A simple model for non-linear stress relaxation

A simple model for the prediction of non-linear stress relaxation following the cessation of steady shear flow is proposed. The model allows the calculation of the shear and first normal stress difference components of the stress. The mathematical flexibility of the model is reduced to a minimum with the result that no adjustable parameters are employed and only linear dynamic deformation data are required to calculate the non-linear behaviour. Verification of the model was carried out with data available for two viscoelastic fluids and good agreement between the predictions and the experimental results was obtained for the range of shear rates examined (0.167 ? γ ? 16.7 sec^?1).     

聚合物流动诱导结晶数值模拟

通过模型定性分析剪切对熔体结晶动力学、晶体取向和流变学的影响.根据Avrami方程和晶体成核速率与第一法向应力差的关系模型模拟剪切对聚合物结晶动力学的加速作用,随着剪切速率和剪切时间的增加,整个结晶过程发展更快,活化晶核数目显著增多,剪切停止,活化晶核数目不再变化.但剪切对结晶的加速作用不是无限的,随着剪切速率和剪切时...     

Viscosity of polydimethylsiloxane gum: Shear and temperature dependence from dynamic and capillary rheometry

The rheology of Dow Corning polydimethylsiloxane gum (PDMS/silicone gum) was studied over a time range of 10^?2 to 10⁵ s^?1 and a temperature range of 23–150°C using both capillary and dynamic rheometry. A low shear Newtonian region is observed at room temperature below 0.01 rad/s (increasing to 0.1 rad/s at 150°C) for which an Arrhenius activation energy for a viscous flow of 13.3 kJ/mol was determined. The Cox–Merz rule for merging of shear and complex viscosities is found to be valid up to 10 s^?1. Viscosity is found to be independent of temperature above 100 s^?1, where terminal power‐law flow is encountered. This is exhibited in the dynamic data as equal plateau moduli for the various temperature curves. Gross wall slippage is seen in capillary flows above approximately 100 s^?1, corresponding to a stress value of 70–100 kPa. Slip‐stick (spurt) flow is not observed. The viscosity data are best fitted by the Carreau–Yasuda model with a fitting parameter a of 0.7, a power‐law index n of 0.05 (low because of slip effect), and a zero shear viscosity of 32 kPa s at 23°C. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2533–2540, 2002     

Shear dependence of thermal conductivity in polyethylene melts

Thermal conductivity measurements with a modified Couette flow cell were obtained as a function of shear rate for two linear polyethylene melts of weight-average molecular weights 27,300 and 56,700, respectively. The lower-molecular-weight polyethylene revealed a maximum decrease in thermal conductivity of 55 percent at 150 s^?1. After shearing at 400 s^?1, approximately 90 minutes was required to recover the value corresponding to the zero shear condition. This was considered consistent with molecular orientation into the flow direction during shear with a subsequent relaxation upon the removal of stress. The higher-molecular-weight polyethylene gave a similar decrease in thermal conductivity at 50 s^?1. Unlike the lower-molecular-weight melt, an increase was observed at higher shear rates. Enhancement of energy transport via cluster flow mechanism was presented as a possible interpretation of these results. A theory of molecular orientation of liquid poly(dimethylsiloxane) (PDMS) under shear flow was previously developed from thermal conductivity and birefringence data of this material. An attempt to clarify the difference in behavior between the two melts examined in this work, and between the polyethylene melts and the PDMS previously studied is presented.     

A novel sliding plate rheometer for molten plastics

A novel sliding plate rheometer has been developed that is suitable for use with molten plastics, concentrated polymer solutions, raw elastomers, and other viscoelastic or thixotropic materials. It can generate steady shear rates from 0.05 to 500 s^?1 and can also be used to measure linear viscoelastic properties. In addition, it can be used to measure a broad spectrum of nonlinear viscoelastic properties such as the nonlinear relaxation modulus and the shear stress growth coefficient. In order to measure these nonlinear properties it is necessary to generate large, uniform, transient deformations Involving high strain rates. Rotational and capillary melt rheometers are not capable of generating this type of deformation, and until now it was not convenient to use sliding plate rheometers for this type of application. However, the recent development of a reliable and robust shear stress transducer makes it very convenient to use the sliding plate geometry to carry out all of these tests. The new rheometer is described, and examples of the types of data it can generate are shown.     

