Performance modeling and analysis of blood flow in elastic arteries

Nomenclature　　τ　　wallshearstressγshearrateτy yieldstressηc Cassonviscosityktheconsistencyindexnnon_Newtonianindexτp shearstressofthepthelementωangularvelocityRvessel’sradiusCwavespeedM　　magneticparameter (Hartmannnumber)u,w　velocitycomponentinther_andz_directions,respectivelyP　　pressureα　　unsteadinessparameter k , R meanparametersTp relaxationtimeofthepthelementρ densityIntroductionTheimportancetoatherogenesisofarterialflowphenomenasuchasflowseparation ,recirculationands…     

Computational intellectual analytical theory of computational analytical approach to rotating flow of non-Newtonian fluid

Ａｎｅｗｆｉｅｌｄｏｆｍｏｄｅｒｎｃｏｍｐｕｔｅｒｓｃｉｅｎｃｅ—ａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅｉｓｄｅｖｅｌｏｐｅｄｒａｐｉｄｌｙ．Ｔｈｅｓｙｍｂｏｌｉｃｍａｎｉｐｕｌａｔｉｏｎｉｓｔｈｅｆｒｏｎｔｄｉｒｅｃｔｉｏｎｉｎｔｈｅａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅ．Ａｓｅｒｉｅｓｏｆｔｈｅｃｏｍｐｕｔｅｒｓｏｆｔｗａｒｅｉｓｄｅｖｅｌｏｐｅｄｆｏｒｔｈｅｃｏｍｐｕｔａｔｉｏｎａｌｍａｎｉｐｕｌａｔｉｏｎ,ｓｕｃｈａｓＭａｃｓｙｍａ,Ｍａｐｌｅ,Ｍａｔｈｅｍａｔｉｃａ,ｔｏｃ…     

Mass transfer enhancement in a sinusoidal wavy channel for pulsatile flow

We report experimental work on mass transfer enhancement through pulsatile flow in an asymmetric channel under the laminar flow condition. Mass transfer experiments were carried out by the electrochemical method. The vortices dynamics were visualized both experimentally and numerically. The present results were compared with previous ones in the case of a symmetric channel with the same sinusoidal wavy walls. The mass transport enhancement factor for the asymmetric channel is found to be larger than that for the symmetric channel, for a wide range of flow parameters. This is a consequence of the specific fluid mixing induced by vortices dynamics. It is also confirmed that the Sherwood number for pulsatile flow can be expressed in terms of the Sherwood numbers for steady and oscillatory flows at large amplitude of fluid oscillation, for both channels.     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

1　ＴｈｅＦｌｏｗＭｏｄｅｌｏｆＰｏｗｅｒ＿ＬａｗＦｌｕｉｄｉｎＲａｄｉｃａｌＦｒａｃｔａｌＲｅｓｅｒｖｏｉｒＴｈｅｔｒａｎｓｉｅｎｔｆｌｏｗｏｆｐｏｗｅｒ＿ｌａｗｆｌｕｉｄｉｎｒａｄｉｃａｌｆｒａｃｔａｌｒｅｓｅｒｖｏｉｒｉｓｓｔｕｄｉｅｄｉｎＲｅｆ.[1 ] ,ａｎｄａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｏｆＬａｐｌａｃｅｓｐａｃｅｉｓｄｅｒｉｖｅｄ .ＩｎＲｅｆ.[2 ] ,ｔｈｅｔｒａｎｓｉｅｎｔｅｌｌｉｐｔｉｃａｌｆｌｏｗｉｓｒｅｓｅａｒｃｈｅｄｏｎｍｏｄｅｌｏｆｅｘｐａｎｄｉｎｇｒｅｃｔａｎｇｌｅ .Ｔ…     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Multiphase non‐Newtonian effects on pulsatile hemodynamics in a coronary artery

Hemodynamic stresses are involved in the development and progression of vascular diseases. This study investigates the influence of mechanical factors on the hemodynamics of the curved coronary artery in an attempt to identify critical factors of non‐Newtonian models. Multiphase non‐Newtonian fluid simulations of pulsatile flow were performed and compared with the standard Newtonian fluid models. Different inlet hematocrit levels were used with the simulations to analyze the relationship that hematocrit levels have with red blood cell (RBC) viscosity, shear stress, velocity, and secondary flow. Our results demonstrated that high hematocrit levels induce secondary flow on the inside curvature of the vessel. In addition, RBC viscosity and wall shear stress (WSS) vary as a function of hematocrit level. Low WSS was found to be associated with areas of high hematocrit. These results describe how RBCs interact with the curvature of artery walls. It is concluded that although all models have a good approximation in blood behavior, the multiphase non‐Newtonian viscosity model is optimal to demonstrate effects of changes in hematocrit. They provide a better stimulation of realistic blood flow analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical simulation of the non-Newtonian blood flow through a mechanical aortic valve

This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonian fluid owing to the action of the cells’ membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonian fluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonian fluid model than for the Newtonian one.     

Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid

Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.     

Decay of shear layers and vortex sheets

An incompressible fluid is contained in the domain between two stationary infinited parallel rigid plates. It is assumed that for shear flows, the shear stress in an element of the fluid depends linearly on history of the velocity gradient in that element. It is supposed that initially two steady shear layers exist in the fluid and are symmetrically disposed with respect to the mid-plane. The time-dependent velocity field which results from the removal of the forces maintaining this steady flow is calculated in the cases when the fluid is Newtonian and when it is Maxwellian. The limiting cases when the shear layers reside in an unbounded space of the fluid and when they further become vortex sheets are discussed.     

Drop shape under slow steady shear flow and during relaxation. Experimental results and comparison with theory

The three-dimensional small deformation of a single Newtonian drop immersed in an immiscible Newtonian liquid was investigated, both in slow steady shear and during retraction after cessation of shear. The experiments were performed in a parallel plate apparatus equipped with video- enhanced microscopy. The drop was observed from two perpendicular directions, and accurate measurements were obtained in each view by image analysis. The results were compared to existing theoretical predictions from the exact fluid dynamic problem, obtained perturbatively for the case of small deformations of the drop. Excellent agreement between data and theory was found, thus providing the first assessment of drop shape predictions in steady flow and relaxation for Newtonian fluids. Received: 6 February 2000 Accepted: 24 May 2000     

Super-stable parallel flows of multiple visco-plastic fluids

We consider the stability of a multi-layer plane Poiseuille flow of two Bingham fluids. It is shown that this two-fluid flow is frequently more stable than the equivalent flow of either fluid alone. This phenomenon of super-stability results only when the yield stress of the fluid next to the channel wall is larger than that of the fluid in the centre of the channel, which need not have a yield stress. Our result is in direct contrast to the stability of analogous flows of purely viscous generalised Newtonian fluids, for which short wavelength interfacial instabilities can be found at relatively low Reynolds numbers. The results imply the existence of parameter regimes where visco-plastic lubrication is possible, permitting transport of an inelastic generalised Newtonian fluid in the centre of a channel, lubricated at the walls by a visco-plastic fluid, travelling in a stable laminar flow at higher flow rates than would be possible for the single fluid alone.     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.     

Steady and unsteady laminar flows of Newtonian and generalized Newtonian fluids in a planar T‐junction

An investigation of laminar steady and unsteady flows in a two‐dimensional T‐junction was carried out for Newtonian and a non‐Newtonian fluid analogue to blood. The flow conditions considered are of relevance to hemodynamical applications and the localization of coronary diseases, and the main objective was to quantify the accuracy of the predictions and to provide benchmark data that are missing for this prototypical geometry. Under steady flow, calculations were performed for a wide range of Reynolds numbers and extraction flow rate ratios, and accurate data for the recirculation sizes were obtained and are tabulated. The two recirculation zones increased with Reynolds number, but the behaviour was non‐monotonic with the flow rate ratio. For the pulsating flows a periodic instability was found, which manifests itself by the breakdown of the main vortex into two pieces and the subsequent advection of one of them, while the secondary vortex in the main duct was absent for a sixth of the oscillating period. Shear stress maxima were found on the walls opposite the recirculations, where the main fluid streams impinge onto the walls. For the blood analogue fluid, the recirculations were found to be 10% longer but also short lived than the corresponding Newtonian eddies, and the wall shear stresses are also significantly different especially in the branch duct. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability of high‐speed two‐layer film casting of Newtonian fluids

The steady‐state flow and its linear stability are investigated for the isothermal two‐layer film casting process. Newtonian fluids are considered in this study. The continuity of traction is ensured at the interface, and the axial velocity is assumed to be uniform across each film layer separately. The effects of inertia, gravity, fluid parameters and processing conditions on the steady‐state flow and its stability are studied. The results indicate that the fluid properties and the processing conditions have significant influence on the flow. The flow stability is strongly dependent on the layer layout with respect to the take‐up rolling process. The frequency of the (unstable) disturbance is insensitive to flow and processing parameters. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Pressure-induced compressible Newtonian flow in a slit

The steady two-dimensional pressure-induced compressible flow of a Newtonian fluid between two fixed parallel planes is considered. Assuming that the width of the slit is much smaller than its length we advance a perturbation theory and obtain simple analytical results with the well-known incompressible formulae as a limiting case.     

Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation

We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference (\(\Delta P\)) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (\(P_t\)), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (\(\Delta P-P_t\)). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.     

平行平板流动腔脉动流切应力的计算

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一。大多数研究者主要对定常层流情进行研究。本文通过对矩形平行平板流动腔内的层流脉动流进行详细分析,给出腔内速和腔室底部切应力的准确计算公式。当Ｗｏｍｅｒｓｌｅｙ数较小时,准确公式简化为准定常公式。数值计算结果表明,在脉动流条件下,对于人们常用的流动腔几何尺寸,准定常公式具有相当高的精度。这为在脉