Shear and elongational flow behavior of acrylic thickener solutions

We investigate the effect of hydrophobic aggregation in alkali-swellable acrylic thickener solutions on shear and extensional flow properties at technically relevant polymer concentrations using the commercial thickener Sterocoll FD as model system. Apparent molecular weight of aggregates in water is M _w  ≈ 10⁸ g/mol and decreases by more than an order of magnitude in ethanol. Zero shear viscosity η ₀ is low and shear thinning is weak compared to the high molecular weight of the aggregates. Linear viscoelastic relaxation is described by the Zimm theory up to frequencies of 10⁴ rad/s, demonstrating that no entanglements are present in these solutions. This is further supported by the concentration dependence of η ₀ and is attributed to strong association within the aggregates. Extensional flow behavior is characterized using the capillary break-up extensional rheometry technique including high-speed imaging. Solutions with ϕ ≥ 1% undergo uniform deformation and show pronounced strain hardening up to large Hencky strains. Elongational relaxation times are more than one order of magnitude lower than the longest shear relaxation times, suggesting that aggregates cannot withstand strong flows and do not contribute to the elongational viscosity.

Shear and elongational flow behavior of acrylic thickener solutions. Part II: effect of gel content

We have investigated the effect of crosslink density on shear and elongational flow properties of alkali-swellable acrylic thickener solutions using a mixing series of the two commercial thickeners Sterocoll FD and Sterocoll D as model system. Linear viscoelastic moduli show a smooth transition from weakly elastic to gel-like behavior. Steady shear data are very well described by a single mode Giesekus model at all mixing ratios. Extensional flow behavior has been characterized using the CaBER technique. Corresponding decay of filament diameter is also well fitted by the Giesekus model, except for the highest crosslink densities, when filament deformation is highly non-uniform, but the non-linearity parameter α, which is independent of the mixing ratio, is two orders of magnitude higher in shear compared to elongational flow. Shear relaxation times increase by orders of magnitude, but the characteristic elongational relaxation time decreases weakly, as gel content increases. Accordingly, variation of gel content is a valuable tool to adjust the low shear viscosity in a wide range while keeping extensional flow resistance essentially constant.     

Analytical prediction of the wave configuration size in steady flow Mach reflections

Analitycal model for predicting the size of the Mach reflection wave configuration in steady flows has been improved (Azevedo 1989; Azevedo and Liu (1993)). Predictions based on the modified analytical model were compared to available experimental results. The agreement was found to be better than that obtained by Azevedo (1989) and Azevedo and Liu (1993). The reason for the better agreement is due to the fact that, unlike Azevedo's original model, downstream effects were not neglected in the modified model which was developed in the course of this study. Received 12 May 1996 / Accepted 15 January 1997     

Criticality and transition for a steady reactive plane couette flow of a viscous fluid

Numerical integration is used to determine critical and transitional values of parameters for steady, reactive, viscous, one dimensional plane Couette flow of an incompressible, homogeneous fluid of third-grade with the lower plate at rest while the upper is in uniform motion. The solutions are found for the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. Specifically, it is shown that the parameter Λ controlling the non-Newtonian fluid does not affect the flow velocity in any sense while the influence on the viscous dissipation parameter Γ is examined. The results obtained are then compared with similar results in the literature.     

Non-linear behaviour of asphalts in steady and transient shear flow

Steady-state and transient shear stress and normal stress data were obtained for four asphalts with a modified Weissenberg Rheogoniometer. Interest was specially related to non-linear behaviour at high shear-rates. The time-temperature superposition principle was found to hold in non-linear behaviour. Moreover, steady-state and transient data could be plotted as master curves irrespective of the nature of the asphalts. In particular, the master curve of steady-state viscosity could be extended to results published in the literature. In the nonlinear region the shear stress relaxation after cessation of a steady shear rate becomes a function of t only and is related to the primary normal-stress coefficient, as predicted by the Yamamoto equation. In the shear stress growth experiment an overshoot is obtained at a constant strain close to 1.5, independent of the rate of strain.     

Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment

In this contribution, a numerical framework for the efficient thermo-mechanical analysis of fully 3D tire structures (axisymmetric geometry) in steady state motion is presented. The modular simulation approach consists of a sequentially coupled mechanical and thermal simulation module. In the mechanical module, the Arbitrary Lagrangian Eulerian (ALE) framework is used together with a 3D finite element model of the tire structure to represent its temperature-dependent viscoelastic behavior at steady state rolling and finite deformations. Physically computed heat source terms (energy dissipation from the material and friction in the tire–road contact zone) are used as input quantities for the thermal module. In the thermal module, a representative cross-sectional part of the tire is employed to evaluate the temperature evolution due to internal and external heat sources in a transient thermal simulation. Special emphasis is given to an adequate material test program to identify the model parameters. The parameter identification is discussed in detail. Numerical results for three different types of special performance tires at free rolling conditions are compared to experimental measurements from the test rig, focusing especially on rolling resistance and surface temperature distribution.     

