Non-symmetric viscoelasticity of anisotropic polymer liquids

The liquid crystalline (LC) polymers are considered as anisotropic viscoelastic liquids with nonsymmetric stresses. A simple constitutive equation for nematic polymers describing the coupled relaxation of symmetric and antisymmetric parts of the stress tensor is formulated. For illustration of non-symmetric anisotropic viscoelasticity, the simplest viscometric flows of polymeric nematics in the magnetic field are considered. The frequency and shear rate dependencies of extended set of Miesowicz viscosities are predicted. Received: 23 March 1999/Accepted: 13 December 1999     

Effect of fillers on the steady state rheological behaviour of liquid crystalline polymers

The effect of fillers on the flow curves of polymeric liquid crystals is investigated. Suspensions of polystyrene particles in liquid crystalline solutions of hydroxypropylcellulose (HPC) in water are used. By reducing the HPC concentration an isotropic solution can be prepared. It serves as a reference to isolate the effect of the isotropic/anisotropic structure of the suspending medium on the rheological behaviour. Suspensions in the isotropic solution behave as expected for filled viscoelastic matrices in general. In the anisotropic medium the shear rate rather than the shear stress seems to govern the changes in the relative viscosity. This behaviour is clearly different from isotropic viscoelastic media. The most dramatic effect however is that even small amounts of particles eliminate or drastically shift the region of negative normal stress differences. As far as the structure is concerned, microscopic observations show that particles align in anisotropic as well as in isotropic media. At rest or at relatively low shear stresses the liquid crystalline structure is, in the present case, hardly affected by the presence of the particles. If anything, it becomes more homogeneous. Received: 28 April 1998 Accepted: 28 July 1998     

Effect of a relaxation time spectrum on mechanics of polymer melt spinning

The mechanics of isothermal melt spinning are determined for a viscoelastic liquid with constant physical properties but with a spectrum of relaxation times. The relaxation time distribution leads to higher forces and more linear velocity profiles than would be obtained for a Maxwellian material of the same mean properties in shear. This result explains the observation of several earlier studies that relaxation times inferred with a Maxwell-type model from spinning experiments are larger than those measured rheogoniometrically.     

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

The linear viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading is investigated in the glass transition range. Using the time-temperature superposition technique, the master curves of the shear dynamic relaxation moduli are obtained at a reference temperature of 566°C. A method to determine the viscoelastic constants from dynamic relaxation moduli is proposed. However, some viscoelastic constants cannot be directly measured from the experimental curves and others cannot be precisely obtained due to non-linearity effects at very low frequencies. The generalized Maxwell model is investigated from the experimental dynamic moduli without fixing the viscoelastic constants. A set of parameters is shown to be in good agreement with the experimental dynamic relaxation moduli, but does not give the correct values of the viscoelastic constants of the investigated glass. The soda-lime-silica glass exhibits a non-linear viscoelastic behavior at very low stress level which is usually observed for organic glasses. This non-linear behavior is questioned.     

An unsymmetric constitutive equation for anisotropic viscoelastic fluid

A continuum constitutive theory of corotational derivative type is developed for the anisotropic viscoelastic fluid–liquid crystalline (LC) polymers. A concept of anisotropic viscoelastic simple fluid is introduced. The stress tensor instead of the velocity gradient tensor D in the classic Leslie–Ericksen theory is described by the first Rivlin–Ericksen tensor A and a spin tensor W measured with respect to a co-rotational coordinate system. A model LCP-H on this theory is proposed and the characteristic unsymmetric behaviour of the shear stress is predicted for LC polymer liquids. Two shear stresses thereby in shear flow of LC polymer liquids lead to internal vortex flow and rotational flow. The conclusion could be of theoretical meaning for the modern liquid crystalline display technology. By using the equation, extrusion–extensional flows of the fluid are studied for fiber spinning of LC polymer melts, the elongational viscosity vs. extension rate with variation of shear rate is given in figures. A considerable increase of elongational viscosity and bifurcation behaviour are observed when the orientational motion of the director vector is considered. The contraction of extrudate of LC polymer melts is caused by the high elongational viscosity. For anisotropic viscoelastic fluids, an important advance has been made in the investigation on the constitutive equation on the basis of which a series of new anisotropic non-Newtonian fluid problems can be addressed. The project supported by the National Natural Science Foundation of China (10372100, 19832050) (Key project). The English text was polished by Yunming Chen.     

