Processing Polymer Melts under Rheo-Fluidification Flow Conditions,Part 2: Simple Flow Simulations

The flow equations for melts submitted to conditions of Rheo-Fluidification processing described in Part 1 are determined and solved numerically. The pressure flow from an extruder feed end and drag flow from the modulated rotation of the rotor, i.e., under extrusion conditions with both cross-rotational and oscillatory flow, are combined. The value of pressure, shear stress, and viscosity along the flow path of the melt (a helicoidal motion around a divergent conic surface), for a given throughput and temperature, as the melt is moved through an annular gap of constant thickness are calculated. The simulation is restricted to the simpler case of low throughput where elongational flow can be assumed to be negligible and shear dominates the viscosity expression. The classic lubrication approximation hypothesis applied to a power law fluid is used. This assumption appears justified because of the geometry of the die, which consists of a thin annulus of 2 mm extended over a die length of 570 mm (see Part 1). The viscosity is expressed as a function of strain rate, which is calculated from the contribution of pressure flow, rotational flow, and superposed oscillation. The combined shear rate is calculated assuming a vectorial combination of the individual shear rates, following Cogswell who verified this hypothesis, and according to our own validation of this assumption on the same polymer, using a Couette without vibration.     

Improving Melt Flow Behavior via Melt Vibration

A self‐made melt vibration extrusion device was used to study the melt flow behavior in a vibration field. A pulse pressure was superimposed on the flowing melt during extrusion, called vibration assisted extrusion (VAE); conventional extrusion (CE) was studied for comparison. A die (L/D=17.5) was attached to the device to study melt flow behavior of an amorphous polymer (polystyrene) and semi‐crystalline polymers (high density and linear low polyethylene). Results show that the melt vibration technique is an effective processing tool to improve polymer melt flow behavior for both crystalline and amorphous polymers. Increasing with vibration frequency for extrusion at constant vibration pressure amplitude, the viscosity decreases sharply, and also with increasing vibration pressure amplitude at a constant vibration frequency. The effect of vibration field on melt flow behavior depends greatly on the melt temperature, with the largest change in viscosity obtained at low temperature. Increasing with vibration frequency at constant pressure vibration amplitude, the maximum decrease percentages of viscosities are 82.9, 66.7, and 48.9%, for HDPE, LLDPE, and PS, respectively; increasing with pressure vibration amplitude at a constant vibration frequency, the maximum decrease percentage of viscosities are 99.0, 94.3, and 99.0%, for HDPE, LLDPE, and PS, respectively.     

水平井体积压裂缝网表征及流动耦合模型

针对岩石脆性系数高且发育天然裂缝的储层,提出表征水平井体积压裂形成裂缝网络的三种基本模式,并将渗流过程划分为油藏流动和缝网内部流动.在此基础上,利用势叠加原理导出油藏流动控制方程,利用有限差分方法建立缝网内部有限导流等式;其次,采用星三角变换法处理人工缝与天然缝的交汇流动;最后,耦合两部分流动矩阵方程得到水平井体积压裂缝网渗流数学模型.该模型表明:当水平井改造段长度一定时,压裂段数与段内分簇数是决定产能的最主要因素,其次是人工裂缝半长和人工缝导流能力,而天然裂缝密度和导流能力对产量影响较小.实例应用表明,实际产油量与模型计算值一致,误差较小.     

Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

Melt Elongation Properties of Linear Low-Density Polyethylene

The melt extensional properties of a linear low-density polyethylene (LLDPE) were measured using melt spinning techniques in a range of temperature varying from 150 to 200°C, and the entry flow method in the capillary extrusion at 170°C was used to investigate the effects of elongation strain rate, temperature, and extrusion velocity in the capillary on the melt elongation stress and viscosity. The melt stretching force at break decreased nonlinearly with a rise of temperature. A low melt elongation viscosity might be beneficial to improve the melt drawability. With the increase of elongation strain rate, the melt elongation stress increased while the melt elongation viscosity decreased nonlinearly. Both melt elongation stress and viscosity decreased with a rise of temperature. Under the experimental conditions, the melt elongation stress and viscosity decreased with an increase of extrusion velocity in the capillary. Moreover, the relationship between the elongation viscosity determined from the entry flow and strain rate was similar to that from the melt spinning flow.     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics. Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid, as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Liquid Flow in a Porous Channel with Electrokinetic Effects

