The role of shear and elongation in the flow of solutions of semi-flexible polymers through porous media

The rheological behavior of hydrophobically modified hydroxyethyl cellulose (HMHEC) and xanthan gum solutions has been characterized in simple shear flow, opposed-jets flow, and flow through porous media. Both polymers exhibit shear thinning in simple shear flow and apparent shear thinning in flow through porous media. Analysis of the results shows there is a direct correspondence between shear viscosities determined in simple shear experiments and apparent viscosities in porous media flow at relatively low shear rates. At high shear rates the extensional component of the flow in porous media appreciably increases the apparent viscosity over the simple shear values. This increase is shown to correlate with results obtained in opposed-jets experiments, and is attributed to formation of transient entanglements.     

颗粒材料剪切流动状态转变的环剪试验研究

颗粒材料的剪切流动行为广泛地存在于滑坡、泥石流等自然灾害以及矿物原料传输、泵送等工业过程中.颗粒材料在不同体积分数、剪切速率和应力约束下会表现出不同的流动状态并发生相互转化.对颗粒材料在剪切流动过程中力学特性的研究有助于加深理解其发生不同流动状态的内在机理,为解决相应的颗粒材料问题提供理论依据.为此,本文研制了颗粒材料剪切流动的中型环剪仪,并对颗粒材料在不同法向约束应力和剪切速率下的剪切应力和体积膨胀率进行了测试.结果表明,剪切应力和体积膨胀率均随剪切速率的增大而增大,但增长速率在临界剪切速率处发生转变,使其随剪切速率的平方呈分段式线性增长.通过对颗粒材料在不同剪切速率和惯性数下有效摩擦系数变化趋势的分析,讨论了颗粒材料由慢速流向快速流转化的基本规律,以及在临界剪切速率处发生流动状态转化的内在条件.此外,通过对不同法向应力下临界剪切速率以及快速流动下运动规律的测试,发现临界剪切速率随法向应力的增加而减小,即法向应力可促进颗粒材料由慢速流向快速流的转化,但在快速流动状态下的有效摩擦系数对法向应力不敏感.以上对颗粒材料在不同剪切速率、法向应力下流动状态的环剪试验研究有助于揭示其发生不同流动状态转化的内在机理.      

刚性圆管中血液周期振荡流的切应力分布

本文通过求解圆管内血液振荡流的基本方程，求得圆管内血液流的压力梯度与切应力之间的关系式。在此基础上，详细讲座了圆管中轴向流速和切变率谐波的变化规律，指出流速谐波和切变率谐波的幅值都将随着谐波次数的增大而逐渐减小。为了使所得结果便于应用。文章通过管轴向中心线流速与压力梯度之间的关系式，进一步给出一种利用管轴向中心线流速计算管内切应力分布的简便方法。该方法用于检测活体血管内血液振荡流的切应力分布，具有操作简单，精度较高的优点。最后，以人体颈动脉为例，讨论血液周期振荡流的切应力的分布特性。发现在任意时刻，除了邻近管壁处切应力急剧增大到一定数值之外，沿管截面切应力分布相当均匀且接近于零，呈现出与定常流不同的切应力分布特征。     

Shear localisation in stirred yoghurt

The shear flow behaviour of stirred yoghurt in the cone-and-plate and cylindrical Couette geometries was studied using diffusing wave spectroscopy (DWS) and nuclear magnetic resonance (NMR) velocimetry. Differences between the transmission and backscattering DWS correlations suggest the formation of a high shear rate band near the surface of a moving cone of a cone-and-plate geometry at low shear rates. At higher shear rates, homogeneous shear flow is indicated. NMR velocimetry unambiguously demonstrated that a high shear rate band forms at the moving inner wall of a cylindrical Couette geometry at low shear rates. At intermediate shear rate, a high shear rate band is formed at the stationary outer wall and plug-like flow is observed mid-gap. At higher shear rates, homogeneous shear flow is observed. Slip is seen at both walls. The three flow regimes appear to correlate loosely with transitions in the pseudo-steady-state flow curve and may reflect a break-up of the protein aggregates observed with confocal microscopy.     

Large eddy simulation of bluff body wake in planar shear flow

Large eddy simulation of planar shear flow past a square cylinder has been investigated. Dynamic Smagorinsky model has been used to model subgrid scale stress. The shear parameter, K, namely the nondimensional streamwise velocity gradient in the lateral direction, is 0.0, 0.1 and 0.2. Reynolds number based on the centerline velocity is fixed at Re=21400. The time and span‐averaged velocity components, pressure coefficient, Reynolds stresses for uniform are in good agreement with the literature. In shear flow the calculated flow structure and mean velocity components are shown to be markedly different from those of the uniform flow. With increasing shear parameter, the cylinder wake is dominated by clockwise vortices. Both the velocity components in shear flow are compared with respective components in uniform flow. Comparison of normal and shear stresses between shear and no shear case have also been presented. Copyright © 2009 John Wiley & Sons, Ltd.     