Smectic rheology

We have studied the oscillatory shear response of three thermotropic smectic-A liquid crystalline materials with no external aligning field (other than the necessary presence of rheometer plates). Two are polymers (one main-chain and one side-chain) and the other is a small molecule smectic. All three exhibit the classical linear response to oscillatory shear characteristic of a viscoelastic solid at sufficiently small strain amplitudes and frequencies. However, for strain amplitudes exceeding a small critical value, these materials exhibit a strongly nonlinear response to strain, which is characterized in detail. While the low-strain moduli and the critical strain of the three smectics are considerably different, the nonlinear response has some universal character which is presumably related to the low energy for the formation of defects in smectic liquid crystals.     

Measurements of Two Independent Viscoelastic Functions by Nanoindentation

Current nanoindentation measurement techniques normally assume that one material function (such as the Poisson's function) is a constant, and measures just one material function, such as the creep compliance in shear. For materials with significant viscoelastic effects and unknown viscoelastic functions, assuming a constant for one material function is not satisfactory. Accurate measurements require simultaneously determining two independent material functions. This paper provides a method to use nanoindentation to measure both bulk and shear relaxation functions. Two different nanoindenter tips, namely Berkovich and spherical indenters, are used for nanoindentation on polymers. Any two independent viscoelastic functions, such as bulk relaxation modulus and shear relaxation modulus, have different representations in the load–displacement curves obtained with these two indenters so that the two independent viscoelastic functions can be separated and determined. Two polymers, poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used in nanoindentation. Nanoindentation measurements were conducted on PVAc above glass transition temperature (Tg) and on PMMA below Tg. Both shear and bulk relaxation functions determined from nanoindentation were found in a reasonably good agreement with data obtained from conventional tests, providing validation of the method presented. The new method can be applied in measurements of two independent viscoelastic functions at sub-micron scale of very small amounts of materials such as polymeric films on a substrate, heterogeneous materials such as bones, tissues, and nanocomposites.     

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melts, using a fractional model. In this paper the authors propose an advanced model for capturing the non-linear trend of the shear viscosity of polymer melts as function of the shear rate. Results obtained with the fractional model are compared with those obtained using a classical model which involves classical Maxwell elements. The comparison between experimental data and the theoretical model shows a good agreement, emphasizing that fractional model is proper for studying viscoelasticity, even if the material exhibits a non-linear behavior.     

Stress relaxation as a microstructural probe for immiscible polymer blends

Relaxation has been investigated in immiscible blends that consist of slightly viscoelastic components. Both the shear and normal stresses have been measured after cessation of steady shear flow as well as after transient shear histories. The latter can generate a fibrillar structure which can relax by either retraction or break-up via end-pinching or Rayleigh instabilities. Each of these three relaxation mechanisms is reflected in the shape of the stress curves, from which also the corresponding structural time scales can be deduced. The experimental results have been used to evaluate the Doi-Ohta and Lee-Park models for immiscible blends. The scaling relations by Doi-Ohta are confirmed by the experimental results, but none of the existing models can correctly predict the complex relaxation behaviour observed for a highly deformed droplet phase. In the present study an alternative approach has been proposed. The stress relaxation due to fibril break-up via Rayleigh instabilities has been predicted successfully by combining physical models for the structural changes with the basic approach of the Doi-Ohta model.     

