Influence of molar mass distribution and long-chain branching on strain hardening of low density polyethylene

Low-density polyethylenes (LDPE) were synthesized in a laboratory-scale autoclave under high pressure. These samples were found to possess a high molar mass tail, resulting in a distinctly bimodal molar mass distribution and a lower concentration of long-chain branching than typical of commercial LDPEs. Rheological experiments in elongation showed that these samples exhibit a very pronounced strain hardening, which could be favorable for distinct processing operations. Although the samples have a rather high molar mass ( g/mol), their zero shear-rate viscosities η ₀ and their shear thinning behavior are still in a range, where thermoplastic processing is possible. A qualitative understanding of the experimental results is tried by the model of the Cayley tree.

Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity

Linear high-density polyethylenes with molar masses M _w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η₀ covered a range from 2.5×10⁻³ to around 10⁸ Pas. Above a critical molar mass of M _c≈2,900 g/mol, the experimental results can be described by the relation η₀ ∼ M _w^3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M _w but not on M _w/M _n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M _w and also on M _w/M _n.

Simultaneous stress and birefringence measurements during uniaxial elongation of polystyrene melts with narrow molecular weight distribution

Tensile stress and flow-induced birefringence have been measured during uniaxial elongation at a constant strain rate of two polystyrene melts with narrow molecular weight distribution. For both melts, the stress- optical rule (SOR) is found to be fulfilled upto a critical stress of 2.7 MPa, independent of strain rate and temperature. Estimation of the Rouse times of the melts, from both the zero-shear viscosity and the dynamic-shear moduli at high frequency, shows that the violation of the SOR occurs when the strain rate multiplied by the Rouse time of the melt exceeds by approximately 3. The presented results indicate that in contrast to current predictions of molecular theories, the regime of extensional thinning observed by Bach et al. (2003) extends well beyond the onset of failure of the SOR, and therefore the onset of chain stretch in the non-Gaussian regime.

Correlation between rheological behaviour in uniaxial elongation and film blowing properties of various polyethylenes

Six various low density polyethylenes and one blend were rheologically characterized in elongation. Their different strain-hardening behaviour could qualitatively be related to their molecular structure. All the materials were blown to films on laboratory equipment under various conditions. The take-up force and the film homogeneity were determined quantitatively, the bubble stability was visually assessed. The bubble stability increased with growing take-up force. The take-up force was found to be the stronger the higher the elongational viscosity was. The homogeneity of film thickness is not related to the bubble stability but to the occurrence of strain hardening in the uniaxial elongational experiment at high Hencky strains. Measurements of the uniaxial elongational behaviour of polyethylene melts are a valuable and promising way to assist the development and optimisation of film blowing materials.

Microscale Synthetic Schlieren

We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range of ecological and environmental oceanic processes on the microscale.

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Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

For processing operations with a pronounced elongational component, it was found that the uniformity of extruded items is improved by the presence of strain hardening usually measured in uniaxial elongation. Many processing operations such as foaming, film blowing, and blow molding are dominated by biaxial deformations, however, and therefore, the question arises how strain hardening in uniaxial and biaxial deformation compares. Besides a linear and long-chain branched PP, one classical LDPE, an HDPE pipe extrusion grade with a bimodal MMD, and a LCB-mPE were also characterized. For the measurements in uniaxial elongation the Münstedt tensile rheometer (MTR) and the ARES-EVF were used, while the lubricated flow method was applied for equibiaxial deformation. It was found that the strain hardening in uniaxial elongation is more pronounced. The dependence of strain hardening on strain rate is qualitatively the same in both modes. In the range of strain rates, the chosen long-chain branched LDPE and PP exhibit a strain hardening, which is approximately independent of the elongational rates applied, whereas for the HDPE it becomes smaller with increasing rate.