In this paper, a fully developed laminar flow in a porous channel between two paralleled flat plates in the presence of a double layer electric field is analyzed. The linear Poisson-Boltzmann equation is suggested to model the double layer electric field near the solid-liquid interface. The equation of motion is extended by including the electrical body force generating from the double layer field and then solved analytically. Different from previous models, our proposed one is continuous in the whole flow field and matches commonly-accepted models in the field of fluid mechanics.Besides, the effects of various physical parameters such as the zeta potential, the electrokinetic separation distance, and the ratio of the streaming current to conduction current on the velocity, the pressure, the apparent viscosity of the fluid,as well as the streaming potential are discussed. Physical explanations on the changing trends of those physical quantities with various parameters are given.     

Endoscopic Effects onPeristaltic Flow of a Nanofluid

In the present investigation we have studied the peristaltic flow of a nanofluid in an endoscope. The flow is investigated in a wave frame of reference moving with velocity of the wavec. Analytical solutions have been calculated using Homotopy perturbation method (HPM) for temperature and nanoparticle equation while exact solutions have been calculated for velocity and pressure gradient. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves.
Streamlines have been plotted at the end of the article.     

Studies on Rheological Behavior and Structure Development of High‐Density Polyethylene in the Presence of Ultrasonic Oscillations During Extrusion

The effects of ultrasonic oscillations on properties and structure of extruded high‐density polyethylene (HDPE) were studied. The experimental results show that ultrasonic oscillations can improve the surface appearance of the HDPE extrudates; increase the productivity of the HDPE extrudates; and decrease the die pressure, melt viscosity, and flow activation energy of the HDPE. The processing properties of the HDPE improve greatly in the presence of ultrasonic oscillations. Linear viscoelastic properties tests show that dynamic shear viscosity and zero shear viscosity decrease in the presence of ultrasonic oscillations. Ultrasonic oscillations can improve crystal perfection and thermal stability of HDPE. At appropriate ultrasound intensity, ultrasonic oscillations could also increase the mechanical strength of extruded HDPE. The gel permeation chromatography (GPC) results show that at high ultrasound intensity and low rotation speed of extrusion, ultrasonic oscillations causes chain scission of HDPE, which result in a decrease of molecular weight and an increase of melt flow index.     

Compressible Flow and Transonic Shock in a Diverging Nozzle

The paper is devoted to the study of compressible flows and transonic shocks in diverging nozzles in the framework of the full compressible Euler system. Consider a nozzle having a shape as a diverging truncated sector with generic opening angle: if the upstream flow at the entrance is supersonic and is near to an axial symmetric flow, and if all parameters of the upstream flow and the receiver pressure at the exit are suitably assigned, then a transonic shock appears in the nozzle. To determine the transonic shock and the flow in the nozzle leads to a free boundary value problem for a nonlinear partial differential equation. We prove that the receiver pressure can uniquely determine the location of the transonic shock, as well as the flow behind the shock. Such a conclusion was conjectured by Courant and Friedrichs, and is confirmed theoretically in this paper for the divergent nozzles. The main advantage of this paper compared with the previous studies on this subject is that the section of the nozzle is allowed to vary substantially, while the transonic shock is not assumed to pass a fixed point. The situation coincides with the requirement in Courant-Friedrichs’ conjecture. To describe the compressible flow we use the full Euler system, which is purely hyperbolic in the supersonic region and is elliptic-hyperbolic in the subsonic region. Solving the free boundary value problem of an elliptic-hyperbolic problem forms the main part of this paper. In our demonstration some new approaches, including the introduction of a pseudo-free boundary problem and the corresponding relaxation, design of a delicate double iteration scheme, are developed to overcome the difficulties caused by the divergence of the nozzle.     

