Constitutive equations from Gaussian slip-link network theories in polymer melt rheology

Allowing for flow-dependent slip in the junctions of a temporary junction network, we derive the constitutive equations of temporary slip-link networks. The stress tensor is determined by three material functions, namely, the time-dependent linear-viscoelastic memory function, and two strain-dependent functions describing slip and disentanglement of network strands. Slip and disentanglement are related via a mass balance for network strands.By specifying slip and disentanglement, the constitutive equations of Lodge, Wagner, Doi-Edwards, and Marrucci are shown to be special temporary slip-link constitutive equations. To demonstrate the predictive power of temporary slip-link network theories, we compare predictions and extensional flow data with step change in flow direction.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Reptation model in polymer melt rheology: On the validity of a useful basic assumption

A mixing rule as suggested by the Doi-Edwards theory is checked experimentally. For this purpose, the dynamic shear moduli as functions of circular frequency are measured first for the melts of a series of polystyrenes of narrow molecular mass distributions. After the careful preparation of mixtures the same moduli are also determined for these mixtures. A discussion is given of the remarkable but limited validity of the additivity of contributions by the single macromolecules to the mentioned moduli.     

Effect of processing and particulate fillers on the rheology of a nematic polymer melt

Processing of a nematic HBA/HNA polymer melt increases the capillary diameter dependence of the viscosity and induces structural changes which are evident in oscillatory shear, but cannot be characterized by DSC. The effect of 6-m calcium carbonate particulate fillers is to increase the viscosity uniformly. Low concentrations of sub-micron carbon black particles cause an unexplained viscosity minimum in a large (30-mil) capillary.     

Experimental observations on the pressure-dependent polymer melt rheology of linear low density polyethylene,using a multi-pass rheometer

We report experimental data for a linear low density grade of polyethylene at elevated temperatures using a newly designed Multi-Pass Rheometer. This rheometer is capable of measuring oscillatory viscoelastic data and steady shear capillary measurements on the same test fluid within an enclosed environment. Data presented in this paper show that at low pressures there is reasonable self-consistency between the Multi-Pass data and separate oscillatory data obtained by using a Rheometrics Mechanical Spectrometer and steady shear data obtained from a Rosand capillary rheometer. In addition, we report experimental data on the pressure dependence for both viscoelastic and steady shear data over the range of 1–230 bar. The steady shear results appear to be consistent with previously published data. The apparent viscosity and the viscoelastic data both show a linear increase of about 20% over the pressure range tested.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Molecular network model for the rheology of gelling polymer solutions

A molecular network model is proposed to describe the rheology of macromolecular solutions undergoing chemical or physical gelation. The model is based on the Bird—Carreau network model [1] with the addition of chemical reaction kinetics to predict the formation of chemical crosslinks among the polymer molecules in solution. The goal is to provide a framework for describing the rheology of gels, that are currently used as fracturing fluids in oil well simulation, formed from polymer solutions that are crosslinked by the addition of transition metal ions. The model has the ability to predict an increase in storage modulus with time, shear thinning viscosity, stress overshoot upon the inception of shear flow, and viscosity changes during the simulation of flow histories that are representative of those encountered in fracturing operations.     

Linear rheology of diluted linear, star and model long chain branched polymer melts

We present experiments and theory on the diluted melt dynamics of monodisperse entangled polymers of linear, star and H-shaped architecture. Frequency-dependent rheological data on a series of progressively diluted linear, star and H-polymers are in good agreement with a refined tube-model theory that, for H-polymers, combines star polymer melt behaviour at high frequency, with linear polymer reptation behaviour at low frequencies. Taking into account the effect of dilution via some simple scaling relations, mild polydispersity and by incorporating the high frequency Rouse modes, we are able to model quantitatively the entire frequency range. This work suggests a novel rheological route to analysing long chain branching in polymer melts. Received: 6 April 2000/Accepted: 21 December 2000     

The contribution of internal degrees of freedom to the non-Newtonian rheology of model polymer fluids

We report non-equilibrium molecular dynamics simulations of rigid and non-rigid dumbbell fluids to determine the contribution of internal degrees of freedom to strain-rate-dependent shear viscosity. The model adopted for non-rigid molecules is a modification of the finitely extensible nonlinear elastic (FENE) dumbbell commonly used in kinetic theories of polymer solutions. We consider model polymer melts — that is, fluids composed of rigid dumbbells and of FENE dumbbells. We report the steady-state stress tensor and the transient stress response to an applied Couerte strain field for several strain rates. We find that the rheological properties of the rigid and FENE dumbbells are qualitatively and quantitatively similar. (The only exception to this is the zero strain rate shear viscosity.) Except at high strain rates, the average conformation of the FENE dumbbells in a Couette strain field is found to be very similar to that of FENE dumbbells in the absence of strain. The theological properties of the two dumbbell fluids are compared to those of a corresponding fluid of spheres which is shown to be the most non-Newtonian of the three fluids considered.Symbol Definition b dimensionless time constant relating vibration to other forms of motion - F force on center of mass of dumbbell - F _i force on bead i of dumbbell - F force between center of masses of dumbbells and - F _ij force between beads i and j - h vector connecting bead to center of mass of dumbbell - H dimensionless spring constant for dumbbells, in units of / ² - I moment of inertia of dumbbell - J general current induced by applied field - k _B Boltzmann's constant - L angular momentum - m mass of bead, (= m/2) - M mass of dumbbell, g - N number of dumbbells in simulation cell - P translational momentum of center of mass of dumbbell - P pressure tensor - P _xy xy component of pressure tensor - Q separation of beads in dumbbell - Q _eq equilibrium extension of FENE dumbbell and fixed extension of rigid dumbbell - Q ₀ maximum extension of dumbbell - r _ij vector connecting beads i and j - r position vector of center of mass dumbbell - R vector connecting centers of mass of two dumbbells - t time - t ^* dimensionless time, in units of m/ - T ^* dimensionless temperature, in units of /k - u potential energy - u velocity vector of flow field - u _x x component of velocity vector - V volume of simulation cell - X general applied field - strain rate, s^–1 - ^* dimensionless shear rate, in units of /m ² - general transport property - Lennard-Jones potential well depth - friction factor for Gaussian thermostat - shear viscosity, g/cms - ^* dimensionless shear viscosity, in units of m/ ² - ^* dimensionless number density, in units of ^–3 - Lennard-Jones separation of minimum energy - relaxation time of a fluid - angular velocity of dumbbell - orientation angle of dumbbell      

