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.     

Characterization of polyacrylamide gels as an elastic model for food gels

Serving as an elastic model system for food gels, characteristics of polyacrylamide (PAAm) gels were investigated using small amplitude and large deformation rheological tests. The PAAm gels displayed elastic or viscoelastic behavior depending on network crosslink density. For elastic PAAm gels, the rheological properties obeyed the theory of rubber elasticity; whereas for viscoelastic PAAm gels, shear modulus depended on temperature. The elastic PAAm gel fracture parameters did not change with deformation rate (0.2–5.5 s^–1), indicating insignificant viscous flow during deformation. Fracture stress was correlated with gel monomer concentration, whereas the fracture strain remained constant regardless of the monomer concentration. In addition, the stress was linearly proportioned with strain up to fracture, indicating that PAAm gels did not experience finite network chain extensibility during large deformation. Consequently, the fracture of PAAm gels did not result from the extensional limitation of network chains, nor did gel fracture result from the nonlinear force–distance relationship between polymer connections. Purportedly, the fracture of PAAm gels was caused by external force overcoming the gel cohesive forces, and low strength of PAAm gels compared to rubbers caused fracture prior to experiencing nonlinear stress-strain deformation.Paper No. FSR04-20 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27695-7643. The use of trade names does not imply endorsement by the North Carolina Agricultural Research Service of products named, nor criticisms of similar ones not mentioned.     

Rheological properties of physical gel formed by hydrophobically modified urethane ethoxylate (HEUR) associative polymers in methanol–water mixtures

We investigated the effects of methanol on the two rheological properties, dynamic modulus and flow behaviour, for an aqueous solution of hydrophobically ethoxylated urethane (HEUR). When the added methanol constitutes 0–10 mol% of the sample, the gel relaxation time shortens; when it constitutes 20 mol% of the sample, the distribution of relaxation times broadens. Relaxation of the physical gel formed by a transient network is directly related to the lifetime of the crosslink points, i.e. flower micelles. We speculate that methanol addition shortens the relaxation time by changing the hydrophobic interactions in the flower micelles. The changed hydrophobic interactions then affect not only the relaxation time but also the shape of the HEUR-chain molecular associating structures which in turn affects the mechanical spectrum. Under constant shear flow, shear thickening increases with increasing methanol concentration, and the increase in stress under constant shear flow shows unusual behaviour. A possible contributing factor to this behaviour may be the non-cosolvency of methanol with polyethyleneoxide (PEO). At some critical concentration, methanol in PEO aqueous solution becomes a poor solvent, which then affects the properties of the PEO chains in the transient networks of HEUR aqueous solution. The rheological properties of the transient networks clearly affect the properties of both the crosslink points and the chains. In short, methanol addition induces complicated changes in gel mechanical properties.     

Effects of compatibilization on rheological properties of PS/PB blends and investigation of Doi–Ohta scaling relationship in double start-up of shear experiments

The rheological properties for the blends of polystyrene and polybutadiene were investigated and the effect of compatibilizer styrene butadiene rubber (SBR), on the blends were studied and the results compared with the non-compatibilized blends. The frequency sweep, step shear strain and shear stress growth experiments were carried out for the blends. The results showed that with addition of compatibilizer the changes in behavior of the rheological properties of blends are observed. These rheological variations could be related to the reduction of interfacial tension and size of dispersed phase. Furthermore, the validity of Doi–Ohta scaling relationship in double start-up experiments was studied. It is shown that this scaling relationship becomes more reliable with increasing the amount of PB and compatibilizer.     

