The flow of polymer-thickened oils in convergent jet-thrust nozzles at a temperature of 84°C

It is shown that an existing form of jet-thrust device may be modified for satisfactory use at elevated temperatures. Jets are produced from a straight capillary tube and from three nozzles designed to provide different rates of uniaxial extension in the flowing oil, with shear present near the nozzle walls.The behaviour of three simulated multigrade motor oils with additives of different chemical type is compared with that of Newtonian oils at temperature of 84°C. In straight-tube flow, no measurable normal stress is detected in one of the oils (that with an alkylmethacrylate as polymer additive), but the other two oils give stresses which are measurable and, in one case, as high as those obtained at ambient temperature (that with the styrene-butadiene copolymer additive). For these oils the normal stresses measured in tubes are much closer to the axial stresses measured in nozzles than was the case at ambient temperature.In nozzle flow, axial stresses are detected in each oil which are rather lower than those measured at ambient temperature, the deviation increasing with increased jet velocity. The relative importance of axial stress, compared with shear stress, is shown to increase with increasing temperature and shear rate. The ration of axial stress to shear may reach a value of 3 or 4 at a shear rate of 10⁵set^?1, the oils with styrene-butadiene and styrene-isoprene copolymer additives being somewhat better performers than that with the alkylmethacrylate copolymer additive.It is suggested that the presence of normal, or axial, stresses might improve lubrication performance in those situations where normal load is applied with little relative movement of the bearing surfaces.     

Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient?

We investigate a variety of different semidilute polymer solutions in shear and elongational flow. The shear flow is created in the cone-plate-geometry of a commercial rheometer. We use capillary thinning of a filament that is formed by a polymer solution in the Capillary Breakup Extensional Rheometer (CaBER) as an elongational flow. We compare the relaxation time measured in the CaBER with relaxation times based on the first normal stress difference and the zero shear polymer viscosity that we measure in our rheometer. All of these three measurable quantities depend on different fluid parameters—the viscosity of the solvent, the polymer concentration within the solution, and the molecular weight of the polymers—and on the shear rate (in the shear flow measurements). Nevertheless, we find that the first normal stress coefficient depends quadratically on the CaBER relaxation time. Several scaling laws are presented that could help to explain this empirical relation.     

Combined slit and plate–plate magnetorheometry of a magnetorheological fluid (MRF) and parameterization using the Casson model

We describe a magneto-slit die of 0.34 mm height and 4.25 mm width attached to a commercial piston capillary rheometer, enabling the measurement of apparent flow curves of a magnetorheological fluid (MRF) in the high shear rate regime (apparent shear rates 276 up to 20,700 s^???1, magnetic flux density up to 300 mT). The pressure gradient in the magnetized slit is measured via two pressure holes. While the flux density versus coil current without MRF could directly be measured by means of a Hall probe, the flux density with MRF was investigated by finite element simulations using Maxwell® 2D. The true shear stress versus shear rate is obtained by means of the Weissenberg–Rabinowitsch correction. The slit die results are compared to plate–plate measurements performed in a shear rate regime of 0.46 up to 210 s^???1. It is shown that the Casson model yields a pertinent fit of the true shear stress versus shear rate data from plate–plate geometry. Finally, a joint fit of the slit and plate–plate data covering a shear rate range of 1 up to 50,000 s^???1 is presented, again using the Casson model. The parameterization of the MRF behavior over the full shear rate regime investigated is of relevance for the design of MR devices, like, e.g., automotive dampers. In the Appendix, we demonstrate the drawbacks of the Bingham model in describing the same data. We also show the parameterization of the flow curves by applying the Herschel–Bulkley model.     

An experimental test of equations predicting the load bearing capacity of squeeze films of elastico-viscous liquid

A form of squeeze film apparatus was recently described in which the movement of one plate towards the other was simulated by the continuous volume generation of liquid over the plate area. The liquid exuded from a large number of holes in the lower plate surface and formed a “continous flow” version of squeeze film apparatus with no moving parts [1]. A later paper gave derivations of equations from which squeeze film load bearing capacity could be evaluated, taking into account viscous, inertial and normal stress effects in the liquid film [2].In order to find the total load in a squeeze film system, it was necessary to obtain the relationship between the first normal stress difference and shear rate for the liquid in use, using an experimental method. At high shear rates, the jet thrust method provided these data [3,4] and from them the load bearing capacity of squeeze films of hot, polymer-thickened oil were predicted [2].A more complete test of the method is possible with a highly elastic liquid because considerable load enhancement due to extra stress is present at moderate deformation rates in squeeze film systems [1,5,6,7]. Thus a 0.1 per cent aqueous polyacrylamide solution gives well-defined load enhancement and (quite independently) the jet thrust method gives the relationship between normal stress and shear rate from which predictions of load enhancement may be made. Furthermore, convergent nozzles may be used in the jet thrust apparatus [3] to measure the stress development in an elastic liquid which is being simulateneously sheared and stretched, a situation which more closely resembles the squeeze film case than that of steady shear.     

