Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates

The use of a sliding plate rheometer (SPR) to determine the first normal stress difference of molten polymers and elastomers at high shear rates is demonstrated. The simple shear flow in this instrument is not subject to the flow instabilities that limit the use of rotational rheometers to shear rates often below 1 s⁻¹. However, issues of secondary flow and wall slip must be addressed to obtain reliable data using an SPR. A highly entangled, monodisperse polybutadiene and a commercial polystyrene were the polymers studied. The inclusion of the polystyrene made it possible to compare data with those obtained by Lodge using a stressmeter, which is an instrument based on the measurement of the hole pressure. The data from the two instruments are in good agreement and are also close to the predictions of an empirical equation of Laun based on the storage and loss moduli.     

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.     

Sliding plate rheometry of planar oriented concentrated fiber suspension

The rheology of concentrated planar fiber suspensions is investigated. A new experimental technique for fiber suspensions based on a sliding plate rheometer incorporating a shear stress transducer is developed. It is shown that this instrument works well for the tested material systems. The rheological behavior in steady shear is subsequently investigated. The results can be largely explained by a combination of frictional and hydrodynamic interaction. Despite this evidence of friction no yield stress could be detected for the investigated shear rates. It was also found that the fiber aspect ratio did not influence the steady shear viscosity.     

Microstructure development in concentrated suspensions in a spinning ball rheometer

The spinning ball rheometer has been proposed as a method to measure the microstructure effect on the bulk rheological properties of concentrated suspensions. Recent experiments have shown that the measured extra torque on the spinning ball decreases as the radius of the spinning ball becomes comparable to the size of the suspended particle. We have performed a series of three‐dimensional boundary element calculations of the rheometer geometry to probe the microstructure effects that contribute to that apparent slip. We present a series of quasi‐static results based on random initial configurations as well as fully three‐dimensional transient calculations, both of which are compared to the available experimental data. For the two cases, the apparent viscosity decreased as the size of the spinning ball decreased relative to the suspended particle. Comparison of the quasi‐static and transient simulations indicates that the microstructure development is critical even at short times. In the transient calculations, the viscosity was observed to increase substantially relative to the torque based on the random initial configuration. Published in 2005 by John Wiley & Sons, Ltd.     

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.The project supported by the National Natural Science Foundation of China (10372090) and Doctoral Program of Higher Education in China (20030335001)The English text was polished by Ron Marshall     

Fiber orientation kinetics of a concentrated short glass fiber suspension in startup of simple shear flow

The common approach for simulating the evolution of fiber orientation during flow in concentrated suspensions is to use an empirically modified form of Jeffery's equation referred to as the Folgar–Tucker (F-T) model. Direct measurements of fiber orientation were performed in the startup of shear flow for a 30 wt% short glass fiber-filled polybutylene terephthalate (PBT-30); a matrix that behaves similar to a Newtonian fluid. Comparison between predictions based on the F-T model and the experimental fiber orientation show that the model over predicts the rate of fiber reorientation. Rheological measurements of the stress growth functions show that the stress overshoot phenomenon approaches a steady state at a similar strain as the fiber microstructure, at roughly 50 units. However, fiber orientation measurements suggest that a steady state is not reached as the fiber orientation continues to slowly evolve, even up to 200 strain units. The addition of a “slip” parameter to the F-T model improved the model predictions of the fiber orientation and rheological stress growth functions.     

Dynamic flow properties of vinylon fibre and glass fiber reinforced polyethylene melts

An experimental study of the dynamic shear flow properties of polyethylene melts filled with glass fibers and vinylon fibers was carried out and comparison with the steady shear flow properties was made. The effects of loading level and the characteristics of the fibers on the rheological properties of the fiber-filled systems is discussed. The rigidity and complex viscosity of the fiber-filled systems is sensitive not only to the quantity of fibers but also to their length, distribution and properties. The Cox-Merz empirical law for complex viscosity and steady shear viscosity, and Roscoe's empirical relation for estimating the normal-stress coefficients are both able to be applied to pure polymer melts but not to fiber-filled systems.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

A domain perturbation study of steady flow in a cone-and-plate rheometer of non-ideal geometry