The rheological behavior of flexible-chain polymers in the region of high shear rates and stresses,the critical process of spurting,and supercritical conditions of their movement at T > Tg

Methods of capillary viscometry were used in studying the rheological properties and behavior of a broad range of rubbers, including polymers with narrow and wide molecular-weight-distribution as well as commercial rubber grades, at widely varying shear rates and stresses. As is shown, in full conformity with the previously conducted experiments, during transition from a fluid to highelastic (quasi-cross-linked) state, they are chracterized by spurting followed by sliding over the channel walls. This relaxation transition is characterized by a critical shear stress value invariant with respect to the molecular weight, molecularweight distribution and temperature. The parameters defining spurting of polymer flow as a function of molecular-weight characteristics, temperature, and channel geometry have been investigated in detail. It is shown for the first time that under supercritical conditions the rate of polymer flow through channels does not depend, in the first approximation, on the molecular weight of the polymer, its molecularweight distribution, temperature, and filling, but is determined only by the shear stress.     

Physical gelation under shear for gelatin gels

Physical gelation is the process of crosslinking which reversibly transforms a solution of polymers into a gel. The crosslinks of the network have a physical origin (hydrogen bonding, Van der Waals forces... ) and therefore are sensitive to variations of temperature, pH, ionic content, etc. (non-permanent crosslinks). Physical and chemical gelation have been extensively studied in quiescent conditions, where rheology experiments have been performed to follow the network formation without disturbing the process. In this study we consider gelation of a well known physical, thermoreversible, gel (gelatin gel), which proceeds under flowing conditions. The gelling solution is submitted to a shearing, with imposed, permanent shear stresses or imposed, permanent, shear rates. Under flow, a competition arises between the formation of clusters by physical crosslinking and their disruption by the shear forces. This investigation defines the flowing conditions which either allow or impede gel formation. In particular, a critical shear rate , related to the gelation temperature and gelatin concentration, is identified which separates the two regimes. A microscopic model is proposed, based on the analysis of flow curves and dynamic measurements, which describes the structure of the gelling solution: microgel particles grow to a maximum size which depends on the flow. When the volume fraction of particles is high enough, percolation between particles occurs suddenly and a yield stress fluid is formed (particulate gel). The differences between gels made in quiescent conditions and gels made under flow are underlined.     

Determination of the wall slip velocity in the flow of a SBR compound

Rubber compounds are known to exhibit slip at the wall in particular flow conditions. The slip velocity is usually determined by using the classical Mooney method. The rheological behavior of a styrene butadiene rubber (SBR) compound was studied with three different rheometers. Biconical rotational, capillary and slit die rheometers were used to define the true viscous behavior of the compound and the slip velocity. It was shown that it was impossible to apply the Mooney method to our experimental data. New characterizations were thus developed for both capillary and slit die experiments. They were based on the dependency of the slip velocity on the local flow gap. Contrarily to the Mooney method, they provided physically acceptable results and led to a power-law relationship between wall slip, wall shear stress and local geometry of the flow.     

Gelation kinetics in elastomer/thermoset polymer blends

The chemical gelation of polymer blends involving a thermoset component has been investigated utilizing multiple waveform dynamic rheology, complemented by differential scanning calorimetry and small angle x-ray scattering measurements. Three epoxy/rubber mixtures, with different degrees of pre-reacted material and catalyst, were used. The curing temperatures were determined with simple temperature ramps, whereas the characteristic gel times were quantified using the well-known self-similarity of the gel structure, which yielded a very low gel exponent (0.05), indicative of the high molecular weights and additives used in the samples; this exponent was unchanged with temperature, suggesting the same gelation mechanism. These times decreased with increasing temperature. Gelation was not affecting the phase-separated morphology. The presence of pre-reacted material and catalyst were found to reduce the gel times (for different temperature steps). Finally, the shear history of the samples did not affet the curing temperatures and kinetics. These results can serve as a useful guide for appropriately blending thermosetting and thermoplastic compounds in order to obtain structural materials for different applications.     

