高分子熔体和浓溶液流变性能的研究

基于多重缠结网络结构模型和高分子链上缠特点在流动中可进行动态解缠和再缠结的多重蠕动机理，用统计力学和动力学相结合的方法，分别了出了缠结链组的末端距分布函数；处于缠结状态下高分子链构象统计分布函数；受力下聚合物是性形变自由能和解除外力下高分子挤出体可回复性粘弹性形变自由能，提出了高分子挤出体可回复形变的粘弹性分子理论。推导出了的高分子熔体的回忆函数、简单剪切流下的本构方程和物料函数，并采用一种新的方法测定出物料的四种参数：η０、Ｇ＾０Ｎ、ｎ′和≤。对于高分子挤出体。可回复性粘弹性形变由快速弹性形变和慢速粘弹性形变两者组成，当把两种变量的复合结构参数－分子链的反式构象分数引入两种形变自由能表达式后，就从理论上得到了可回复形变量同挤出胀大比间的定量表达式，从而建立起一具有分子链结构参数的新的挤出胀大比方程，可回复形变     

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusion: Correlations of Total and Ultimate Extrudate Swell Effects to Growth Time, Shear Stress and Aspect Ratio Under the Free States

利用挤出胀大动力学理论研究稳态剪切流下HDPE 和PBD液体的挤出胀大行为,建立了自由动态下线团回复和挤出胀大增长时间的回复机制和动力学. 结果表明在自由回复过程中自由线团回复和挤出物胀大增长可分为两个区域(瞬间和推迟区)、三个增长阶段(瞬间、推迟和最终阶段). 证明了自由线团回复和挤出胀大增长可表征为增长时间、剪切应力和长径比的函数。从而从动力学理论推倒出了三种挤出胀大效应(瞬间、推迟和最终)同分子结果参数和挤出操作条件间的相关性. 并建立了总合(TESE)和最终(UESE)两组挤出胀大效应的普适方程.     

均聚物结晶与熔融化转变的稳态和亚稳态统计理论Ⅴ 分子分凝统计结晶动力学—结晶增长速率对结晶生长机制和高聚物起始结构的依赖性

首先对结晶增长速率同浓度、分子量和链柔性依赖性进行总结，然后基于微晶核和粒——高分子键组网络结构模型和高分子分子分凝统计结晶动力学，根据高分子链组是微晶粒同连接链段复合体的结构特征及它们间存在的四个相关性（并存性、简并性、顺反式构象共存性和物料守恒性）的事实，成功地把连接链段缩短增长动力方程同微晶粒体积增大增长动力方程有机结合在一起，从理论上创建出一种微晶粒数增长速率和微晶粒尺寸增长速率表达的一般化计算法，推导出结晶体系的微晶粒数增长速率和微晶粒尺寸增长速率同四种增长机制（近邻折叠，近邻伸直，近邻折叠同近邻伸直并联并存和近邻折叠同近邻伸直串联并存）、结晶温度和高分子起始结构（分子量）间定量表达式．当把分子量的指数同链的构象分数相连后，就又从理论上得到了分子量指数同温度和链柔性间的关系式，并讨论了它们同增长机制间的关系，最后以大量结晶动力学实验数据对上述所得到的关系式进行了验证，结果表明它们均能同实验结果很好符合．     

Correlation of Cooperatively Localized Rearrangement on the “Fluidized Domain” of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

基于α-和β-微区、微晶、交联和缠结链组网络结构和非线性粘弹性复相涨落模型,提出了双重(物理和力学)老化下不同尺寸和末端向量高分子链组的流动化微区内关联性局部化重排动力学新理论,它能把初级α-微区的降解作用和次级β-微区的再生效应对剪切速率、尺寸大小和温度依赖性有机结合起来．然后用统计力学和动力学结合法计算了三种不同类型高聚物在等温等压双重老化过程中多元链组的总构象改变自由能,证实了它起源于多元链组的尺寸大小、形状和体积的变化．推导出了它们单向拉伸下的本构方程、应力松弛模量和蠕变柔量表征式以及它们相对应的两组对比态普适方程．结果表明该两组对比态下应力松弛模量和蠕变柔量普适方程均具有同K-W-W伸展指数函数完全一致的形式．最终又建立了该两组对比态普适方程中三个分子参数同老化条件、温度和高聚物起始结构之间的相关性．     

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.     

Numerical Simulation of the Melt Spinning Process of Noncircular Fibers Incorporating Surface Tension

Incorporating surface tension, a mathematical modeling system was established to simulate the melt spinning process of a noncircular fiber. A Newtonian fluid was assumed and an isothermal spinning process was considered. Finite element method was adopted to solve the system. The predicted shape of as‐spun fiber was compared with experiments. It was found that surface tension was a key factor in the spinning process of noncircular fibers, which would greatly change the fiber cross‐sectional shape. Simulation would fail to predict the noncircular fiber shape accurately if surface tension was ignored. The fiber shape change caused by the velocity rearrangement only occurs near the spinneret, but surface tension would keep changing the curvature of the fiber surface along the spinline. Die swell of fiber extrudate during the spinning process was also investigated and it was found that die swelling of fiber extrudate near the spinneret was greatly suppressed by the stretch imposed by a take‐up device, when compared with the free extrusion process.     