Effect of shear stress on the growth of continuous culture of Synechocystis PCC 6803 in a flat-panel photobioreactor

The effect of hydrodynamic forces generated by air bubbles on cell growth of continuous culture of Synechocystis PCC 6803 was studied in a flat-panel photobioreactor. Keeping all relevant parameters constant enables the optimization of individual parameters, for which a continuous cultivation approach has significant advantages. Continuous culture of Synechocystis PCC 6803 was cultivated under different gas velocities from 0.022 m s^?1 up to 0.128 m s^?1. Based on direct determination of effective growth rate at constant cell densities, cell damage due to shear stress induced by the increasing gas velocity at the sparger was directly observed. A significant decrease of effective growth rate was observed at gas velocity of 0.085 m s^?1 generated at the gas flow rate of 200 ml min^?1, indicating cell damage by shear stress. Optimization of gas volume and the development of an effective aeration system corresponding to a given reactor setup is important to realize a reliable cell growth.     

The rheology and spin coating of polyimide solutions

The rheological properties of five types of concentrated polyamic acid and polyimide solutions are characterized by non-Newtonian shear viscosity η(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) and primary normal stress coefficient Ψ₁(\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma} $\end{document}) measurements over a wide range of shear rates. Onset of non-Newtonian flow of the polyamic acid solutions was observed in the shear rate range 30 to 400s^?1 and of the fully imidized polyimide solution at below 3 × 10^?2s^?1. Significant viscoelastic properties exemplified by normal stresses were observed in all the solutions. The solution rheology results are discussed in the context of spin coating for the deposition of thin films. The relative magnitude of effects of non-Newtonian flow on the dynamics of spin coating is assessed with a Deborah number characteristic of the flow.     

Nylon 6/poly(ethylene terephthalate) polymer blends: Rheological properties of melts

Melt rheological studies of nylon 6/polyethylene terephthalate (PETP) blends (PETP content varying from 10 to 50%) were carried out using capillary rheometer in the shear rate range of 58 s^?1 to 1.15 · 10³ s^?1. With increasing PETP content in the blend a decrease of the melt viscosity as well as non-Newtonian behaviour was observed. The model equation developed by Uemura and Takayanagi for viscoelastic melt blends has been used to understand the state of dispersion and morphology of a nylon 6/PETP blend system. Further, an inverse relationship between polymer melt viscosity (η) and elastic modulus (E') of fibres was observed.     

Yield stress and rheological characterization of the low shear zone of an epoxy molding compound for encapsulation of semiconductor devices

In encapsulation molding of IC packages, the melt flow inside the cavity is generally controlled in a low shear to prevent wire sweep, and other molding defects. Therefore, it is important to evaluate the rheological properties of epoxy molding compounds (EMC) in a low shear zone including determining the yield stress. In this study, a newly specialized Parallel‐Plate Plastometer for EMCs was built up. Using this plastometer, the yield stress and its temperature dependence were clarified, and the rheological properties in the low shear zone were evaluated. As a result, the rheological properties in a low shear zone of 0.1–10 s^?1 were characterized using the Herschel–Bulkley viscosity model which introduced the yield stress, the Castro–Macosko equation as a dependency model of cure, and the WLF equation as a dependency model for temperature. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Flow of slurries of coarse particles at high solids concentrations

Using a lock hopper feeding system, gravel and coal shale slurries containing particles of median diameter approximately 4 mm were transported at high concentrations through a pipe of I.D. 7.87 cm at velocities below 3.5 m/s^?1. In addition to the usual measurements of velocity, delivered concentration and hydraulic gradient, in-situ concentrations and particle velocities were determined. With these measurements, a two-layer model of stratified flow of the type proposed by Wilson was examined and found to give satisfactory predictions. Coefficients of wall friction were found to vary with velocity. Minimum values of these coefficients agreed with the results of direct shear tests. This variation could be attributed to stick-slip processes at low velocities and a change in the nature of the interparticle stress at higher velocities.     