Melt Vibration Improved Melt Flow Behavior and Mechanical Properties of High Density Polyethylene

A pulse pressure was superimposed on the melt flow resulting in melt vibration. With application of the melt vibration technology, the melt flow behavior and mechanical properties of high‐density polyethylene were studied. For vibration‐assisted extrusion (VAE) at constant vibration pressure amplitude, the viscosity decreases sharply with increasing vibration frequency, and also does so when increasing vibration pressure amplitude for VAE at constant vibration frequency. The effect of vibration field on melt rheological behavior is also related to the melt temperature; a large decease in viscosity is obtained at low melt temperature. Compared with the mechanical properties obtained by conventional injection molding (CIM), the mechanical properties for vibration‐assisted injection molding (VAIM) samples were improved by changing the vibration frequency and vibration pressure amplitude. Injected at constant low vibration pressure amplitude, the VAIM sample prepared at high vibration frequency shows large elongation at break; injected at constant low vibration frequency, the VAIM sample prepared at high vibration pressure amplitude shows greatly improved yield strength. The above two VAIM processing routes produce different VAIM samples with different fracture behaviors; a distinct layered structure for VAIM samples was observed by SEM.     

Imaging the velocity profiles in tubeless siphon flow by NMR microscopy

We report on the use of NMR micro-imaging to observe flow within a tubeless siphon. The flow is maintained in a visco-elastic liquid of high extensional viscosity, namely 0.5% w/v 8 million Dalton polyethylene oxide in water. The velocity profiles reveal a significant velocity gradient in the vertical direction as well as a transition from near-Poiseuille flow at the pipe entrance to plug flow far from the pipe entrance towards the base of the tubeless siphon.     

Effect on flow properties of tin-stabilized rigid PVC by PE paraffins having different degrees of branching

The processing properties of a rigid PVC compound with various amounts of different lubricants were studied with a torque rheometer. The plasticizing behavior was measured in a mixer and recorded as torque versus time. The fusion time and the torque at fusion and of the molten material were evaluated. The compounds were extruded with a laboratory extruder and a capillary die. The torque of the screw, the melt pressure, and temperature in the barrel and the die and the output were measured. The shear stress and shear rate were calculated from these results. The lubricants, one paraffin and five polyethylenes, had molecular weights of 700 to 3500. The dependence of the processing behavior on the molecular weight of the lubricants is discussed. There is no single value which can be given but numerous interdependent parameters can be used to obtain a prediction of the processing properties of the material.     

Flow boiling heat transfer of refrigerant R21 in microchannel heat sink

Boiling heat transfer in a refrigerant R 21 flow in a microchannel heat sink is studied. A stainless steel heat sink with a length of 120 mm contains ten microchannels with a size of 640×2050 μm at cross-section with a wall roughness of 10 μm. The local heat-transfer coefficient distribution along the heat sink length is obtained. The ranges of parameters are: mass flow from 68 to 172 kg/m²s, heat fluxes from 16 to 152 kW/m², and vapor quality from 0 to 1. The maximum values of the heat transfer coefficient are observed at the inlet of microchannels. The heat transfer coefficients decrease substantially along the length of channels under high heat flux conditions and, on the contrary, change insignificantly under low heat flux condition. A comparison with the well-known models of flow boiling heat transfer is performed and the range of applicability is defined.     

锯齿型通道流动和换热的周期性研究

本文对锯齿型通道内流动与换热的周期性进行了数值模拟.在Re=550～700范围内,入口段后的各几何周期的平均Nu数已随时间发生振荡,且随Re数增大,振荡起始位置朝入口方向移动;发生振荡的各几何周期的流场、无量纲温度场虽然在同一时刻不尽相同,但在不同的时刻可以找到近乎相同的流场和温度场,而且各几何周期平均Ⅳu数其振荡幅度基本相同,对时间求平均值后也基本相同,因此仍具有周期性充分发展的一些特性.     