宽γ辐照剂量范围内硅泡沫本构模型研究

基于实验和理论建模研究了白炭黑增强硅泡沫材料在γ辐照剂量范围为0~1000kGy作用后的单轴压缩力学行为。实验结果表明辐照导致硅泡沫出现明显硬化现象，初始杨氏模量和固定应变下应力幅值均随γ辐照剂量近似线性增加。辐照后硅泡沫泡孔结构完整，硅橡胶基体中高分子交联反应占主导，且交联密度随辐照剂量线性增大。基于实验分析结果，实现了Ogden Hyperfoam超弹本构模型参数与辐照剂量的关联。结果表明初始剪切模量参数与辐照剂量成线性关系，硬化指数和泊松比参数与辐照剂量无关。基于应力应变实验数据拟合得到模型参数，并与未参与拟合的实验数据对比，验证了模型的准确性，表明该模型能够表征宽辐照剂量范围内硅泡沫的压缩力学行为。     

Wall shear stress and void fraction in Poiseuille bubbly flows: Part II: experiments and validity of analytical predictions

In a companion paper, a simple analytical formulation has been established which provides the wall shear stress in laminar bubbly flows for idealised transverse void fraction distributions. In the present paper, this approach is applied to Poiseuille bubbly flows in circular ducts. New measurements of the void fraction profiles and wall friction angular distribution in a pipe are presented for a wide range of flow parameters. Approximating the void profiles by step-functions allows us to evaluate the wall friction with the above mentioned model. Results are shown to agree satisfactorily with measurements. Notably, negative wall shear stress and wall shear stress much higher than their single-phase flow counterpart at the same liquid flow rate are recovered. Therefore, the principal mechanisms responsible for friction modification are captured with this simple model.     

一种改进的颗粒移动床μ(I)拟流体模型及应用

颗粒移动床在工业领域应用广泛, 发展实用可靠的颗粒移动床模型具有理论和应用价值. 本文基于颗粒流μ(I)模型, 补充局部颗粒体积分数与颗粒局部压力和局部颗粒流密度的关系式, 将移动床内密集颗粒处理成可压缩拟流体, 建立了颗粒流单相可压缩流μ(I)模型, 并建立了颗粒流?壁面摩擦条件, 在计算中对颗粒流拟黏度和拟压力项进行正则化处理. 采用上述模型与方法对3种典型散料在移动床缩口料仓内的流动进行模拟, 与实验对比, 得到了玻璃珠、刚玉球和粗沙的μ(I)模型参数, 分析了3种不同散料在料仓内的颗粒速度、体积分数等分布特性, 模拟结果较好地揭示了料仓内不同物料的整体流和漏斗流特性; 进而以玻璃珠为例, 对移动床颗粒单管绕流流动进行了模拟, 所得结果合理揭示了管流附近的流动特性. 计算结果表明, 对于本文的计算工况, 颗粒体积分数变化最大范围为0.510 ~ 0.461, 绝大部分区域流动惯性数小于0.1, 改进的单相μ(I)模型能合理预测出密集颗粒流移动床内的流动特性, 方法可行且较多相流算法能明显减小计算量.      

A Kolsky Torsion Bar Technique for Characterization of Dynamic Shear Response of Soft Materials

A novel Kolsky torsion bar technique is developed and successfully utilized to characterize the high strain rate shear response of a rate-independent end-linked polydimethylsiloxane (PDMS) gel rubber with a shear modulus of about10 KPa. The results show that the specimen deforms uniformly under constant strain rate and the measured dynamic shear modulus follows reasonably well the trend determined by dynamic mechanical analysis (DMA) at lower strain rates. For comparison, Kolsky compression bar experiments are also performed on the same gel material with annular disk specimens. The dynamic moduli obtained from compression experiments, however, are an order of magnitude higher than those obtained by the torsional technique, due to the pressure caused by the radial inertia and end constraints.     

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ^° pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (R e _d =32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10^°. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.     