The method of domain perturbation developed by Joseph is used to calculate velocity and stress profiles in a slightly misaligned cone-and-plate rheometer where the cone is spinning and the plate is stationary. Results for a Newtonian fluid, a Criminale-Ericksen-Filbey fluid, an upper-convected Maxwell fluid, and a White-Metzner fluid are presented and compared with earlier results in which the cone is stationary and the plate is spinning (Dudgeon and Wedgewood, 1993). Streamlines calculated for the Newtonian fluid show a very small recirculation region near the stationary plate. Velocity and stress contours are symmetric around the plane of largest gap width. For the elastic fluids studied, streamlines are asymmetric. The fluid response lags where the fluid is dominated by memory effects. Much larger recirculation regions are calculated for fluids dominated by shear thinning. These recirculation regions contain a large fraction of the fluid in the apparatus and have the effect of changing the shape of the flow domain for the remaining fluid that rotates around the cone's axis. Elasticity also has a pronounced effect on the stress profile, indicating that the accuracy of the cone and plate may be compromised even for small mis-alignments.     

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     

An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transition

Concentrated, non-crystallizing colloidal suspensions in their approach of the glass state exhibit distinct dynamics patterns. These patterns suggest a powerlaw rheological constitutive model for near-glass viscoelasticity, as presented here. The rheological parameters used for this model originate in the mode-coupling theory. The proposed constitutive model provides explicit expressions for the steady shear viscosity, the steady normal stress coefficient, the modulus-compliance relation, and the α peak of G″. The relaxation pattern distinctly differs from gelation.     

Laser Doppler measurements of flow in a cone-and-plate rheometer and the effect of cone misalignment

Laser Doppler velocimetry (LDV) is used to measure the flow profile of a Newtonian fluid in a cone-and-plate rheometer. The primary and secondary flow patterns are measured in the ideal geometry. The results confirm prior predictions of flow patterns. Flow profiles are also measured in the misaligned geometry in which the cone axis of rotation is tilted slightly off the perpendicular with the plate surface. Numerical predictions of these flow patterns (Dudgeon and Wedgewood, 1994) are also confirmed.     

钨纤维增强金属玻璃复合材料分段弹体侵彻性能研究

结合穿甲实验,基于复合材料细观有限元模拟,系统开展针对钨纤维增强金属玻璃复合材料分段弹体侵彻性能的研究,并与复合材料长杆弹进行对比分析。结果表明,相对于复合材料长杆弹显著的穿甲“自锐”行为和优异的侵彻性能,复合材料分段弹体在侵彻过程中的“自锐”特性有所减弱,且弹体结构容易发生分散,进而导致弹体侵彻能力明显降低。另外,分段数目和分段间隔等因素对复合材料分段弹体的侵彻性能具有一定影响,但总体而言,不同构型分段弹体的侵彻能力均弱于复合材料长杆弹。

     

Stability analysis in spatial mode for channel flow of fiber suspensions

Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.     

On the orientation of ellipsoidal particles in a turbulent shear flow

Direct numerical simulation (DNS) of small prolate ellipsoidal particles suspended in a turbulent channel flow is reported. The coupling between the fluid and the particles is one-way. The particles are subjected to the hydrodynamic drag force and torque valid for creeping flow conditions. Six different particle cases with varying particle aspect ratios and equivalent response times are investigated. Results show that, in the near-wall region, ellipsoidal particles tend to align with the mean flow direction, and the alignment increases with increasing particle aspect ratio. When the particle inertia increases, the particles are less oriented in the spanwise direction and more oriented in the wall-normal direction. In the core region of the channel, the orientation becomes isotropic.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

An experimental study of flow-induced fiber orientation and concentration distributions in a concentrated suspension flow through a slit channel containing a cylinder

Flow-induced fiber orientation and concentration distributions were measured in a concentrated fiber suspension (CFS) and a dilute one (DFS). The channel has a thin slit geometry containing a circular cylinder. In the previous work, many researchers have qualitatively studied fiber orientation and concentration distributions in injection-molded products of fiber-reinforced plastics. In the present work, however, they are quantitatively estimated by direct observation of fibers in the concentrated suspension flow. For the CFS, some fibers rotate in an expansion part between the channel wall and the circular cylinder, and the fiber orientation becomes almost random state. On the other hand, fibers are perfectly aligned along the flow direction owing to the elongational flow near the centerline downstream of the cylinder. The fiber concentration has a flat distribution except near the channel wall and the centerline. For the DFS a minimum in the fiber concentration distribution was clearly observed on the centerline, and two peaks beside the centerline and near the channel wall. This characteristic distribution is caused by the fiber-wall and fiber-cylinder interactions. It is found that the obstacle such as the circular cylinder in the channel significantly affects the fiber orientation downstream of the obstacle for the CFD, while it affects the fiber concentration distribution for the DFS.     

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expression, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expres- sion, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.