An outline of the non-linear viscoelastic behaviour of wheat flour dough in shear

Creep and creep recovery, stress relaxation and small- and large-amplitude oscillatory shear experiments have been used to study the steady-state flow behaviour and the transient viscoelastic response of wheat flour dough in shear over large ranges of time, stress and strain. The results are discussed with reference to the limited body of reliable literature data. Dough does display a linear viscoelastic domain. The complex character of its non-linear viscoelastic properties is essentially due to the extremely low shear rate limit of the initial Newtonian plateau and to the onset of time-dependent flow behaviour above a certain strain threshold, which explain qualitatively the discrepancies observed in certain cases on a part of the range of the rheological variables explored, despite global self-consistency of the results. Comparison of gluten and dough linear viscoelastic properties shows that dough cannot be viewed simply as a concentrated suspension of starch granules in the hydrated viscoelastic gluten matrix.Paper presented at the second Annual European Rheology Conference (AERC 2005) held in Grenoble, France on April 21–23, 2005.     

流变学的前沿方向—液晶高分子流变学

简要叙述液晶高分子的结构,论述液晶分子流变学特征,液晶高分子流体的各类本构方程,其中包括作者发展的液晶高分子流体型本构方程。     

On the modeling of fluidity loss phenomena in Couette and Poiseuille flows of elastic liquids

Some effects of the possible relaxation transition from viscoelastic liquid state to highly elastic solid state were theoretically and numerically investigated in the shear situations, within the approach proposed in papers [1, 2, 5, 16]. It was found that for a single Maxwellian model the constitutive equations developed in [1, 2, 5] are not valid at elevated shear stresses. Some new aspects of the possible rheological behavior of elastic liquids in subcritical (before transition) and supercritical (after transition) regimes were demonstrated. The mechanism of fluidity loss studied in this paper could serve as a possible trigger mechanism for the melt flow instabilities.     

Viscoelastic plastic rheological model for particle filled polymer melts

A viscoelastic plastic model for suspension of small particles in polymer melts has been developed. In this model, the total stress is assumed to be the sum of stress in the polymer matrix and the filler network. A nonlinear viscoelastic model along with a yield criterion were used to represent the stresses in the polymer matrix and the filler network, respectively. The yield function is defined in terms of differential equations with an internal parameter. The internal parameter models the evolution of structure changes during floc rupture and restoration. The theoretical results were obtained for steady and oscillatory shear flow and compared with experimental data for particle filled thermoplastic melt. The experimental data included the steady state shear strress over a wide range of shear rates, the transient stress in a start up shear flow, stress relaxation after cessation of a steady state shear flow, the step shear and the oscillatory shear flow at various amplitudes.     

Theoretical and experimental investigation of the flow of a viscoelastic fluid in the gap between two rotating disks

A theory of the nonlinear viscoelastic behavior of polymer fluids has been constructed in [1]. The theory was used in [2] to investigate the motion of a nonlinear viscoelastic medium under steady and unsteady deformation rates in simple shear flow, and a comparison was made with experiment. The experiments in [2], which were performed on a cone-plate Weissenberg rheogoniometer, indicate that this arrangement is unsuitable for measurements of normal stresses under unsteady conditions in fluids with a fairly high viscosity. Below, we will show the suitability of using a disk-disk Weissenberg rheogoniometer to measure normal stresses in this case for unsteady conditions (transition to steady flow and stress relaxation). In this regard, a theoretical study of the flow of a viscoelastic fluid in the gap between rotating disks is needed. Note that in this case new information will be obtained from a comparison with simple uniform shear flow, since in the flow of a polymer between two disks all three normal stress components contribute to the axial force, while in the gap between a cone and a plate only the first normal stress difference contributes to the normal force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 25–30, March–April, 1976.     

Surface rheology

This review article approaches the subject of surface rheology from a phenomenological point of view. Operational definitions are given for the four surface rheological parameters: modulus and viscosity in either dilation or shear. Results of recent measurements are discussed. Observed non-Newtonian or viscoelastic behaviour has in some cases been interpreted in terms of known relaxation processes. The surface rheological behaviour affects the flow of bulk liquid near the surface; coupling occurs through the tangential stress boundary condition.     