Molecular interactions and structural effects on mixing pentanol in polyethylene glycol diacrylate and polyethylene glycol dimethacrylate

To understand the intermolecular interactions in binary mixtures of pentanol with polyethylene glycol diacrylate and polyethylene glycol dimethacrylate respectively, absolute viscosity and refractive index have been measured over the whole composition range, at 298.15 K, 303.15 K and 313.15 K, under atmospheric pressure. Molar refraction and interaction parameter have been calculated. The experimental data have been used to evaluate deviation in viscosity, deviation in refractive index and excess Gibb's free energy of activation for viscous flow, and the results have been fitted to Redlich-Kister polynomial equation.     

界面常质量流湍流（火用）传递

导出了常温下充分发展湍流传递方程组,依此研究了界面常质量流管内湍流传递,研究了由于粘性耗散、径向和轴向传质不可逆性引起的损率随流体性质、边界条件及空间位置的变化规律,分析了不同地点由于不同过程产生损失的机理.对单位长度的总损率计算表明,对给定的流体单位长度总损率是传质单元几何参数、边界条件和雷诺数的多元函数,通过损率最小化可设计和优化传质单元.     

Effects of Roller Speed,Die Temperature,Volumetric Flow Rate,and Multiple Extrusions on Mechanical Strength of Molten and Solidified LDPE under Tensile Deformation

An experimental rig coupled with a high speed data-logging and recording system and a personal computer was specially designed and constructed for the real-time measurement of mechanical strength (in terms of drawdown force) as a function of volumetric flow rate and roller speed for virgin low-density polyethylene (LDPE) and reprocessed LDPE during a filament stretching process. The effect of the number of extrusion passes for the reprocessed LDPE was our main interest. The experimental rig was connected to the end of a single-screw extruder, which was used to melt and extrude the polymers. The LDPE filaments were then solidified and collected for studying the mechanical properties. The mechanical strength of the virgin LDPE and reprocessed LDPE were investigated in both molten and solidified states. The mechanical strengths of the virgin and reprocessed LDPEs under these two states are discussed and compared in terms of change in magnitude under a wide range of processing conditions (volumetric flow rate, die temperature, and roller speed). The results suggested that in the molten state the drawdown force for LDPE melts was dependent on volumetric flow rate, die temperature, roller speed, and the number of reprocessing passes. The drawdown force being affected by the number of reprocessing passes could be explained by molecular degradation and gelation effects when using high volumetric flow rates. In the solidified state, the tensile properties of the solidified LDPE increased with roller speed. The effect of the number of extrusion passes for the solidified LDPE was similar to that for the molten LDPE. In the case of volumetric flow rates, the mechanical properties of the solidified LDPE decreased with increasing volumetric flow rate, whereas those of the molten LDPE exhibited the opposite effect. Thus, the mechanical strength of the molten LDPE could not always be used to assess the mechanical properties of the solidified LDPE.     

Experimental studies on natural convection of water in a closed-loop vertical annulus

Experimental studies on heat transfer and fluid flow of water in a vertical annulus, circulating through a cold leg forming a closed loop thermo-siphon, have been carried out in this article. The annulus has a radius ratio (outer radius to inner radius) of 1.184 and aspect ratio (length to annular gap) equal to 352. The experiments were conducted for constant heat fluxes of 1, 2.5, 5, 7.5, 10, 12.5, and 15 kW/m². Transient behavior during the heat-up period of the system until the steady-state condition is attained and discussed. Variation in the heat transfer coefficient and Nusselt number along the annulus height represent the developing boundary layer at the entrance and fully developed flow in the remaining length. A large drop in the differential pressure is experienced when the liquid is circulated through the flow meters, which restrict the flow due to their very small passages. Flow restriction causes mass accumulation and rise of pressure at the exit of the annulus. It also causes a decrease in liquid head in the cooling leg. An increase in the heat flux leads to an increase in the heat transfer coefficient and Nusselt number. As a result of the data analysis correlations for the average Nusselt number, Reynolds number and circulation rate have been developed in terms of the heat flux.     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.