The stresses of an upper convected Maxwell fluid in a Newtonian velocity field near a re-entrant corner

We investigate the stresses of an upper convected Maxwell fluid in the neighborhood of a re-entrant 270° corner. It is assumed (incorrectly, of course) that the velocity field is Newtonian. Both asymptotic analysis and numerical solutions are presented. It is found that, for a fixed angle, the stresses behave approximately as r^−0.74, which contrasts with a behavior as r^−0.91 at the walls (the latter is simply the square of the Newtonian shear rate at the wall, where the flow is viscometric). The analysis shows that there are boundary layers near the walls, in which there is a transition from the viscometric behavior at the wall to a core region which the behavior is dominated by the convected derivative in the constitutive equation. Moreover, our computations show large spurious stresses downstream resulting from numerical errors.     

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.      

一种预测层合板层间剪应力的新后处理方法

层合板是航空航天领域典型的承力构件,过大的层间应力是导致其分层失效的主要原因.准确的层间应力预测往往依赖于三维平衡方程后处理方法(TPM).然而,该方法需要计算面内应力的一阶导,使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力.本文在三维平衡方程后处理方法的基础上,提出了一种新后处理方法(NPM).新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导.基于提出的新后处理方法和C0型板理论,仅需使用线性单元就可以预测层合板的横向剪应力.为了验证所提方法的有效性,本文基于修正锯齿理论(RZT)和所提方法构造了一种C0连续的三节点三角形线性板单元.数值算例表明,所提方法和三维平衡方程后处理方法具有相同的计算精度,提出的板单元能够准确高效地预测层合板的横向剪应力.此外,所提方法便于结合现有的有限元商用软件使用,基于商用软件中板壳单元获得的节点位移,使用新后处理方法极易获得准确的层间剪应力.     

Load enhancement effects by polymer-thickened oils in strip squeeze film flow

A modification to existing equipment is described which permits continuous squeeze-film flow to be obtained between parallel-sided strips of material rather than between disc-shaped surface. Squeeze film flow is simulated by having liquid move through one of the surfaces via an array of equispaced holes. The Squeeze-film behavior of a Newtonian base oil is first tested at temperatures of 24°C and 55°C. It is shwon that loads are in reasonable agreement with theretical predictions and that end effects (corrected by means of a guard ring) and fluid maldistribution effects are of small proporitons. At the very highest liquid flowrates, the rapid liquid flow through the holes may influence the measured load. The Polymer-thickened oils, representinhg 10 W/30 and 10 W/50 motor oils, are tested at temperatures of 24°C and 55°C. Both oils five marked load enhancement, compared with Newtonian oil under similar flow conditions, at the higher flowrates used. The 10 W/50 oil gives load enhancement of 76 per cent at 55°C, increasing rapidly with the simulated approach velocity. Fluid inertia effects in the squeeze film flow aslo increase the load significantly. The results confirm earlier data using disc-shaped surfaces; load enhancement is greater in the present work on strip squeeze films because the fluid deformation rates are greater (2000 s^t-1 in planar extention and 2 x 10⁵ s^t-1 in shear). It is suggested that the fuel consumption of cars could be improved by the development of elastic, shear stable oils of lower viscosity than those currently in use.     

Shear rheology of polymer solutions near the critical condition for elastic instability

The use of constant viscosity, highly elastic polymer solutions, so called Boger fluids, has been remarkably successful in elucidating the behavior of polymeric materials under flowing conditions. However, the behavior of these fluids is still complicated by many different physical processes occurring within a narrow window of observation time and applied shear rate. In this study, we investigate the long-time shear behavior of an ideal Boger fluid: a well characterized, athermal, dilute, binary solution of high molecular weight polystyrene in oligomeric polystyrene. Rheological measurements show that under an applied steady shear flow, this family of polymer solutions undergoes a transient decay of normal stresses on a timescale much longer than the polymer molecule's relaxation time. Rheological and flow visualization results demonstrate that the observed phenomenon is not caused by polymer degradation, phase separation, viscous heating, or secondary flows from elastic instabilities. Although the timescale is much shorter than that associated with polymer migration in the same solutions (MacDonald and Muller, 1996), the appearance of this phenomenon only at the rates where migration has been observed suggests that it may be a prerequisite for observing migration. In addition, we note that through sufficient preshearing of the sample, the normal stress decrease suppresses the elastic instability. These results show that there is considerable uncertainty in choosing the appropriate measure of the fluid relaxation time for consistently modeling the critical condition for the elastic instability, the decay of normal stresses, and the migration of polymer species.     