具有切应力梯度的平行平板流动腔的构造

在近年来关于流体切应力与细胞力学行为之间关系的研究中,流体切应力梯度被认为是诱发动脉粥样硬化和内膜增生的重要因素之一.本文探讨如何利用常用的离体细胞力学实验工具--平行平板流动腔模拟具有梯度的定常流切应力环境.结果表明,根据Hele-Shaw流的原理和常用复势W(Z)=AZn(n＞1)的特性,可构造出具有各种切应力梯度分布的流动腔.与其它模拟切应力梯度的方法比较,本文的方法更加简洁、可行.     

Exponential shear flow of branched polyethylenes in rotational parallel-plate geometry

Exponential shear flow, as a strong flow with the potential to generate a high degree of molecular stretching, has attracted considerable interest in recent years. So far, exponential shear flow has been realized by either sliding-plate or cone-and-plate (CP) geometry. Both geometries guarantee homogeneous shear flow. Here, we present experimental data on exponential shear flow of several long-chain branched polyethylene melts with different degrees of strain hardening obtained by using parallel-plate (PP) geometry in a rotational rheometer. This type of geometry, which is standard in linear-viscoelastic characterization of polymer materials, produces inhomogeneous shear flow. A comparison of exponential shear flow data obtained by PP and CP geometry is made. Additionally, the experimental data are compared to predictions of the rubber-like liquid (RLL) and the molecular stress function (MSF) theories. For this purpose, the relaxation spectra of the polymer melts considered were obtained by standard linear-viscoelastic characterization. In addition, two irrotational parameters and one rotational parameter are required by the MSF theory. While the irrotational parameters were obtained from fitting to elongational viscosity data, the value of the rotational parameter was used as given in the literature. It can be concluded that viable experimental data in exponential shear flow can be obtained by PP geometry. For finite linear-viscoelasticity (RLL theory), predictions of reduced shear stress for CP and PP geometry coincide, but nonlinear material behavior (as modeled by the MSF theory) leads to small differences between both geometries. Furthermore, it is shown that the MSF predictions are in excellent agreement with the experimental data in exponential shear flow and that this type of flow leads to much less chain stretching than elongational flow.Dedicated to the memory of Prof. Arthur S. Lodge (1922–2005).     

Solutions of xanthan gum/guar gum mixtures: shear rheology,porous media flow,and solids transport in annular flow

Mixtures of xanthan and guar gum in aqueous solution were studied in two flow situations: simple shear and porous media. In addition, solids transport in vertical annular flow of sand suspensions was explored. The zero shear rate viscosity of the solutions displayed a pronounced synergy: the viscosity of the mixture is higher than that of the polymer solutions in a wide range of relative concentrations of the two polymers, in agreement with previous literature. However, at relatively high shear rates, the viscosity approaches the value of the more viscous xanthan gum solutions at mass fractions of xanthan gum between 0.1 and 0.15, and the degree of synergy substantially decreases. Stress relaxation experiments in simple shear indicate that the polymer mixtures exhibit a well-defined yield stress after relaxation that is absent in solutions of pure polymers. In porous media flow experiments, a synergistic behavior mimicking the shear flow results was obtained for the polymer mixtures at low shear rates. However, at a critical shear rate, the apparent viscosity in porous media flows exceeds the shear viscosity due to the elongational nature of flow in the pores. The solids transport capacity in annular flows is well-represented by trends in shear viscosity and stress relaxation behavior. However, the lack of viscosity synergy at high shear rates limits the applicability of the mixtures as a way to improve solids suspension capacity in annular flows.     

Particle imaging velocimetry of a wet aqueous foam with an underlying liquid film

 We investigate the utility of particle imaging velocimetry (PIV) for performing kinematic measurements in wet aqueous foam with a liquid film beneath it. The flow velocities are measured near the walls of a square cross-section horizontal duct. The flow velocities are useful for validating the rheological models. We show that there is a discrepancy between the velocity profiles in the wet foam and the Bingham plastic model of flow. The velocity measurements reveal a more complex flow pattern, which may be analysed following three different regimes: a plug flow, a shear flow in a vertical plane and a three-dimensional shear flow. The transition between the plug flow and the shear flows may be explained by a shear-induced migration of bubbles. Received: 25 April 2000 / Accepted: 26 February 2001     