Rheological study of concentrated suspensions in pressure-driven shear flow using a novel in-line ultrasound Doppler method

 In this work a novel in-line non-invasive rheological measuring technique is developed and tested in pilot plant and industrial-scale applications. The method is based on a combination of the ultrasonic pulsed echo Doppler technique (UVP) and pressure difference method (PD). The rheological flow properties are derived from simultaneous recording and on-line analysis of the velocity profiles across the tube channel and related radial shear stress profiles calculated from the pressure loss along the flow channel. It is shown that the in-line UVP-PD technique allows for the non-invasive rheological flow behaviour characterization of non-transparent and highly concentrated suspensions. Received: 8 May 2000 / Accepted: 22 June 2001 Published online: 29 November 2001     

Theoretical correlation of linear and non-linear rheological symptoms of long-chain branching in polyethylenes irradiated by electron beam at relatively low doses

Dynamic and transient shear and elongation flow experiments along with gel permeation chromatography (GPC) and differential scanning calorimetry (DSC) analysis are performed on linear low-density polyethylenes (LLDPEs) irradiated at doses below 25 kGy. GPC data indicate no changes in the molar mass distribution, and there are almost no changes in melt and crystallization temperatures, likewise. Contrary, dynamic shear rheological behavior including thermorheological complexity, type of reduced van Gurp-Palmen curves, and zero shear-rate viscosities all disclose growing levels of long-chain branching with irradiation dose. An inverse tube model is developed for binary blend of linear and star chains and used to extract the fraction of the branched components. Modeling results reveal progressive increase in the length and fraction of star chains, as evidenced by appearance of an anomalous double overshoot in the transient shear viscosities. Detection of strain hardening in extensional stress growth coefficient data, well-quantified by molecular stress function model, is also in agreement with the predictions of tube model.     

Mechanisch-dynamische und kalorimetrische Untersuchungen an Phenolharz-Kautschuk-Mischungen

Zusammenfassung Die mechanisch-dynamischen und kalorimetrischen Untersuchungen an den Polymersystemen Phenolnovolakharz mit SBR, NR und NBR haben gezeigt, daß in diesen Mischsystemen nur ein Einfluß des Mischungsverhältnisses auf den Umwandlungsbereich des Kautschuks, dessen Temperaturlage in allen Konzentrationsbereichen unbeeinflußt bleibt, beobachtet werden kann. Ab einer Kautschukkonzentration von 10 Gew.-% im Harz bildet sich neben der kontinuierlichen Harzphase allmählich eine weiche Phase aus. Der Einfluß des Kautschuks auf das Harz zeigt sich am deutlichsten im kautschukelastischen Bereich. Hier werden die mechanischen Eigenschaften weitgehend von der Kautschukphase bestimmt. Die mit dem Torsionsschwingversuch ermittelten Speichermodulwerte der Mischungen werden mit den theoretischen Überlegungen über den Schubmodul von Polymermischungen und Polymerverbunden verglichen.

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Summary Dynamic-mechanical and calorimetric measurements on the polymer system phenolic novolac resin (PF) with styrene-butadiene rubber (SBR), natural rubber (NR) and nitrile-butadiene rubber (NBR) have shown that there only is observed an influence of the mixing ratio on the glass-transition of the rubber. For all compositions the position of the glass-transition of the rubber remains unchanged. From a rubber content of 10 weight-% onwards, a soft phase is being formed beside the rigid matrix phase of the resin. The dominating influence of the rubber on the resin is most evident in the region of rubber elasticity. The mechanical properties in this temperature range are vastly influenced by the rubber phase. The results of the torsional pendulum measurements of the resin-rubber blends at room temperature are compared with the prediction of the elastic properties of polymer blends and composite materials.

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Auszugsweise vorgetragen auf der Jahrestagung der Deutschen Rheologischen Gesellschaft in Dortmund vom 9.–11. März 1977 und in Berlin vom 8.–10. Mai 1978.