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p _c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.     

Rheology and flow-birefringence from viscoelastic polymer-clay solutions

 The shear orientation of viscoelastic clay-polymer solutions was investigated by means of rheology and flow birefringence (Δn). The polymer chains are in dynamic adsorption/desorption equilibrium with the clay particles to form a “network”. The elastic behavior of the network was characterized by constant stress, oscillatory shear, and stress relaxation experiments. Constant stress experiments indicated a yield stress upon which shear flow started and no strain recovery could be observed. Oscillatory shear experiments showed a broad elastic region followed by flow when a critical strain was reached. Stress relaxation experiments showed several relaxation times when the same critical strain was reached. Experiments under steady flow characterized the transient behavior of the network. With increasing steady shear rate a pronounced minimum in birefringence was observed at a critical shear rate. The shear rate dependent viscosity showed near power law behavior and no corresponding critical feature. While birefringence detects orientational effects on a microscopic length scale, rheology averages over macroscopic changes in the sample. The same degree of orientation could be achieved under constant shear rate or constant stress conditions. Received: 25 January 2001 Accepted: 22 May 2001     

Effect of purely elastic flow instability on molecular conformation and drag

Linear stability analysis has shown that viscoelastic creeping flow of an Oldroyd-B liquid through a sinusoidal channel is unstable to stationary, wall-localized and short wavelength perturbations [B. Sadanandan, R. Sureshkumar, Global linear stability analysis of non-separated viscoelastic flow through a periodically constricted channel, J. Non-Newtonian Fluid Mech. 122 (2004) 55]. In this work, time-dependent simulations are performed to determine the nonlinear evolution of finite amplitude disturbances in the post-critical flow regime. It is shown that a nonlinear transition, which is facilitated by a supercritical pitchfork bifurcation, establishes a finite amplitude state (FAS) in which the average polymer stretch is highly modulated. The maximum normal stress, observed at the channel nip, can increase by up to approximately 100% when the Weissenberg number, defined as the ratio of the fluid relaxation time to an inverse characteristic shear rate, is increased by only 10% beyond its critical value. This is attributed to the amplification of configurational perturbations by the base flow shear rate, which attains its maximum at the channel nip. The effect of finite chain extensibility on the critical condition and nonlinear instability is investigated using the FENE-CR model. The stabilizing effect of finite extensibility can be expressed through a renormalization of the Weissenberg number by accounting for the screening effect of the nonlinear force law on the transmission of configurational perturbations to polymeric stress. The principal features of the FAS are qualitatively model-independent. The FAS exhibits a small, but numerically perceptible increase in the friction factor as compared to the base flow. The implication of the findings on the experimentally observed flow resistance enhancement phenomenon in viscoelastic creeping flows through converging/diverging geometries is discussed.     

A finite element method for liquid with memory

Steady, two-dimensional flows of viscoelastic liquid with memory are analyzed by means of a nonlinear integral constitutive equation, novel streamlined finite elements, Galerkin's method of weighted residuals, and Newton iteration. By their relation to streamlines the new elements allow, for the first time, full Newton iteration of the algebraic equation set to which the governing integrodifferential system reduces. Streamlines are computed simultaneously with velocity components and pressure, the primary unknowns; to track the history of liquid particles the deformation equations are solved analytically in a Protean system of coordinates that conforms to the streamlines. In the cases studied the Newton iteration converges quadratically to a creeping flow state of Weissenberg number (product of upstream wall shear rate and relaxation time of the liquid) up to about 20 in channel flow, 10 in film flow, and 2 in die-swell flow. Shear-thinning shrinks the domain of convergence; it also reduces die-swell. A slip boundary condition in the vicinity of the contact line extends the domain of convergence.