Joule heating and viscous dissipation effects on MHD flow past a semi-infinite inclined plate with variable surface temperature

A numerical investigation is performed to study the MHD free convection flow past a semi-infinite inclined plate subjected to a variable surface temperature. The Joule heating and viscous dissipation effects are taken into account in the energy equation. The governing equations of the flow are transformed into a nondimensional form using suitable dimensionless quantities. A fully developed implicit finite-difference scheme of Crank-Nicolson type is engaged to solve the dimensionless governing equations, which is more accurate, fast convergent, and unconditionally stable. The effects of the MHD, inclination angle, power law, Grashof number, Prandtl number, Joule heating, and viscous dissipation effects are studied on the velocity, temperature, shear stress, and heat transfer coefficients during transient periods. It is observed that the MHD has retarding effects on velocity.     

The Sharkskin Onset and Stability Diagram

The onset of sharkskin extrudate was investigated in terms of molecular structure, molecular weight, temperature, and die geometry. The recoverable shear S_R or the ratio of wall shear stress over the storage modulus was determined and found to be independent of molecular weight, temperature, and die geometry for linear low-density polyethylenes (LLDPEs), but it depended critically on these factors and the molecular weight distribution for high-density polyethylenes (HDPEs). The plot of S_R versus λ _s /? _s , or the sharkskin wavelength roughness amplitude ratio, constituted a sharkskin marginal stability curve common for all molecular weights, temperatures, and die geometry investigated; it is unique for each polymer type or molecular structure. Sharkskin instability occurred without hysteresis effect.     

Stripe patterns in the magnetic reorientation of a glass-forming nematic liquid crystal

We study spontaneous pattern formation in a glass-forming nematic liquid crystal during the magnetically induced dynamic Fréedericksz transition. Pattern growth rates and wavelengths as functions of the magnetic field are extracted from optical transmission textures of thin planar cells. The characteristics of the observed stripe pattern can be related to viscoelastic parameters of the nematic by means of a linear stability analysis of director fluctuation modes. The viscous properties of the material allow to vary the time scales of the experiment with temperature by orders of magnitude, leaving the spatial structure of the pattern essentially unchanged. We find that the ratios of shear and rotational viscosity coefficients relevant for the pattern wavelength selection remain constant in the temperature range investigated, whereas their absolute values change by almost two orders. Received 23 November 2001 and Received in final form 19 April 2002     

An elastic,plastic, viscous model for slow shear of a liquid foam

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called “quasi-static”) limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.     

Activation energy of shear transformation zones: a key for understanding rheology of glasses and liquids

Key manifestations of the glassy and liquid states, such as viscous flow and structural relaxation, occur spatial and temporal heterogeneously, within highly localized rare events, termed shear transformation zones. Characterization of these basic entities with respect to thermal activation and mechanical response is vital for understanding the rheology of glasses across length scales. This is achieved in classical molecular dynamics computer simulations on the model glass, CuTi, by determining the activation energy barrier and plastic yield strain of individual shear transformation zones as a function of size and external stress loading. Sizes of approximately equal to 140 atoms are identified to be especially energetically favorable with an activation energy barrier of approximately equal to 0.35 eV. Using these parameters, a rheology model is proposed to quantitatively explain viscosity.     

Exact closed-form frequency equations for thick circular plates using a third-order shear deformation theory

This paper presents, for the first time, exact closed-form frequency equations and transverse displacement for thick circular plates with free, soft simply supported, hard simply supported and clamped boundary conditions based on Reddy's third-order shear deformation theory. Hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate. The new formulation is verified by comparing the results with their counterparts reported in open literature. Natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness-radius ratios. The results presented on the basis of exact, closed-form frequency equations are expected to serve as reliable benchmarks.     

An analysis of the semi-analytic solutions of a viscous fluid with old and new definitions of fractional derivatives

In this paper we present the natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion using a recently developed definition of the Caputo–Fabrizio fractional derivative. Boundary layer equations in dimensionless form are obtained by means of dimensionless variables. The expressions for the temperature, concentration and velocity fields are obtained in the Laplace transformed domain. The inverse Laplace transform for the temperature, concentration and velocity field are found numerically by means of Stehfest's and Tzou's algorithms. A comparative analysis has been carried between the Caputo–Fabrizio and the Caputo fractional model obtained by Vieru (2015) through graphical illustration. At the end, we can see the impact of the flow parameters, including the new fractional parameter, on the flow which is presented graphically. As a result, the fractional viscous fluid model with the Caputo–Fabrizio fractional derivative has a higher velocity than with the Caputo.