Viscosity of non-Newtonian media in pure shear

On the basis of Geisekus's rheological equation of state the viscosity of a non-Newtonian fluid is investigated in relation to the particular mode of deformation (pure shear, axisymmetric deformation, simple shear), The intrinsic viscosity is calculated for pure shear, the following model being used: rigid ellipsoids of revolution uniformly distributed in an incompressible viscous Newtonian fluid. The dependence of the intrinsic viscosity on the parameter =(2/3)(q/D) (q is strain rate, D is the rotational diffusion coefficient) is obtained in specific form for various ratios of the ellipsoid semiaxes.Mekhanika Polimerov, Vol. 3, No. 5, pp. 927–932, 1967     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Structural rheological model of two-phase interlayer shear flow

This paper presents a study of an epitropic liquid crystal layer formation at a metal substrate. Such layer structurization leads to non-Newtonian flow of thin interlayer with wall-adjacent orientation-ordered layers. Rheological characteristics of micron interlayers of n-hexadecane and Vaseline oil with surfactant addition are investigated. The features of structural “variable viscosity” layer are defined within the framework of a proposed rheological model. An increase in the rate of shear deformation leads to a reduction in near-surface layer viscosity due to molecular reorientation. Estimation of model parameters, performed on basis of the experimental rheological data, is carried out.     

Features of thermomechanical properties of radiation-modified blends of high-density polyethylene with liquid-crystalline copolyester

The present paper surveys the investigation results of gamma-irradiated blends of high-density polyethylene (PE) with thermotropic liquid-crystalline polymer (LCP). The LCP used was a liquid crystalline copolyester of 40% poly(ethyleneterephthalate) with 60% p-(hydroxybenzoic acid). The LCP content in the blends was 0,5, and 10 wt.%. The constituents were blended with the use of a single-screw extruder. The samples were prepared by compression molding and irradiated by a Co⁶⁰ -radiation source in an inert atmosphere (argon) to relatively low absorbed doses (up to 200 kGy; 1 Mrad=10 kGy). Morphological, thermal, and mechanical properties in a wide temperature range were investigated for the irradiated and nonirradiated samples. The effects of gamma-irradiation and LCP addition on the thermomechanical behavior of PE are discussed. It was found that the LCP addition affected significantly the stress-strain behavior of PE at temperatures above the melting point. The features of thermorelaxation properties of the PE/LCP blends previously irradiated and oriented, particularly thermorelaxation and residual shrinkage stresses at isometric heating and cooling, were also established. The results obtained testify that the LCP addition makes it possible to improve considerably the thermosetting properties of irradiated PE.Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 124–139, January–February, 1998.     

壁面效应对剪切稀化流体内气泡上浮特性的影响

数值研究了壁面效应对剪切稀化流体内气泡上浮运动特性的影响,气液两相的界面捕捉采用流体体积(VOF)法,剪切稀化流体流变特性和气液相间表面张力的计算分别采用Carreau模型和连续表面张力模型.详细研究了不同流变指数下,壁面效应对气泡形状、液相流场和气泡终端速度的影响.结果表明,强的壁面效应或弱的剪切稀化程度会限制气泡的变形和尾涡的形成,使气泡的终端速度减小;气泡终端速度最易受壁面效应的影响;强的壁面效应和强的剪切稀化程度会导致高剪切速率区域出现在壁面附近,引起壁面附近液相表观黏度大幅度的下降.     

Rheology and molecular structure of polyethylene melts. 2. Effect of molecular structure on the viscoelastic characteristics

The viscoelasticity of low-density polyethylene is investigated as a function of molecular structure. The viscoelasticity is characterized by three numbers — the zero-shear viscosity, the characteristic relaxation time, and the index of the rate of fall of dynamic viscosity with deformation frequency. The molecular structure is also characterized by three numbers — , , g_w. The zero-shear viscosity is shown to depend on the polydispersity of the molecules and a corresponding analytic expression is obtained. The method of determining the characteristic relaxation time from the maximum of the frequency relaxation spectrum is justified and an expression giving the characteristic relaxation time as a function of the principal characteristics of the molecular structure is derived. It is shown that long-chain branching of the molecules has an incommensurably greater (several orders) effect on the rheological characteristics of the branched polymer than the polydispersity of the molecular weight. The effect of the polydispersity of the molecules of commercial low-density polyethylenes on the viscoelastic characteristics cannot be established without taking the branching of the molecules into consideration.For communication 1 see [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 120–127, January–February, 1976.     

