Dynamics of Polymeric Fluids：Part Ⅱ The Molecular Theory of Die Swell： Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear (tan ) to the molecular parameters and the shear rate ( ) was deduced. It shows that the simple shear (tan ) may be resolved into free recoil (recoverable strain) and viscous heating (unrecoverable strain). The magnitudes of the simple shears for recoil (tan E) and (tan V) for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable (1- ) and unrecoverable ( ) conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears (tan E) for recoil and (tan V) for viscous heating are, respectively, expressed as the partition function to the (1- )th power and the partition function to the ( )th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( ), (L=D) and tr) were deduced respectively, which show that at very different shear rates ( ) the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [ , a, η0, GN0 and (1- )] and the operational variables ( , (L/D) and tr) were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

Dynamics of Polymeric Fluids: Part II The Molecular Theory of Die Swell: Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear (tan(?)) to the molecular parameters and the shear rate (γ) was deduced. It shows that the simple shear (tan(?)) may be resolved into free recoil (recoverable strain) and viscous heating (unrecoverable strain). The magnitudes of the simple shears for recoil (tan(?)E) and (tan(?)V) for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable (1-Wγ) and unrecoverable (W-γ) conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears (tan(?)E) for recoil and (tan(?)V) for viscous heating are, respectively, expressed as the partition function to the (1-Wγ)th power and the partition function to the (Wγ)th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n', a,η0, GN0 and (1-Wγ)] and the operational variables (γ, (L/D) and tr) were deduced respectively, which show that at very different shear rates (0≤γ≤∞) the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n', a,η0, GN0 and (1-Wγ)] and the operational variables (γ, (L/D) and tr) were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

Dynamics of Polymeric Fluids: Part Ⅱ The Molecular Theory of Die Swell: Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear(tanφ)to the molecular parameters and the shear rate(γ)was deduced. It shows that the simple shear(tanφ)may be resolved into free recoil(recoverable strain)and viscous heating(unrecoverable strain). The magnitudes of the simple shears for recoil(tanφE)and(tanφv)for viscous heating not only depended on the molecular parameters and the operational variables,but also on the exponential fractions of the recoverable(1-(W)γ)and unrecoverable((W)γ)conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears(tanφE)for recoil and(tanφv)for viscous heating are, respectively, expressed as the partition function to the(1-(W)γ)th power and the partition function to the(-(W)γ)th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n', a, η0, G0NN and(1--(W)γ)] and the operational variables(·γ, (L/D)and tr)were deduced respectively, which show that at very different shear rates(0≤·γ≤∞)the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=(L/D)], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n', a, η0, G0N and(1--(W)·γ)] and the operational variables(·γ,(L/D)and tr)were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene (HDPE) which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.     

气辅挤出胀大比与滑移段长度的关系

采用参数渐变法和Thompson变换,对粘弹性高分子熔体在不同气体辅助挤出口模内的流动进行了数值模拟研究。考察了体积流量、松弛时间和滑移段长度对挤出物挤出胀大比的影响。研究表明,熔体在滑移段的停留时间与材料松弛时间之比与挤出胀大比之间存在指数衰减关系,其实质是熔体在滑移段处于形变衰减过程。理论分析与数值模拟具有高度的一致性,表明该方程可用于指导气辅口模设计。     

聚合物熔体复合挤出胀大过程的数值模拟及可恢复弹性形变分析

建立了两种聚合物熔体流经矩形流道共挤出的三维数值计算模型,采用有限元方法数值模拟了共挤出成型过程及胀大过程,得到了速度场、压力场、应力场,并利用数值计算方法得到了共挤出流动过程的可恢复弹性形变场,分析了挤出胀大率以及可恢复弹性形变的变化过程。结果表明,在共挤出流动的胀大段,共挤出界面的形状和位置发生了改变;经矩形流道共挤出得到的挤出胀大末端截面形状为不对称的鼓形;在共挤出界面附近可恢复弹性形变值存在极值,运用数值方法计算可恢复弹性形变可以对流动过程中可能存在的缺陷进行预测。     

Transient Nonequilibrium Molecular Dynamic Simulations of Thermal Conductivity: 1. Simple Fluids

