Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic(EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem.Using the relaxation time as the small ordering parameter,analytical solutions are deduced for the leading-as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman–electric double layer(EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.     

Squeezing a viscoelastic liquid from a wedge: an exact solution

The paper reports an exact solution for the squeezing flow from a wedge of a general viscoelastic liquid. To obtain numerical values for the field variables, a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow is adopted. It is found that both these features are important in this transient flow; stress overshoot is responsible for a stiffer response of the fluid (compared to the inelastic case) at moderate time —at large time, shear-thinning dominates and the fluid behaves like an inelastic fluid. On the other hand, the Oldroyd-B fluid always predicts a softer response than the Newtonian one. Furthermore, there is a limiting Weissenberg number above which one component of the stresses of the Oldroyd-B fluid increases unboundedly with time. This limiting Weissenberg number is approximately $\text{sol2}\text{3}$.     

On the stability of the torsional flow of a class of Oldroyd-type fluids

It is shown that the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid. Furthermore, it is shown by a linearized stability analysis and by numerical integration, that the basic flow is unstable at high Weissenberg numbers. An Oldroyd fluid which has a negative second-normal stress coefficient is found to be more stable than one with zero (or positive) second-normal stress coefficient in this flow.     

Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.     

Analysis of lubricated squeezing flow

A thin film of low-viscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full two-dimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness of each of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated or autolubricated flows in processing situations.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

Drop oscillations under simple shear in a highly viscoelastic matrix

Recent two-dimensional numerical simulations and experiments have shown that, when a drop undergoes shear in a viscoelastic matrix liquid, the deformation can undergo an overshoot. I implement a volume-of-fluid algorithm with a paraboloid reconstruction of the interface for the calculation of the surface tension force for three-dimensional direct numerical simulations for a Newtonian drop in an Oldroyd-B liquid near criticalities. Weissenberg numbers up to 1 at viscosity ratio 1 and retardation parameter 0.5 are examined. Critical capillary numbers rise with the Weissenberg number. Just below criticality, drop deformation begins to undergo an overshoot when the Weissenberg number is sufficiently high. The overshoot becomes more pronounced, and at higher matrix Weissenberg numbers, such as 0.8, drop deformation undergoes novel oscillations before settling to a stationary shape. Breakup simulations are also described.     

模拟微可压粘弹性流体的WCCBS_SU方法

针对微可压缩粘弹性流动问题,发展了微可压缩流的WCCBS方法,详细推导了基于Oldroyd-B本构模型的WCCBS_SU方法的求解过程。在流场微可压的条件下,分别对平面Poiseuille流和4：1粘弹性收缩流进行了数值模拟。Poiseuille流在不同We数下数值结果与解析解的比较,验证了本文方法具有较高的精度和较好...     

暖季强降雨对多年冻土南界斜坡路基稳定性影响分析

为阐明表面活性剂水溶液的减阻作用,使用LDV对零压梯度的二维湍流平板边界层中的CTAB 表面活性剂水溶液的湍流特性进行了实验研究. 结果表明：与牛顿流体相比,CTAB水溶液边 界层的粘性底层增厚;主流时均速度分布有被层流化的趋势,对数分布域上移;主流方向速 度湍动强度峰值减小,且远离壁面,在靠近边界层中部,出现第2峰值;垂直于主流方向的 速度湍动强度受到了大幅度抑制,雷诺应力沿着边界层厚度方向几乎为零. 结果说明CTAB 水溶液具有减弱湍流湍动各个成分相关度的作用,从而能够使雷诺应力降低、湍流能量生成 项减小最终降低流体的输送动力.     

Calibration of and measurements on a rheogoniometer by means of a small computer

Summary In this paper we propose a method for measurements with and calibration of the Weissenberg Rheogoniometer by means of a small computer.For Newtonian fluids we found that the dynamic viscosity is changed by a superposition of a steady shear flow on an oscillatory one, dependent on the direction of the steady shear flow.

---

Zusammenfassung In diesem Aufsatz wird eine neue Methode zur Eichung eines Weissenberg-Rheogoniometers und für das Messen mit diesem Apparat dargestellt. Wir haben an newtonschen Flüssigkeiten beobachtet, daß die dynamische Viskosität bei der Überlagerung einer stationären und einer oszillierenden Scherströmung je nach der Richtung der stationären Strömung ihren Wert ändert.