A model of a subcritical Joule–Thomson cryocooler with condensation inside the recuperator

To develop a tool for predicting of heat and mass transfer in Joule–Thomson cryocoolers working at subcritical pressures, we study a counter flow heat exchanger with condensation by employing the integral method. The effects of inlet pressure and working fluid are predicted. We also show that there is an optimal value of the enthalpy difference along the heat exchanger for which its length is minimal.

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Turbulence measurements in a swirling pipe flow

This paper reports laser-Doppler measurements of the mean flow and turbulence stresses in a swirling pipe flow. Experiments were carried out under well-controlled laboratory conditions in a refractive index-matched pipe flow facility. The results show pronounced asymmetry in mean and fluctuating quantities during the downstream decay of the swirl. Experimental data reveal that the swirl significantly modifies the anisotropy of turbulence and that it can induce explosive growth of the turbulent kinetic energy during its decay. Anisotropy invariant mapping of the turbulent stresses shows that the additional flow deformation imposed by initially strong swirling motion forces turbulence in the core region to tend towards the isotropic two-component state. When turbulence reaches this limiting state it induces rapid production of turbulent kinetic energy during the swirl decay.

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Variational optical flow estimation for particle image velocimetry

We introduce a novel class of algorithms for evaluating PIV image pairs. The mathematical basis is a continuous variational formulation for globally estimating the optical flow vector fields over the whole image. This class of approaches has been known in the field of image processing and computer vision for more than two decades but apparently has not been applied to PIV image pairs so far. We pay particular attention to a multi-scale representation of the image data so as to cope with the quite specific signal structure of particle image pairs. The experimental evaluation shows that a prototypical variational approach competes in noisy real-world scenarios with three alternative approaches especially designed for PIV-sequence evaluation. We outline the potential of the variational method for further developments.The publications of the CVGPR Group are listed under .

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An application of Gappy POD

An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt Soc Am A 12(8):1657–1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38, and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge by examining the subspace spanned by the POD eigenfunctions.

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Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing

The understanding of the physics of flapping flight has long been limited due to the obvious experimental difficulties in studying the flow field around real insects. In this study the time-dependent three-dimensional velocity field around a flapping wing was measured quantitatively for the first time. This was done using a dynamically-scaled wing moving in mineral oil in a pattern based on the kinematics obtained from real insects. The periodic flow is very reproducible, due to the relatively low Reynolds number and precise control of the wing. This repeatability was used to reconstruct the full evolving flow field around the wing from separate stereoscopic particle image velocimetry measurements for a number of spanwise planes and time steps. Typical results for two cases (an impulsive start and a simplified flapping pattern) are reported. Visualizations of the obtained data confirm the general picture of the leading-edge vortex that has been reported in recent publications, but allow a refinement of the detailed structure: rather than a single strand of vorticity, we find a stable pair of counter-rotating structures. We show that the data can also be used for quantitative studies, such as lift and drag prediction.

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Two- and three-dimensional flows in nearly rectangular cavities driven by collinear motion of two facing walls

Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Γ. The axial aspect ratio Λ > 10 is large to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes which defines two Reynolds numbers Re _1,2. Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re _1,2 for Γ = 0.76 and Γ = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with corresponding linear-stability calculations. Particular attention is paid to the flow for Γ = 1 under symmetric and parallel wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional velocity field and the bifurcation show an excellent agreement with numerical simulations.

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DPIV study of the effect of a gable roof on the flow structure around a surface-mounted cubic obstacle

The present paper reports a thorough comparison of the turbulent flow characteristics exhibited by a cubic surface-mounted obstacle and a simple geometric variant (gable roof of 30° roof pitch). The measurements supporting this study were obtained by the use of a 2D-DPIV system. Significant differences in the large-scale vortical structures and turbulent kinetic energy fields implied drastic consequences with respect to the advective and turbulent dispersive characteristics of the flow at roof and ground levels.