Performance of a flapping foil flow energy harvester in shear flows

Through numerical simulations, we investigate the energy harvesting performance of a heaving/pitching foil in shear flow. With two-dimensional Navier–Stokes simulations, we examined the energy harvesting efficiencies of such a system in linear shear flows and compared the results with those in uniform flows. It is found that in low shear rates, the performance of the system in linear shear flow is slightly higher than that in uniform flow, whereas the energy harvesting efficiency is greatly diminished if the shear rate is sufficiently high (this effect is more pronounced in higher frequencies). This is attributed to the effects of linear shear on the vorticity generation and the synchronization between fluid forcing and foil motion – when a strong shear flow is introduced the lift force induced by the leading edge vortex that is in phase with the heaving motion of the foil is diminished. Furthermore, by studying the instability of the wake behind the foil, we confirm that the optimal performance of the foil in linear shear flows is associated with the same physical mechanism that controls the performance of the foil in uniform flows, i.e. the excitation of the most unstable modes in the wake when the oscillation frequency of the foil is close to the frequencies of these modes.     

On the Relation between Fronts and High-Shear Layers in Wall Turbulence

Direct numerical simulation results of turbulent channel flow are analyzed in order to examine the relation between two kinds of near-wall flow structures, namely the instantaneous shear layers and the fronts which are derived from two-point statistics of the streamwise velocity component. The near-wall shear layers are analyzed by flow visualizations and conditional sampling, while the fronts are examined by means of space-time correlations and spatial two-point correlation functions. The present study focuses on the analysis of the propagation speed and the spatial shape of the structures. Concerning the propagation speed it is shown that the results obtained from flow visualizations are in close agreement with the propagation velocities derived from space-time correlation functions. The comparison of VISA results for the instantaneous shear with spatial structures obtained from two-point correlations of the streamwise velocity and the shear gives evidence that the fronts are intimately related to the pronounced near-wall shear layers.     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象,采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟,分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算,更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果,建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程,并通过剪切室实验结果验证了它的合理性.     

Influence of superimposed steady shear flow on the dynamic properties of non-Newtonian fluids

Summary Experiments in which an oscillatory shear flow is superimposed on a steady-state circular shear flow between a cone and a plate were performed on non-Newtonian solutions by means of aWeissenberg Rheogoniometer. The steady-state shear stress and in a first approximation also the normal stress difference arising from the steady shear flow appear not to be influenced by the superimposed oscillatory flow. On the other hand, the dynamic moduli as obtained from the oscillatory parts of shear stress and shear flow are highly dependent on the superimposed steady rate of shear. The absolute value of the complex shear modulus decreases and the phase difference between oscillatory shear stress and shear flow increases in all cases and for all frequencies if the superimposed shear rate is increased. Consequently, this phase difference can become equal to and even larger than /2. Between the angular frequency ₀ at which the phase difference is /2 and the steady shear rateq the relation ₀= 1/2,q was experimentally found to exist in most cases. These dynamic results cannot be described by the current theories of viscoelasticity. The large and fast deformations imposed on the material should explicitly be taken into account.     

Influence of shear and orthogonal vibration on semisolid aluminum flow properties

Understanding flow properties and flow effects of liquid and semisolid aluminum became a key solution for know-how of the casting processes. It is essential to find and study a new solution of interactive and efficient structure control of processed aluminum suspension. This task was solved by an adaptation of an electromagnetic actuator and high-resolution tempering unit to a conventional rotational rheometer. Initially, the research reveals a precise detection of transition temperatures in steady and transient shear flow. It was found that superposition of mechanical vibration orthogonal to the shear flow radically decreases shear viscosity of semisolid slurry. However, liquid state rheological properties show structural behavior, but stayed insensitive to mechanical oscillations. Analysis of boundary conditions before fundamental experiment shows that no considerable side effects were present during the experiment under vibration. The study reveals transition of strongly shear-thinning concentrated aluminum suspension to almost Newtonian fluid under vibration in shear flow. It is recommended to relate such phenomenon to non-equilibrium between structure formation and structure break-up under vibration and hydrodynamic forces of shear flow. The results illustrate how sensitive the structure of slurry is to vibration in general and in particular during the solidification phase. The revealed results provide a solid basis for further fundamental investigations.     