---

---

With 3 figures     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

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…     

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

The influence of elasticity of a fluid exiting a channel is examined on transient coating downstream. A hybrid spectral/boundary element approach is proposed to solve the problem. The flow inside the channel is assumed to be fully developed. A viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson–Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating. Copyright © 2003 John Wiley & Sons, Ltd.     

Some tests of constitutive equations for entangled polymers based on planar-extension flow histories in a periodically constricted channel

Stress and velocity were determined locally by birefringence measurements and laser Doppler velocimetry for a mildly entangled polystyrene solution flowing at steady state in a rectangular channel with sinusoidally varying wall spacing. Having measured both the velocity and stress fields, we were able to test constitutive equations locally, i.e., without solving the equations of motion for the entire flow. Four were examined for the periodic planar extensions on the channel centerplane: the Newtonian model, the Lodge network model, the Doi-Edwards tube model, and the Wagner-Schaeffer modification of Doi-Edwards. High enough Weissenberg and Deborah numbers were reached to produce sizable departures from the Newtonian predictions. The Doi-Edwards model underpredicted the stress, as did Wagner-Schaeffer, although to a lesser extent. Predictions of the Lodge model were best of all, a surprising result in view of its inadequacy for simple shear deformations. The predictions of the Lodge model, without parameter adjustment, agreed remarkably well with the planar extension data over the accessible range for our apparatus: Deborah numbers up to 2.0, extensional Weissenberg numbers up to 6.5, and a maximum extension ratio of about 2.3.     

High shear rate viscometry

We investigate the use of two distinct and complementary approaches in measuring the viscometric properties of low viscosity complex fluids at high shear rates up to 80,000 s^?1. Firstly, we adapt commercial controlled-stress and controlled-rate rheometers to access elevated shear rates by using parallel-plate fixtures with very small gap settings (down to 30 μm). The resulting apparent viscosities are gap dependent and systematically in error, but the data can be corrected—at least for Newtonian fluids—via a simple linear gap correction originally presented by Connelly and Greener, J. Rheol, 29(2):209–226, 1985). Secondly, we use a microfabricated rheometer-on-a-chip to measure the steady flow curve in rectangular microchannels. The Weissenberg–Rabinowitsch–Mooney analysis is used to convert measurements of the pressure-drop/flow-rate relationship into the true wall-shear rate and the corresponding rate-dependent viscosity. Microchannel measurements are presented for a range of Newtonian calibration oils, a weakly shear-thinning dilute solution of poly(ethylene oxide), a strongly shear-thinning concentrated solution of xanthan gum, and a wormlike micelle solution that exhibits shear banding at a critical stress. Excellent agreement between the two approaches is obtained for the Newtonian calibration oils, and the relative benefits of each technique are compared and contrasted by considering the physical processes and instrumental limitations that bound the operating spaces for each device.     

Effect of viscoelasticity on the rotation of a sphere in shear flow

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress.In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.     

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.     

Large-amplitude oscillatory shear flow from the corotational Maxwell model

Using the single relaxation time corotational Maxwell fluid, we derive explicit analytical expressions for the first, third, and fifth harmonics of the alternating shear stress response in large-amplitude oscillatory shear (LAOS). We also derive corresponding expressions for the zeroth, second, and fourth harmonics of both the first and second normal stress differences. These harmonics are found to depend upon just two dimensionless groups: the Deborah and Weissenberg numbers, each of which causes non-Newtonian behavior. The form of the solution for the corotational Maxwell model in LAOS matches the forms of the analytical solutions for two molecular models for dilute solutions and one for concentrated solutions or melts. We also derive an analytical solution for the corotational Maxwell model after startup of LAOS. For this we find that both small and large amplitude cases approach a periodic limit cycle (alternance) at the same rate for both the shear stress response and for the normal stress differences. For molten high density polyethylene that is lightly filled with carbon black, we find good quantitative agreement with measured LAOS behavior when our analytical solution is superposed for multiple relaxation times.