Thermal conductivity has been previously obtained from molecular dynamics (MD) simulations using either equilibrium (EMD) simulations (from Green--Kubo equations) or from steady-state nonequilibrium (NEMD) simulations. In the case of NEMD, either boundary-driven steady states are simulated or constrained equations of motion are used to obtain steady-state heat transfer rates. Like their experimental counterparts, these nonequilibrium steady-state methods are time consuming and may have convection problems. Here we report a new transient method developed to provide accurate thermal conductivity predictions from MD simulations. In the proposed MD method, molecules that lie within a specified volume are instantaneously heated. The temperature decay of the system of molecules inside the heated volume is compared to the solution of the transient energy equation, and the thermal diffusivity is regressed. Since the density of the fluid is set in the simulation, only the isochoric heat capacity is needed in order to obtain the thermal conductivity. In this study the isochoric heat capacity is determined from energy fluctuations within the simulated fluid. The method is valid in the liquid, vapor, and critical regions. Simulated values for the thermal conductivity of a Lennard-Jones (LJ) fluid were obtained using this new method over a temperature range of 90 to 900 K and a density range of 1–35 kmol · m^-3. These values compare favorably with experimental values for argon. The new method has a precision of ±10%. Compared to other methods, the algorithm is quick, easy to code, and applicable to small systems, making the simulations very efficient.Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22--27, 2003, Boulder, Colorado, U.S.A.     

Study on Modification Mechanism of Rare Earth in ZA27 Cast Alloy with Electronic Theory and Molecular Dynamics Method

A model of liquid ZA27 cast alloy is established according to molecular dynamics theory and an atomic structural model of co-existent a phase and liquid is also presented by means of computer programming. Recursion method is adopted to calculate the electronic structure of RE (rare earth) in grains and around phase boundaries respectively. The calculation shows that RE is more stable around phase boundaries than in grains, which explains the fact that the solution of RE in a phase is less, and RE mainly aggregates in front of phase boundary. The calculations of bonding order integrals also show that RE in front of phases hardly solidify onto the grain surfaces as active element so as to prevent grains growth and refine the grains. As a result, the modification mechanism of RE may be explained from the view of electronic structure.     

The Zeno (Z=1) Behavior of Water: A Molecular Simulation Study

The regularity of fluid properties observed at the Zeno or Z=PV/RT=1 point has been proposed as a means of testing and improving volumetric equations of state. Previous research has shown that molecular interactions can be qualitatively and quantitatively related to the linear Z=1 contour of T_r vs _r for pure fluids from the Boyle temperature to the triple point. In this study, we expand the molecular simulation analysis of previous work to gain a detailed microscopic understanding of the properties of Zeno-point systems. Our calculations show that popular semiempirical water models, such as SPC and SPC/E water, are able to replicate closely experimentally determined water properties in the Zeno-point region. Detailed molecular dynamics simulations of Z=1.00 and adjacent Z=0.75 and Z=1.25 states reveal common features over a wide range of temperatures and densities, from 77 to 1097°C and 1.01 to 0.029 g·cm^–3. Radial distribution functions of high-temperature, high-density Zeno-point fluids display remarkable long-range structural correlation well above the critical temperature and pressure, and examination of hydrogen bonding within each system shows that large water–water hydrogen-bonded clusters persist at high temperatures and supercritical densities. These results are compared to the existing extended corresponding-states approaches for pure fluid properties.     

A Schottky-Diode Model of the Nonlinear Insulation Resistance Effects in SPRTs—Part 1: Theory

The decreasing insulation resistance of standard platinum resistance thermometers (SPRT) above about 850 °C makes a major contribution to uncertainties in measured temperatures. In principle, the insulation breakdown ought to be easily modeled as a temperature-dependent shunt resistance depending principally on the insulator materials and dimensions. However, the phenomenon exhibits a complex nonlinear behavior that, to date, has defied explanation. The lack of an explanation is a major obstacle to improvements in SPRT design and to assessments of uncertainty caused by the insulation breakdown. This article suggests that the nonlinear effects are due to metal–semiconductor diodes, also known as Schottky-barrier or point-contact diodes, formed at the points of contact between the fused-silica insulators and the platinum of the SPRT sensing element and lead wires. The article presents an overview of the theory underlying Schottky diodes, shows that this model qualitatively explains the observations, and suggests practical experiments to verify the model.