Rheology of polymer melts in high shear rate

Little is known of the rheology of polymer melts in the high shear rate up to 10⁶ s^?1 or more. A specially designed high-shear-rate rheometer was developed, by which the rheology of polymer melts for shear rates up to 10⁸ s^?1 can be investigated. Two non-Newtonian regions and a transition or the second Newtonian region were observed in the wide range of shear rates up to 10⁷ s^?1. The observed flow curves for various polymer melts are classified into three typical patterns. One is the flow curve typically shown of high-density polyethylene in which a clear second Newtonian region appears after the first non-Newtonian region. The second is the typical flow curve of polystyrene in which a “transition region” appears instead of the second non-Newtonian region. The third is the flow curve shown of acrylonitrile-styrene copolymer, which exhibits behavior between the two types. A generalized flow curve is proposed to explain the observed flow behaviors of various polymers over a wide range of shear rates. The flow behavior in high shear rate results from high orientation and scission of polymer molecules.     

Finite element simulation of three-dimensional viscoelastic planar contraction flow with multi-mode FENE-P constitutive model

Viscoelasticity is a characteristic of many complex fluids like polymer melts, petroleum, blood, etc. The investigation of viscoelastic flow mechanism has practical significance in both scientific and engineering field. Owing to strongly nonlinear, numerical method becomes a practical way to solve viscoelastic flow problem. In the study, the mathematical model of three-dimensional flow of viscoelastic fluids is established. The planar contraction flow as a benchmark problem for the numerical investigation of viscoelastic flow is solved by using the penalty finite element method with a decoupled algorithm. The multi-mode finitely extensible nonlinear elastic dumbbell with a Peterlin closure approximation (FENE-P) constitutive model is used to describe the viscoelastic rheological properties. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids.     

Rheological properties of poly(trimethylene terephthalate) in capillary flow

The shear viscosity, extensional viscosity, and die swell of the PTT melt were investigated using a capillary rheometer. The results showed that the PTT melt was a typical pseudoplastic fluid exhibiting shear thinning and extensional thinning phenomena in capillary flow. There existed no melt fracture phenomenon in the PTT melt through a capillary die even though the shear rate was 20,000 s^?1. Increasing the shear rate would decrease the flow activation energy and decline the sensitivity of the shear viscosity to the melt temperature. The molecular weight had a significant influence on the flow curve. The flow behavior of the PTT melt approached that of Newtonian fluid even though the weight‐molecular weight was below 43,000 s^?1 at 260°C. The extensional viscosity decreased with the increase of the extensional stress, which became more obvious with increasing the molecular weight. The sensitiveness of the extensional viscosity to the melt temperature decreased promptly along with increasing the extensional strain rate. The die swell ratio and end effect would increase along with increasing the shear rate and with decreasing the temperature, which represented that the increase of the shear rate and the decrease of temperature would increase the extruding elasticity of the PTT melt in the capillary die. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 705–709, 2005     

Entrance flows of polymeric materials: Pressure drop and flow patterns

Flow at the entrance of a tube or channel is of interest in many polymer processes. Except for mathematical treatments at high Reynolds numbers and in creeping Newtonian flow, one must turn to empirical correlating equations and qualitative observations. These are discussed in two parts, one on pressure drop and the other on flow patterns. The discussion of pressure drop is largely a review, dealing with inertial, viscous, and elastic contributions to the pressure drop in tapered and sharp-edged entrances; also presented are new data for a viscoelastic polymer solution in tapered cone entrances. In the section on flow patterns, stress birefringent data for a very elastic solution flowing into a channel entrance show an unusual effect: stress discontinuities, not unlike “shock waves,” upstream and downstream of the entrances. This is in contrast to Newtonian and less elastic materials in which the stress patterns change gradually between the developed flow region and the entrance region.     

螺旋迭错式空间全曲面生物填料流场模拟分析

引言 填料是生物膜法装置的核心组成部分,除了提供生物膜生长的环境,还能过滤水中悬浮物.本课题组于2009年开发出了一种具有螺旋迭错式空间全曲面结构的生物填料(专利号:200920256153.7.以下简称空间全曲面填料).其结构如图1所示,由波纹状的三维全曲面结构PVC薄片构成,具有近似圆锥状的孔隙,使水流紊乱,产生许多旋涡.旋涡使浮游物依密度分离,滞留在填料内部的不同位置,其中含有细菌、真菌、藻类、原生动物和后生动物等微生物,这些微生物与填料表面结合并大量繁殖,从而形成生物膜(挂膜).大颗粒悬浮物易于被波纹状的孔隙拦截,孔隙率高(根据填料大小在82%～92.4%之间),过滤阻力小,可高效、顺畅地进行过滤.     