Rheology of filled polymers. Steady-state shear flow and periodic deformation. 1. Relaxation time spectra,viscosity

Conclusions 1. The validity of the temperature-frequency superposition in the finite relaxation region has been confirmed for a concentrated solution of PIB filled with solid dispersed particles;2. the apparent heat of activation of the viscoelastic relaxation times increases at and above a certain filler concentration (c=15%);3. in the case of fillers for which the apparent heat of activation of the viscoelastic relaxation times is independent of the filler concentration, the filler only shifts the frequency functions of the components of the complex shear modulus along the logarithm of the modulus axis and the relaxation time spectrum H() along the log H axis. In this case G_C/G_M=G_C/G_M=_OC/_OM=_rel;4. the effective filler concentration for ccrit, as determined from the concentration dependence of the initial viscosity, exceeds the nominal filler concentration by a factor of 2.4 to 2.8;5. at a filler concentration c>c_crit, the contour of the relaxation time spectrum changes on account of the formation of a secondary filler structure;6. when the filler concentration ccrit, the dependencies of the viscosity on the shear rate for the composites and the matrix can be reduced with respect to two parameters;7. possible methods for the reduction of flow curves by means of linear coordinate transformations have been systematized.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1075–1083, November–December, 1977.     

Influence of magnetic field on the rheological properties of liquid GaInSn alloy

In this work we studied experimentally the effect of an applied magnetic field and shear rate on the viscosity of a liquid GaInSn alloy. The experimental investigations were performed at room temperature in a homebuilt shear stress controlled rheometer. To consider the magnetohydrodynamical effects occurring in the melt numerical simulation of the flow field in the melt have been made. The results show a remarkable increase of the viscosity with increasing magnetic field strength. With increasing shear rate applied to the liquid GaInSn alloy a reduction of the change of viscosity is found. As first assumption this rheological behavior of GaInSn can be accounted to the presence of solid oxide fractions in the melt. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of temperature and strain rate on the adhesion of polyvinyl butyral to glass

The shear strength of silicate glass bonded with polyvinyl butyral has been investigated over a broad temperature interval together with the effect of plasticization of the polymer on the strength of the bond. The _adh ^–t curves have intervals corresponding to adhesion failure, cohesion failure of the substrate, and cohesion failure of the adhesive, respectively. The dependence of adhesion on strain rate has been investigated and a maximum observed at 20 mm/min.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1104–1107, November–December, 1970.     

Nonlinear shear response of fluid polymers during periodic deformation. Basic harmonics

Conclusions 1. A model with a relaxation spectrum independent of accumulated elastic strains describes the combination of data on the amplitude and frequency dependences of the components of the shear modulus in terms of basic harmonics for low-molecular-weight polyisobutylene and a filled-polyethylene melt.2. The greater the amplitude of the shear strain, the broader the region of invariance of the relaxation functions relative to the amplitude of the rate of oscillatory shear.3. The kinetic (s) function affects the amplitude dependences of the modulus in terms of basic harmonics. Its effect is significantly greater on the real component of the modulus than on the imaginary one.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1093–1100, November–December, 1977.     

Effect of filler on the viscosity and viscoelasticity of melts of low-density polyethylene. Communication 2

Conclusions 1. A filler causes a change in the viscoelastic functions of melts, which in general cannot be described in linearly transformable coordinates.2. With rising filler concentration, the maximum of the frequency of the relaxation spectrum N(s) increases, but the frequency corresponding to the maximum decreases.3. The dynamic viscosity and rigidity of matrices and composites as functions of frequency are satisfactorily described by a three-parameter relationship. The relationship derived contains parameters of the degree of filling. Using the dimensionless viscosity '/_o and deformation frequency '₁ it was possible to obtain a relationship which is invariant with respect to the filler in a limited range of change in and which can be used for approximate calculations.4. The initial shear modulus of a composite with a filler concentration corresponding to formation of a secondary network can be lower than the shear modulus of the matrix.For communication 1 see [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 122–126, January–February, 1977.     