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Mit 13 Abbildungen und 2 Tabellen     

射流对绕水翼云空化流动抑制机理研究

为理解绕水翼云空化流动的发展机理和探究水翼吸力面开孔射流的影响,采用密度 修正的RNG $k$-$\varepsilon $湍流模型和Schnerr-Sauer空化模型对原始NACA66(mod) 水翼和采用射流后的 水翼的云空化非定常过程进行模拟和对比分析;采用在水翼吸力面近壁区设立监测线的方法对近壁区的流场进行监测,得到 近壁区汽相体积分数、回射流速度、压力及压力梯度的时空分布云图;开展了云空化流场特性的涡动力学分析,进而分析水 翼云空化的发生机理和射流抑制空化的抑制机理. 结果表明:游离型空泡在下游溃灭时产生强烈的局部高压,其向上游传播 导致前缘空穴的一次回缩,而空穴的二次回缩受回射流的影响. 回射流的发展区域受限于较高的压力梯度,高的压力梯度一 直存在,但回射流在一个周期内的首次出现需要时间的积累. 在水翼吸力面射流使得射流孔附近压力升高,弥补了由于空化 和绕流造成的压降,压力梯度增大,抗逆压能力增强,对回射流起到阻挡作用;另一方面,射流使得回射流区域面积和回射 流的强度也有所减小,从而对云空化的发展起到抑制的效果. $Q$准则的涡结构云图相比于汽相体积分数云图能显示复杂的 流动结构,前缘附着型空穴和尾缘游离型空穴内存在旋涡,回射流对空穴存在剪切作用造成空穴脱落. 而射流对空穴和回射 流的剪切和阻挡使云空化发展得到抑制.      

宽γ辐照剂量范围内硅泡沫本构模型研究

基于实验和理论建模研究了白炭黑增强硅泡沫材料在γ辐照剂量范围为0~1000kGy作用后的单轴压缩力学行为。实验结果表明辐照导致硅泡沫出现明显硬化现象,初始杨氏模量和固定应变下应力幅值均随γ辐照剂量近似线性增加。辐照后硅泡沫泡孔结构完整,硅橡胶基体中高分子交联反应占主导,且交联密度随辐照剂量线性增大。基于实验分析结果,实现了Ogden Hyperfoam超弹本构模型参数与辐照剂量的关联。结果表明初始剪切模量参数与辐照剂量成线性关系,硬化指数和泊松比参数与辐照剂量无关。基于应力应变实验数据拟合得到模型参数,并与未参与拟合的实验数据对比,验证了模型的准确性,表明该模型能够表征宽辐照剂量范围内硅泡沫的压缩力学行为。     

Impact of mixing procedure on phase morphology and fracture mechanical properties of carbon black-filled NR/SBR blends

Based on a viscoelastic model, the filler distribution and the amount of interphase of carbon black-filled blends of natural rubber (NR) with styrene-butadiene rubber (SBR) are evaluated. Hereby, the total dissipated energy \(G''\) during dynamical straining is decomposed into the contributions of the different polymer phases and the interphase. For the NR/SBR blends, we find a higher filling of the SBR phase and the interphase and a lower filling of the NR phase. The filler distribution itself depends not only on the affinity of the polymer to the filler but also on the mixing procedure. This is investigated by studying NR/SBR blends prepared by two different mixing procedures. In the standard mixing procedure, the polymers are mixed first, and then, the filler is added. In the batch mixing procedure, the filler is previously mixed in the NR only and then blended with SBR. Batch mixing is resulting in an increase in the filling of the interphase due to filler transfer from NR to SBR. The results for the filler distribution are compared to fatigue crack propagation rates under pulsed excitation. The crack propagation is accelerated when substituting NR with SBR. The batched samples show higher crack propagation rates at higher tearing energies due to a worse dispersion of the carbon black and/or higher filler loading of the interphase.     

GRT节能油添加剂的实用性能研究

在不同地区采用多种车型对GRT节能油添加剂的实用性能进行了不同条件下的远程行车试验和短程技术经济性能的考察,并与国外同类产品作了比较。结果表明,应用GRT节能油添加剂可以分别节约燃料油5％以上和机油50％以上,达到了八十年代国外同类产品的先进水平;能使东风牌汽车和解放牌汽车的汽缸磨损分别降低24％和33％以上;使用GRT添加剂可以明显地改善发动机汽缸的密封性,不仅提高了汽缸压力和发动机的输出功率,使其具有良好的加速性和冷起动性,而且改善了燃料油的燃烧状况,从而减少了汽车尾气对环境的污染。