Two problems of the semi-conductor physics discussed with the point of view of the fluid dynamics

In this article, we discuss two problems of the semi-conductor physics from the point of view of the fluid dynamics. Firstly, we discuss the problem of thep-n junction, and find that the previous treatment and the previous conclusion of the problem are somewhat erroneous. Secondly, we discuss the coefficientC of the block resistance, and find that the mathematical method of the previous treatment is erroneous.     

Comparison of the rheology of polymer melts in shear,and biaxial and uniaxial extensions

The experimental properties of different polymer melts, polystyrene, high density polyethylene and low density polyethylene are compared for the first time in three different deformations: step shear, step biaxial extension and steady uniaxial extension. Properties of three other melts are also studied in step biaxial and shear experiments. For our comparative purposes some data of Laun and Winter from the literature are used, as well as new data reported here. In all the step strain experiments, the stresses can be factored into a time dependent relaxation modulus and a strain dependent damping function. The data are interpreted using a differential constitutive equation of Larson which satisfies this time-strain separability and has a single parameter that describes the strain softening character of the material. Results show that differences in the properties of the melts are most pronounced in uniaxial extension and least in biaxial extension. All melts follow the Doi-Edwards prediction relatively closely in biaxial extension. In uniaxial extension, the branched material shows a strong strain hardening effect although its shear and biaxial properties are similar to the other melts. The constitutive model gives a reasonably good fit to the data in all three deformations for unbranched materials for the same value of the adjustable parameter; the model, however, fails for the branched low density polyethylene.     

Diffusion of the dicumyl peroxide in molten polymer probed by rheology

The mutual coefficient of diffusion of the dicumyl peroxide (DCP), which diffuses into an ethylene–octene copolymer above its T _g was measured from an innovative rheological experiment. The experiments were carried out on a parallel plate geometry rheometer. The method is based on the cross-linking of a two-layer sample; the upper layer contains 2 wt% of DCP, and the lower layer is free of DCP. Actually, this experiment is based on the competition between the reaction of cross-linking and the diffusion of DCP in the lower layer. Comparing this rheological behavior with the rheological kinetic of cross-linking of an homogeneous sample with 1 wt% DCP, we are able, from an inverse fitting procedure, to calculate the mutual coefficient of diffusion. Our hypothesis is that the diffusion of DCP in the copolymer above T _g, can be described by Fick’s classical law. Using Fick’s law, the concentration of the DCP was established for any given point of the thickness of the two-layer sample at any time. Using a one-dimensional grid to solve continuous equations that describe the different rheological contributions of each abscissa, we determined the linear viscoelastic response of the whole sample. Comparing the experimental storage modulus of the two layer sample to the values measured from an homogeneous sample, we found the values of the mutual coefficient of diffusion. Finally, a simple relation, which describes the mutual coefficient of diffusion of DCP into melt ethylene–octene copolymer was established according to an Arrhenius law as:

Rheological properties of materials from the point of view of physical kinetics

Zhurkov and Kauzmann rheological bodies, reflecting the physical regularities of plastic deformation of materials, are studied. Solutions of differential equations of flow for composite rheological bodies are obtained. Examples of using structural models of materials that consist of new rheological bodies and describe the inelastic behavior of alloys for various types of temperature-force loading are given. The obtained solutions of the differential equations are used for analysis of the creep of a structurally unstable alloy. Chaplygin Siberian Aviation Research Institute, Novosibirsk 630051. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 119–128, January–February, 1998.     

从SCI论文统计数据看中国力学学科的国际地位和趋势

从统计角度看,一个国家在某学科上的相对国际地位的一个客观衡量指标,是该学科高水平论文的发表情况。我们在清华大学图书馆计算机国际联机检索中心的帮助下,以１９９８年进入ＳＣＩ源刊目录的所有４４种力学期刊（参见附录）为对象;逐年检索了从１９９０年至１９９９年９月底,这些刊物上所发表的全部论文数,以及责任作者为中国（不含我国的台湾、香港和澳门地区）、美国、英国、法国、德国、意大利、日本、俄罗斯、加拿大、波兰、以色列、澳大利亚、荷兰、印度、巴西等１５个国家的逐年论文数．同时还检索了上述国家所有学科总的ＳＣ…