Pressure-shear waves in 6061-T6 aluminum and alpha-titanium

Thepressure-shear plate impact technique is used to study material behavior at high rates of deformation. In this technique, plastic waves of combined pressure and shear stresses are produced by impact of parallel plates skewed relative to their direction of approach. Commercially pure alpha-titanium and 6061-T6 aluminum are tested under a variety of pressure and shear tractions by using different combinations of impact velocities and angles of inclination. A laser interferometer system is used to monitor simultaneously the normal and transverse components of motion of a point at the rear surface of the target plate. The experimental results are compared with numerical solutions based on an elastic/viscoplastic model of the material. Both isotropic and kinematic strain hardening models are used in the computations. The results indicate that unlike the normal velocity profiles, the transverse velocity profiles are sensitive to the dynamic plastic response and, thus, can be used to study material behavior at high strain rates. For the materials tested the results suggest that the flow stress required for plastic straining increases markedly with increasing strain rate at strain rates above 10⁴s^?1. Hydrostatic pressure of the order that exists in the tests (up to 2 GPa) does not affect the plastic flow in 6061-T6 aluminum and appears to have at most a minor effect on the deformation of the titanium.     

Interfacial stress analysis of a thin plate bonded to a rigid substrate and subjected to inclined loading

The so-called peel test, in which a thin plate bonded to a substrate is subjected to an inclined pulling force, has been widely used to characterise the bond behaviour of adhesives. This paper presents an analytical solution for the interfacial normal and shear stresses in such a peel test to provide an improved understanding of its underlying mechanism. An approximate closed-form solution is also presented. The effect of the peel angle (i.e. the angle between the applied force and the substrate) on the interfacial stresses is discussed. Apart from being a widely used test for quantifying adhesive characteristics, the process of debonding in a peel test resembles that of intermediate flexural-shear or shear crack induced debonding in flexurally strengthened RC members, where a relative vertical displacement exists between the two sides of the crack, leading to an angle between the external plate and the concrete substrate. Therefore, the results of this study also offer some insight into the latter failure mode which is very important in the flexural strengthening design of RC members.     

An experimental investigation into the kinematics of a concentrated hard-sphere colloidal suspension during Hopkinson bar evaluation at high stresses

The behavior of a concentrated, hard-sphere colloidal suspension is evaluated using the split Hopkinson pressure bar (SHPB) experimental technique. The composition of the suspension is measured using thermograviometric analysis before and after loading. This, combined with recorded pressure distributions, result in the conclusion that the suspension undergoes high rate squeezing flow. Experimental results demonstrate that the suspension exhibits shear thickening consistent with that observed in standard rotational rheometry. At sufficiently high stresses the suspension exhibits a second regime of shear thinning behavior that is consistent with elastohydrodynamic theory that incorporates the shear modulus of the particles themselves. Further increases in stress result in irreversible behavior, i.e., rather than fracturing or crushing, the particles form non-reversible agglomerates during testing. This fact is demonstrated through the use of dynamic light scattering and electron microscopy. This behavior occurs within a regime of viscous material response which is seen to occur at normal strain rates and stresses over 10⁴ s^?1 and 40 MPa, respectively.     

A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow

An overview of present understanding of microstructure in flowing suspensions is provided. An emphasis is placed on how the microstructure leads to observable bulk flow phenomena unique to mixtures. The bridge between the particle and bulk scales is provided by the mixture rheology; one focus of the review is on work that addresses the connection between microstructure and rheology. The non-Newtonian rheology of suspensions includes the well-known rate dependences of shear thinning and thickening, which have influence on bulk processing of suspensions. Shear-induced normal stresses are also measured in concentrated suspensions and include normal stress differences, and the isotropic particle pressure. Normal stresses have been associated with shear-induced migration, and thus have influence on the ultimate spatial distribution of solids, as well as the flow rate during processing; a second focus is on these uniquely two-phase behaviors and how they can be described in terms of the bulk rheology. An important bulk fluid mechanical consequence of normal stresses is their role in driving secondary flows.     