On analysis of the steady flow in an irrectangular parallel-plate flow chamber

I.IntroductionForthestudyofrelationshipbetweencell'sgrowthandshearstress,thesubjectthatshouldbeworkedoutatfirstishowtosimulateshearstressenvironnlelltwhichsuitcell'sgrowthandofwhichtheshearstresscanbecalculatedconvelliently.NowthePPFCisoneofthemainapparatusesthatsimulatetheshearstressenvironmelltforcell'sgrowthinvitro.Forexample,tilerectangularPPFCisusedforthestudyoftherelationshipbetweentheendotheliumcells'injuryinartery,orplatelet'sadhesionordeformationalldatherosclerosisl3].Apartfromthe…     

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.     

Molecular models and flow calculations: II. Simulation of steady planar flow

A multibead-rod model is used to replace the constitutive equation of continuum mechanics in solving flow problems of steady-state planar flows of rigid-rodlike molecular suspensions. The governing equations then constitute a set of differential equations of the elliptic type, which is more amenable to numerical treatment than those of the mixed type. The conservation equations of the flow fields are solved by the boundary element method with linear boundary elements in physical space and the diffusion equation of the distribution function is solved separately by the Galerkin method in phase space. The solution to the flow problem is obtained when the convergence of the iteration procedure between the two spaces has been reached. Several numerical examples are shown and the interesting features of the present method are discussed in this paper. The project supported by the National Nature Science Fundation of China.     

Viscosity enhancement in non-Newtonian flow of dilute aqueous polymer solutions through crystallographic and random porous media

We report results on the flow of dilute aqueous solutions of hydrolysed poly(acrylamide) (HPAA) through beds of spheres packed in simple cubic and body-centred cubic crystallographic arrays. Pressure drop measurements made across the arrays as a function of the flow rate have been used to estimate the specific viscosities of the HPAA solutions as a function of the superficial strain rate. It is found that greater non-Newtonian increases in the specific viscosity occur in the body-centred cubic array, which is thought to be due to the presence of trailing stagnation points, which are not present in the simple cubic array. Experiments have been performed using HPAA solutions in the presence of mono- and divalent cations at various concentrations and, for validity, have been compared with results obtained from a traditional randomly packed porous medium. In addition, a study of mechanical degradation of the polymer in flow through the crystallographic arrays has been carried out and reveals a greater rate of degradation in the body-centred array and also a significant increase in degradation with salt concentration.     

Vortex shedding in cylinder flow of shear-thinning fluids: II. Flow characteristics

A detailed experimental study on the flow characteristics of various vortex shedding regimes was carried out for the flow of non-Newtonian fluids around a cylinder. The fluids were aqueous solutions of carboxymethyl cellulose (CMC) and tylose at weight concentrations ranging from 0.1 to 0.6%, which had varying degrees of shear-thinning and elasticity. Two cylinders of 10 and 20 mm diameter were used in the experiments, defining an aspect ratio of 12 and 6 and producing blockages of 5 and 10%, respectively. The Reynolds number (Re) ranged from 50 to 9×10³.Shear-thinning gave rise to a decrease of the cylinder boundary-layer thickness and to a reduction of the diffusion length (l_d), which raised the Strouhal number, St. In the laminar shedding regime, a modified Strouhal number was successful at overlapping the shedding frequency variation with the Reynolds number for the various solutions. In contrast, fluid elasticity was found to increase the formation length (l_f), and this contributed to a decrease of the Strouhal number. The overall effect of shear-thinning and elasticity was an increase in the Strouhal number.The increase in polymer concentration and the corresponding increase in fluid elasticity were responsible for the reduction of the critical Reynolds number marking the sudden decrease of the formation length, Re_lf. In the shear layer transition regime, the formation length and Strouhal number data collapsed onto single curves as function of a Reynolds number difference, which confirmed Coelho and Pinho (J. Non-Newtonian Fluid Mech. (2003), accepted for publication) finding that an important effect of fluid rheology was in changing the demarcations of the various flow regimes.     

Axial annular flow of plastic fluids: dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ _c, λ will be such that flow commences when τ(κR) = τ(R) = τ _c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.