A thermodynamic model for magnetorheological fluids

An analysis of the dynamic behavior of a magnetorheological (MR) fluid is given in terms of a vectorial internal variable describing the change of the macroscopic average of the relative position vector of suspensions. Under the restriction of the second law, the constitutive equations of the MR fluid for stress, heat flux, magnetization and internal variable can be derived. The related issue of dissipative and energy transfer mechanisms is treated at some length. Studies on the steady shear flow indicate the direction of the internal variable is independent of shear rate. The Bingham-type constitutive equation for shear stress is obtained and endowed with a new meaning. The pressure-driven flow, another significant flow type for the design of MR devices, is also analyzed to study the plug flow region and the relationship between yield stress and flow rate. In addition, a criterion of flow initiated by the applied shear force is proposed based on the saturation of the internal variable and the condition of the equilibrium of forces in the fluid and solid regions. Received April 08, 1997     

平行平板流动腔的数值优化设计

平行平板流动腔系统是研究切应力对细胞影响的体外实验装置之一。前期研究发现,流动腔的高度存在一个最佳高度,使用这个高度可以有效地减小或避免由于装配所引起的高度误差对切应力的影响。为了获得这一最佳高度,本文使用数值方法研究了平行平板流动腔的几何尺寸、流体粘度与集中液阻之间的关系,并拟合得到了集中液阻的函数关系式。利用液阻关系式和切应力计算公式,求得了对底部切应力影响最小的最佳高度的表达式。同时,研究还发现,对于相同的底部切应力,当高度取最佳高度时,所需的入(出)口压差最小。这样在流动腔底部沿轴向的压力梯度也就越小,沿轴向不同位置之间的压力差别也越小,这将有利于细胞力学实验结果之间的比较。     

The interface migration in shear-banded micellar solutions

In this work, we study the diffusion of the interface between bands in wormlike micellar solutions that exhibit shear banding flow regimes, namely, systems undergoing coexistence of states of different shear rates along a constant stress plateau. The migration of the interface between bands possessing different birefringence levels is predicted by the BMP (Bautista-Manero-Puig) model in which a structural parameter (the fluidity) presents two states with differing order separated by an interface. The mechanical potential derived from the constitutive equations and a diffusion term for the structure evolution equation predict various time scales of interface migration at the inception of shear flow and under shear-rate changes along the plateau stress. It is shown that the extremes of the plateau (binodals) correspond to the minima in the mechanical potential as a function of fluidity or shear rate. We also predict the dependence of the diffusive length scale on the applied shear rate.     

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针对多孔介质网状纤维的渗流和生物体内组织液流动等问题，研究多孔介质中圆柱 方形阵列的低$Re$流动，以及流动所导致的圆柱表面的剪切应力. 鉴于迄今为止的研究均限于 圆柱实体模型的情况，重点分析将圆柱实体模型推广到可渗透时所导致的流动特性和表 面剪切应力的变化. 可渗透圆柱及圆柱阵列之间的间隙物使用具有不同渗透率的多孔介质模 型，基于Brinkman方程，配以适当的边界条件，采用有限体积法进行数值求解. 计算结果表 明，圆柱的渗透特性改变了流场的流动特性，显著减小了流动在圆柱表面所产生的剪切应力， 改变了阵列的渗透性.     

Experimental study on near wall transport characteristics of slug flow in a vertical pipe

In this work, the wall shear stress and the mass transfer coefficient of the gas–liquid two-phase upward slug flow in a vertical pipe are investigated experimentally, using limiting diffusion current probes and digital high-speed video system. In experiments, the instantaneous and averaged characteristics of wall shear stress and mass transfer coefficient are concerned. The experimental results are compared with the numerical results in previous paper of the authors. Both experiment and numerical simulation show that the superficial gas and liquid velocities have an obvious influence on the instantaneous characteristics of the two profiles. The mass transfer coefficient has characteristics similar to the wall shear stress. The instantaneous wall shear stress and mass transfer coefficient profiles have the periodicity of slug flow. The averaged wall shear stress and mass transfer coefficient increase with increased superficial gas velocity. However, there is inconsistency in the variation trends of the averaged wall shear stress and mass transfer coefficient with superficial liquid velocity between experimental result and numerical simulation result, which can be attributed to the difference in flow condition. Moreover, the Taylor bubble length is also another impacting factor. The experimental and numerical results all shows that the product scale can not be damaged directly by the flow movement of slug flow. In fact, the alternative forces and fluctuations with high frequency acting on the pipe wall due to slug flow is the main cause for the slug flow enhanced CO₂ corrosion process.     

Dynamics of rigid dumbbells in confined geometries Part II. Time-dependent shear flow

This paper describes analytical solutions to the response of a rigid dumbbell to a time-dependent simple shear flow in a channel of arbitrary size. The results were applied for specific flows, such as the sudden inception and cessation of simple shear and oscillatory shear flow. The introduction of confining walls leads to several qualitative differences compared with an unbounded flow such as initial negative jumps in the contribution of the dumbbell to the viscosity and the first normal stress coefficient. In addition, wall effects lead to a breakdown of well-known relationships between the complex viscosity and the complex normal stress coefficient during oscillatory flow.