Recoil in macromolecular solutions according to rigid dumbbell kinetic theory

A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S _∞ is developed as a power series in κ^?, the shear rate prior to the cessation of the steady shear flow: $$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$ where η₀ and θ₀ values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ^?)³ is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ₂₂?τ₃₃ has the opposite sign from τ₁₁?τ₂₂.     

A reassessment of the wall effect of non-newtonian flow of polymer solutions

An apparatus for checking slip interpretation of flow anomalies in the laminar capillary flow of macromolecular solutions is described. It consists of a two-dimensional flow channel, having a uniform width of 1.5 inch and an alternative, convergent taper that is adjustable. Dilute aqueous solutions of the polymers Carbopol, Natrosol, and Polyox are recirculated in steady laminar flow from a large reservoir. Velocities, pressures, and wall shear stresses are measured. Local velocities are obtained by the local injection of conductive tracer fluid, whose passage is sensed by sets of electrodes stationed along the flow. Wall shear stresses are measured on a small, freely displaceable, traction surface flush with the channel wall. The tests cover concentrations of Carbopol of 0.1% to 0.4%, Natrosol of 0.5% to 1%, and Polyox of 0.5% to 1%. Approximate viscosities range from about 10 to 1000 cP. Wall shear rates up to 1000 s^–1 are attained.The results are in good agreement with the established viscometric properties of the tested materials. Actual shear stresses agree with those calculated from pressure drops, and velocities exhibit no detectable anomaly near the wall. Any velocity anomaly in the experiment would have to be less than 3% of the mean flow velocity.An order of magnitude analysis, based on particulate behavior, is made in an attempt to delineate an underlying mechanism.     

Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.     

Reverse squeeze film flow in a continous flow system

The continuous-flow squeeze film apparatus has been adapted to permit flow to take place in either direction. This simulates normal and reversed squeezing flow between discs by having liquid moving through the lower plate, with neither plate moving. The liquid exudes from 1580 uniformly-distributed holes in the plate surface. All tests were performed at a temperature of 24.0°C.Water is used in early tests, and it is shown that the contribution to load bearing from the inertia of the fluid is comparable in reverse and normal flows; fluid inertia increases the force which would be required to move the plates in either direction. A novel “mirror image” graphical presentation is used.Tests using a dilute polymer solution show load enhancement effects for both normal and reversed squeeze film flow. The enhancement is roughly equal in both directions of flow, with no transient effects, and fluid elasticity increases the force which would be required to move the plates in either direction. It is suggested that the stress developed in the fluid is independent of the direction of flow.The significance of the tests regarding lubricating problems is mentioned; the important case of rapid load reversal requires further attention.     

Theoretical and experimental investigation of the flow of a viscoelastic fluid in the gap between two rotating disks

A theory of the nonlinear viscoelastic behavior of polymer fluids has been constructed in [1]. The theory was used in [2] to investigate the motion of a nonlinear viscoelastic medium under steady and unsteady deformation rates in simple shear flow, and a comparison was made with experiment. The experiments in [2], which were performed on a cone-plate Weissenberg rheogoniometer, indicate that this arrangement is unsuitable for measurements of normal stresses under unsteady conditions in fluids with a fairly high viscosity. Below, we will show the suitability of using a disk-disk Weissenberg rheogoniometer to measure normal stresses in this case for unsteady conditions (transition to steady flow and stress relaxation). In this regard, a theoretical study of the flow of a viscoelastic fluid in the gap between rotating disks is needed. Note that in this case new information will be obtained from a comparison with simple uniform shear flow, since in the flow of a polymer between two disks all three normal stress components contribute to the axial force, while in the gap between a cone and a plate only the first normal stress difference contributes to the normal force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 25–30, March–April, 1976.     

Steady and transient shear flows of polystyrene solutions I: Concentration and molecular weight dependence of non-dimensional viscometric functions

Start up from rest and relaxation from steady shear flow experiments have been performed on monodisperse polystyrene solutions with molecular weight ranging from 1.3 × 10⁵ to 1.6 × 10⁶ and concentration c ranging from 5% to 40%. A method of reduced variables based on the use of a characteristic time τ_w is proposed. τ_w is defined as the product of zero shear viscosity with the steady state elastic compliance.Reduced steady and transient viscometric functions so obtained depend on the ratio M/M_e (where M_e is the entanglement molecular weight). Limiting forms are obtained when M/M_e ? 18. In steady flow, a simple correlation is found between shear and normal stresses.In stress relaxation experiments, independent of shear rate, the long-time behaviour can be characterised by a single relaxation time τ₁, which is identical for shear and normal stresses. τ₁ can be simply related to the zero shear rate viscosity and the limiting elastic compliance.