Capillary rheometry for polymer melts revisited

Capillary rheometry provides an efficient access to high shear rate flow properties relevant for processing. An automated gas driven capillary rheometer developed at BASF enables accurate measurements at imposed wall shear stress, thus supplementing instruments operating at imposed flow rate. A simplified treatment of dissipative heating based on the assumption of a radially flat temperature profile is outlined and justified by means of finite element simulations. The combined treatment of dissipation and pressure dependent viscosity yields relations to treat throttling experiments at imposed flow rate. Throttle pressure coefficients from a long die and an orifice agree for LDPE but significantly differ for PMSAN. The effect is explained on the basis of identical pressure coefficients for shear and elongational flows, with regard to a constant stress, however. The effect of melt compressibility is negligible in practical capillary rheometry if the temperature and pressure coefficients of the melt density are by an order of magnitude smaller than those of the viscosity. Gas pressure driven instruments allow an effective determination of wall slip velocities from Mooney plots. This is of advantage for the investigation of the mechanism of additives or processing aids. Furthermore, imposed pressure experiments are pertinent to investigate the spurt effect of HDPE and to demonstrate that two different slip processes contribute to the apparent flow curve above spurt.

A random synthetic jet array driven turbulence tank

We measure the flow above an array of randomly driven, upward-facing synthetic jets used to generate turbulence beneath a free surface. Compared to grid stirred tanks (GSTs), this system offers smaller mean flows at equivalent turbulent Reynolds numbers with fewer moving parts.

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The dynamics of a boiling bubble before and after detachment

An overview is given of prediction methods for motion and deformation of a bubble that is created by boiling at a wall, at times before and after detachment, with a focus on added mass forces in the vicinity of the wall. The possibility to apply added mass coefficients derived in potential flows also to flows with vorticity is examined. An introduction to Lagrangian methods is given. Added mass tensors are derived for deforming bubbles at and away from a plane wall. Expressions for induced hydrodynamic lift forces are given, and validation experiments are briefly discussed.

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A distributed parameter integral model for predicting the thermal performance characteristics of single- and multi-wall radiation heat shield systems

Heat shielding has become an increasingly necessary means for protecting temperature-sensitive components from direct exposure to thermal radiation from high temperature sources. A simple but comprehensive distributed parameter integral model has been developed for predicting the temperature distribution of the shield and the protected component for a variety of heat shield systems. The integral model presented here is seen to be more accurate than lumped models, and can be computed with much greater speed than that required for numerical models.

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Investigation of the three-dimensional intermediate wake topology for a square cylinder at high Reynolds number

Simultaneous multi-point hotwire measurements are used to investigate the three-dimensional wake topology of a square cylinder at high Reynolds numbers. Wavelet techniques are applied to detect the flow structures and to inquire on the validity or extension of previously proposed low Reynolds number topological models to turbulent wakes. Our results suggest that a flow topological model similar to the horizontal perturbation model proposed by Meiburg and Lasheras (J Fluid Mech 190:1–37, 1988) but with alternate rib cuts in the horizontal plane is plausible for the intermediate wake topology.

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Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.

The entrainment behavior of a turbulent axisymmetric jet in a viscous host fluid

Although turbulent jets have been studied extensively, one configuration that has not received much attention is the viscosity-stratified jet, wherein a turbulent jet of lower viscosity issues into a density-matched host liquid of higher viscosity. We present experimental data for scalar dispersion and two-dimensional velocity measurements in the axial plane of a turbulent axisymmetric jet with a Reynolds number (Re) of 2,000 issuing into a viscous host liquid at viscosity ratios (m) ranging from 1 to 55. The presence of a strong viscosity discontinuity across the jet edge results in a significant decrease in the scalar spread rate. We attribute this to the rapid reduction in turbulence intensity and the suppression of large engulfing eddies at the jet edge. The velocity profile, on the other hand, indicates that the velocity width and mass flux reduce with increasing m up to about 20, but then increase for higher values of m. This non-monotonic variation is explained by the growing influence of viscous stress for m>20. The scalar spread rate, the velocity spread rate, the centerline velocity decay rate, and the jet mass flux are all minimized for m20 for Re=2,000.

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