Structural rheological model of two-phase interlayer shear flow

This paper presents a study of an epitropic liquid crystal layer formation at a metal substrate. Such layer structurization leads to non-Newtonian flow of thin interlayer with wall-adjacent orientation-ordered layers. Rheological characteristics of micron interlayers of n-hexadecane and Vaseline oil with surfactant addition are investigated. The features of structural “variable viscosity” layer are defined within the framework of a proposed rheological model. An increase in the rate of shear deformation leads to a reduction in near-surface layer viscosity due to molecular reorientation. Estimation of model parameters, performed on basis of the experimental rheological data, is carried out.     

Stability of the Kolmogorov flow and its modifications

Recurrence formulas are obtained for the kth term of the long wavelength asymptotics in the stability problem for general two-dimensional viscous incompressible shear flows. It is shown that the eigenvalues of the linear eigenvalue problem are odd functions of the wave number, while the critical values of viscosity are even functions. If the velocity averaged over the long period is nonzero, then the loss of stability is oscillatory. If the averaged velocity is zero, then the loss of stability can be monotone or oscillatory. If the deviation of the velocity from its period-average value is an odd function of spatial variable about some x ₀, then the expansion coefficients of the velocity perturbations are even functions about x ₀ for even powers of the wave number and odd functions about for x ₀ odd powers of the wave number, while the expansion coefficients of the pressure perturbations have an opposite property. In this case, the eigenvalues can be found precisely. As a result, the monotone loss of stability in the Kolmogorov flow can be substantiated by a method other than those available in the literature.     

Instabilities and bifurcations of von Kármán similarity solutions in swirling viscoelastic flow

We derive an asymptotic model that describes the swirling flow of a viscoelastic fluid between a rotating cone and a stationary plate when the gap angle, , is small and inertia is neglected. The model, which uses the Phan-Thien Tanner (PTT) constitutive law, is valid in the limit a 0 and for Deborah number, De, order unity. We show that the model admits similarity solutions of von Kármán type. A solution corresponding to a viscometric flow is obtained. This base flow, which exhibits shear thinning if the PTT parameter 0, is linearly stable if the Deborah number De is less than a critical value De _c and unstable if De > De _c . The critical Deborah number is a decreasing function of the retardation parameter , and an increasing function of . The method of Lyapunov-Schmidt is used to determine the nature of bifurcation when De is close to De _c . Our analysis shows that there is a supercritical pitchfork bifurcation at De=De _c .     

Bending of prestressed glass-reinforced plastic beams

Initial waviness of the fibers and prestressing are investigated in relation to their effect on flexural stiffness and strength for beams with low shear strength. It is shown that prestressing the reinforcement increases the flexural stiffness but at the same time adds to the shear correction as a result of an increase in the modulus of elasticity E_x in the direction of reinforcement and the insensitivity of the shear modulus G_xz to prestress. It is established that prestressing increases the shear strength and the degree of anisotropy . Materials of two types are investigated: unidirectional (AG-4S) and cloth-reinforced (SKT-11).Mekhanika Polimerov, Vol. 3, No. 5, pp. 888–893, 1967     