Elastic recovery of immiscible blends 1. Analysis after steady state shear flow

Due to the interfacial tension, immiscible blends can show an elastic recovery that is substantially larger than that of their pure components. Here it is attempted to relate the elastic recovery after steady shear flow to the underlying morphology. On the one hand, the predictions of the Palierne and the Doi-Ohta models are calculated for the flow conditions during recoil. On the other hand, systematic recoil experiments after steady state shearing have been performed on a model blend. As the component polymers hardly show any recoil under the stresses applied in these tests, the measured recovery can be attributed completely to the action of the interface. Comparison of the model predictions with the experimental results shows that the recoverable strain can be derived quantitatively from the linear Palierne theory. Although the droplet deformation remained limited during the preshear, the retardation time predicted by this model has to be multiplied by the aspect ratio of the droplet phase to the power 2/3 to describe the experiments. For conditions in which the material does not show an intrinsic length scale, particular scaling relations as derived from the Doi-Ohta theory are found to apply also to recoil. Received: 5 August 1998 Accepted: 17 November 1998     

一般物态方程形式下爆轰产物的一维等熵流动

研究了一般物态方程形式下一维平面和柱、球面对称CJ爆轰波后产物的等熵流动,给出Riemann不变量的表达式、Euler和Lagrange形式的自相似流动方程组,得到一个高精度近似解析解,在实验测量合理的范围内本文理论与实验基本符合。为了具体应用上述理论,给出四种普遍公认的物态方程(律、JWL、HOM和W.C.Davis近来提出的形式)的等熵线和声速曲线,以及较一般情形中产物或惰性介质沿等熵线的比内能表达式。四种等熵线差别不大,表明爆轰数值模拟中不但要应用产物的等熵线,还应注意产物能量状态方程是否适当。本文的理论计算方法,可作为产物一维流动数值模拟正确性的有效校核手段。     

基于扰动状态概念与E-B模型的粗粒料力学行为模拟

考虑到基于复杂弹塑性模型与扰动状态概念的本构模型在数值积分时的困难,以Duncan-Chang(E-B)模型描述材料在相对完整状态(RI)下的响应,用临界状态模型描述材料在完全调整状态(FA)下的力学行为。依据常规三轴试验曲线判断材料状态的转变并建议了相应的扰动因子计算方法。利用Abaqus软件实现了相应的程序代码,数值算例模拟了堆石料的三轴试验,结果表明邓肯-张模型与扰动状态概念的结合在模拟应变软化、剪缩与剪胀方面具有良好能力。在此基础上进一步模拟了某混凝土面板堆石坝的施工、蓄水、退水的过程,数值结果表明变形分布符合一般规律,且在定量上与原型观测吻合较好。     

Thermoelectroelastic state of a piezoceramic body with a spheroidal cavity in a uniform heat flow

An exact solution is obtained to the three-dimensional problem of thermoelectroelasticity for a piezoceramic body with a spheroidal cavity. The solutions of static thermoelectroelastic problems are represented in terms of harmonic functions. Far from the cavity, the body is in a uniform heat flow perpendicular to the axis of symmetry of the cavity __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 57–66, November 2005.     

A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves

A type of numerical scheme for 2D and 3D steady non-linear water wave problems is described. It is based on the finite process method and is insensitive to initial solutions. The relationship between the finite process method and iterative techniques is discussed. As a numerical example the flow past a submerged vortex is solved and the results are compared with those of other authors.     

Transient behavior of Boger fluids under extended shear flow in a cone-and-plate rheometer

Three different dilute solutions of high molecular weight polymers in viscous, binary solvents were used in experiments performed in a cone-and-plate rheometer. The solutions all fall into the class of fluids referred to as Boger fluids and were previously used in studies of viscoelastic Taylor-Couette instabilities. Under prolonged shearing in the cone-and-plate geometry, these fluids all exhibited a decrease of the first normal stress growth function N₁⁺(t) from an initial plateau value to a second, lower plateau value. This behavior has been previously observed, but is here reported for widely used polyisobutylene-based Boger fluids for the first time. As in earlier studies (Magda JJ, Lee C-S, Muller SJ, Larson RG (1993) Macromolecules 26:1696–1706; MacDonald M, Muller SJ (1997) J Rheol Acta 36:97–109), the time at which this decrease occurs (the decay time) is much longer than the polymer molecules relaxation time. Here, we focus on three issues: 1) the time-temperature superposition of the first normal stress growth function N₁⁺(t), including the decay time and the value of the second plateau, 2) the sample recovery time required to reproduce the initial plateau value of N₁⁺ and the decay time, and 3) the relationship between the time scales for this decay of normal stresses and the onset of viscous heating induced instabilities in the Taylor-Couette geometry. Our results suggest that shear-induced conformational changes, possibly coupled to viscous heating of the sample, may be responsible for the decrease in the first normal stress growth function during prolonged shearing.