Numerical analysis of injection molding of glass fiber reinforced thermoplastics. Part 1: Injection pressures and flow

Numerical calculations of flow and injection pressures during injection molding of fiber-filled thermoplastics are compared to experimental measurements. The flow is modeled as a 2–D, nonisothermal, free-surface flow with a new viscosity model dependent upon temperature, pressure, and fiber concentration. The steady-state viscosity model is developed to account for the fiber-concentration and shear-thinning viscosities of the polymer based upon combining the Dinh-Armstrong fiber model with the Carreau viscosity model. The new model has four parameters, three from the Carreau model and one from Dinh-Armstrong for fiber concentrations. The new model calculates reasonably well the steady-state viscosity of fiber-filled polypropylene over the shear rate range of 0.01 s^?1to 20 s^?1. The numerical work successfully describes the flow of fiber-filled polymers during injection molding using finite-difference solutions for the transport equations and marker particles to track the flow front. The comparisons between the calculated and measured pressure drops for an injection molded part were reasonable for the unfilled and fiber-filled polypropylene materials. The pressure drop comparison is very good for slow fill of a base case resin, Himont polypropylene, but not as good for fast fill of the resin. The pressure drop comparison is very good for fast fill of glass-filled resin, DSM polypropylene with 10% and 20% short fibers, but not as good for slow fill of the resin and resin plus fibers.     

壁面润湿性对蛇形微通道内两相流流动特性影响的格子Boltzmann模拟

在90°Y形汇流的矩形截面蛇形微通道内,采用格子Boltzmann方法对不同接触角的蛇形微通道内气液两相流动进行了数值计算。首先以空气和水为工作流体对气液两相流动进行模拟研究并通过实验进行验证。验证模型合理性后,根据模拟计算结果,以气液相流速为坐标绘制了不同接触角下的流型图并分析其差异性及原因;同时深入研究了液相黏度和接触角对于弹状流流体力学性质的综合影响;比较了具有不同接触角壁面的蛇形微通道内两相流压降、摩擦因子、壁面摩擦系数和剪切应力的分布规律,并讨论了蛇形微通道内气液两相流动的影响因素。研究表明疏水壁面即接触角大于90°时,微通道内两相流压降、摩擦因子、壁面摩擦系数和剪切应力均低于亲水壁面微通道内相关参数,更利于流体流动。     

Shear viscosity,extensional viscosity,and die swell of polypropylene in capillary flow with pressure dependency

The shear and extensional viscosities of a polypropylene resin were studied using a capillary rheometer and capillary dies of 1‐mm diameter and length of 10, 20, and 30 mm. Melt temperatures at 190, 205, and 220°C and shear rates between 100 and 5000 s^?1 were used. At the highest shear rate a visible melt fracture was observed. An equation relating the pressure drop and die length was derived with consideration of pressure effects on melt viscosities and the end effect. After the correction for pressure effects the true wall shear stress and end effect at zero pressure were calculated. The end effect showed a critical stress of melt fracture around 10⁵ Pa, and increased rapidly when shear stress increased above the critical stress. From shear stress the shear viscosity was calculated, and a power law behavior was observed. Extensional viscosity was calculated from the end effect and showed a decreasing trend when strain rate increased. After time–temperature superposition shift shear viscosity data correlated well, but an upward trend was observed in extensional viscosity when melt fracture occurred. Die swell ratio at different temperatures can be plotted as a function of wall shear stress and was higher for shorter dies. © 2002 Wiley Perioodicals, Inc. J Appl Polym Sci 84: 1269–1276, 2002; DOI 10.1002/app.10466     

Rheological Behavior of Wastewater Sludge Following Cationic Polyelectrolyte Flocculation

The rheological characteristics of the wastewater sludge were investigated by using a Haake Rheostress RS 75 rheometer. The shear creep compliance experiments and the dynamic viscosity measurements were conducted. The shear creep compliance experiments indicate the addition of polymer coagulants to the sludge samples will form more rigid structures. The elastic solid-like behaviors were always observed in the samples with polymers. The Voigt model was successfully employed in modeling the viscoelastic retardation behavior of sludge samples in the shear creep compliance tests. Moreover, the dynamic viscosity curves of the sludge samples with/without polymer could be described by the power law model of Ostwald and de Waele at the medium shear rates, ca. 100–300 s^?1. Consequently, addition of polymer to the sludge tends to extend the applicable ranges of the shear rates for the power law model as well as to decrease the power law index.