Analytic Perturbation Theory for QCD Observables

We investigate the connection between ghost-free formulations of the RG-invariant QCD perturbation theory in the spacelike and timelike regions. Our basic tool is the double spectral representation, similar to the representation for the Adler function, which stems from the first principles of local QFT and relates real functions in the Euclidean and Minkowskian (i.e., timelike) regions. On this base, we establish a simple relation between the approach (known from the early 1980s) of resumming the ² terms for the invariant coupling function and QCD observables in the timelike region and the invariant analytic approach (devised a few years ago) leading to the analyticized coupling function _an(Q ²) and nonpower expansion for observables in the spacelike domain. The function _an(Q ²) and the expansion are free of unphysical singularities. The formulated self-consistent scheme, analytic perturbation theory (APT), relates renorm-invariant, effective coupling functions _an(Q ²) and , as well as nonpower perturbation expansions for observables in the Euclidean and Minkowskian domains, free of extra singularities and with better convergence in the infrared region. We present a global generalization of the new APT scheme in the case of real QCD, including the domain with various numbers of active quarks. Preliminary estimates indicate that calculations in the framework of the global scheme can produce results quite different from the usual ones for , even in the five-quark region. Numerical examples are given.     

Linear complementarity as absolute value equation solution

We consider the linear complementarity problem (LCP): $Mz+q\ge 0, z\ge 0, z^{\prime }(Mz+q)=0$ as an absolute value equation (AVE): $(M+I)z+q=|(M-I)z+q|$ , where $M$ is an $n\times n$ square matrix and $I$ is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generated random solvable instances of the LCP with $n=10, 50, 100, 500$ and 1,000. The algorithm solved $100\,\%$ of the test problems to an accuracy of $10^{-8}$ by solving 2 or less linear programs per LCP problem.     

Effect of ultrasonic vibrations on the flow of a viscoelastic liquid

The rheological characteristics of a viscoelastic liquid flow, on which finite-amplitude ultrasonic shear vibrations have been superimposed, are investigated. It is shown that at periodic deformation amplitudes of 5 µ or more there is a thixotropic reduction of the viscosity and elasticity of the system owing to the destruction of certain types of structural bonds. The experimental apparatus is described.Moscow Institute of Chemical Machine Building. Translated from Mekhanika Polimerov, No. 6, pp. 1097–1099, November–December, 1971.     

Multicritical phenomena in flow of viscoelastic liquids. 1. Zaremba-Fromm-De Witt liquid

It has been shown that multicritical phenomena caused by nonlinearity of viscosity and high elasticity, and forced anisotropy at finite shear rates take place during flow of viscoelastic polymer melts which are isotropic in the resting state. The sign of the low-frequency asymptotic values of the dynamic viscosity and elasticity measured during steady flow is a criterion of the appearance of instability. These arguments are illustrated by the solution and analysis of the complex reaction to low-amplitude, periodic shear of a steady-flowing, very simple viscoelastic liquid — ZFD liquid. It was shown that the instability of viscoelastic liquids for a given steady shear rate is due to the effect of perturbations lasting for no less than some limiting value and its manifestations are caused by superposition of different types of instability — multicritical phenomena.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 555–572, July–August, 1995.The study was conducted based on Topic 93,177 of the Latvian Science Council.     

Bernstein functions, complete hyperexpansivity and subnormality—I

Special classes of functions on the classical semigroupN of non-negative integers, as defined using the classical backward and forward difference operators, get associated in a natural way with special classes of bounded linear operators on Hilbert spaces. In particular, the class of completely monotone functions, which is a subclass of the class of positive definite functions ofN, gets associated with subnormal operators, and the class of completely alternating functions, which is a subclass of the class of negative definite functions onN, with completely hyper-expansive operators. The interplay between the theories of completely monotone and completely alternating functions has previously been exploited to unravel some interesting connections between subnormals and completely hyperexpansive operators. For example, it is known that a completely hyperexpansive weighted shift with the weight sequence {_n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {1/_n}(n0). The present paper discovers some new connections between the two classes of operators by building upon some well-known results in the literature that relate positive and negative definite functions on cartesian products of arbitrary sets using Bernstein functions. In particular, it is observed that the weight sequence of a completely hyperexpansive weighted shift with the weight sequence {_n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {_n+1/_n}(n0). It is also established that the weight sequence of any completely hyperexpansive weighted shift is a Hausdorff moment sequence. Further, the connection of Bernstein functions with Stieltjes functions and generalizations thereof is exploited to link certain classes of subnormal weighted shifts to completely hyperexpansive ones.