Testing viscometric predictions of the internal viscosity model,using dilute viscous theta solutions

A stress-symmetrized internal viscosity (I.V.) model for flexible polymer chains, proposed by Bazua and Williams, is scrutinized for its theoretical predictions of complex viscosity ^* () = – i and non-Newtonian viscosity (), where is frequency and is shear stress. Parameters varied are the number of submolecules,N (i.e., molecular weightM = NM _s ); the hydrodynamic interaction,h ^*; and/f, where andf are the I.V. and friction coefficients of the submolecule. Detailed examination is made of the eigenvalues _p (N, h ^*) and how they can be estimated by various approximations, and property predictions are made for these approximations.Comparisons are made with data from our preceding companion paper, representing intrinsic properties [], [], [] in very viscous theta solutions, so that theoretical foundations of the model are fulfilled. It is found that [ ()] data can be predicted well, but that [ ()] data cannot be matched at high. The latter deficiency is attributed in part to unrealistic predictions of coil deformation in shear.     

Some general rheological properties of dilute polymer solutions predicted from intrinsic viscosity measurements

Expressions for the rheological properties of dilute polymer solutions at low and moderate deformation rates are established through the computation and analysis of exact Zimm's eigenvalues. It is shown that they can be expressed in terms of measurable parameters from intrinsic viscosity data. Under moderate deformation rates one needs to introduce a slippage between the solvent and the smoothed polymer to be able to describe shear-thinning behaviour.     

Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model)

The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Theory of oscillatory experiments with a coaxial cylinder viscometer

Equations are derived for the coaxial cylinder system in the combined oscillatory and steady-state shear mode. The limitations of the use of the various equations are presented. If the usual linear equations are used, the main limitation, in the case of oscillatory shear only, is that the frequency of measurement should be below 0.016 | ^*|/(r ₂ –r ₁ )². Here | ^*| is the modulus of the complex viscosity, is the density of the liquid andr ₁ andr ₂ are the radii of the cylinders. Furthermore it is shown that there is a small error in the numerical factor of the usually applied equations. The calculations are set up in such a way that extension to higher harmonics follows in a natural way. An experimental example illustrates the use of the derived equations.     

A new semi-empirical spectrum model for complex steady shear viscosity of complex fluids

A semi-empirical spectrum model is proposed to describe the experimental data of the steady shear properties of a Shengli waxy crude oil near its gel point, where sophisticated structural effects become apparent due to the existence of waxy crystals in the crude oil. The model, consisting of a time spectrum, can well fit the steady shear viscosities of the waxy crude oil over the whole experimental shear rate region from 10-4 to 102 s- 1. Two other experiments on complex fluids reported recently in the literature are also well described by this model demonstrating the applicability and accuracy of the model.     

Hydrodynamic interactions of dilute polymer solutions under shear flow in a narrow channel

Hydrodynamic interactions on dilute solutions of spherical beads under shear flow are calculated with the method of induced forces. The Navier-Stokes equation is considered in the Stokes approximation. Hydrodynamic interactions cause the drag to be anisotropic in space.Numerical solutions are obtained for the added stress, caused by polymeric molecules in solution in a narrow channel under shear flow. The polymeric molecules are considered as Hookean spring-dumbbells.Slip velocity and the effective viscosity are obtained taking different dumbbells' bead radii. Transversal migration in the channel is obtained for different bead radii.     

Rheo-NMR study of a non-flow-aligning side-chain liquid crystal polymer in nematic solution

The flow behavior of a highly concentrated solution of a nematic side-chain liquid crystal polymer in a low molecular mass nematic solvent is investigated by deuterium nuclear magnetic resonance with simultaneous measurement of the shear viscosity in a cone-and-plate NMR viscometer. The director orientation under shear in the magnetic field is determined from the quadrupole splitting of the NMR spectra. The orientation as a function of shear rate is analyzed in terms of the Ericksen-Leslie-Parodi theory, yielding the Leslie coefficients ₂ and ₃ and thus the flow alignment parameter . From the combined analysis of orientation and viscosity as a function of shear rate a total of four independent viscosity parameters is obtained for the nematic solution. The value determined for the flow-alignment parameter, 0.2, and the analysis of the data based on Brochard's theory show that the polymer is of the non-flow-aligning type and has a slightly prolate shape.     

Bead-spring chain model for the dynamics of dilute polymer solutions : Part 2. Comparisons with experimental data

Comparisons are made between experimental rheological data and theoretical predictions obtained from a recently developed algorithm which incorporates three major molecular concepts in a theory for dilute polymer solutions (hydrodynamic interaction, excluded volume and nonlinear springs). These predictions include the radius expansion factor, the apparent chain expansion factor, the molecular weight dependence of the intrinsic viscosity, the frequency dependence of oscillatory flow birefringence, and the shear rate dependence of the intrinsic viscosity. This paper shows that a bead-spring chain model quantitatively predicts these quantities when the relevant molecular concepts are incorporated, suggesting that the rheological properties of dilute polymer solutions can be explained and predicted in terms of these molecular parameters.     

Chebyshev super spectral viscosity solution of a two‐dimensional fluidized‐bed model

The numerical solution of a model describing a two‐dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite‐difference method. The mixed SSV/finite‐difference method produces physically shaped bubbles, on a very coarse grid. Fine scale details, which were not present in previous finite‐difference solutions, are present in the solution. Copyright © 2003 John Wiley & Sons, Ltd.     

Disappearance of criticality for reactive third-grade fluid with Reynold's model viscosity in a flat channel

In this paper, we consider how a model for the motion with exponential viscosity of a third-grade fluid flowing between parallel plates, under the action of externally imposed pressure gradient, affects the fully developed and laminar reactive flow. The non-dimensional form of the coupled equations are solved numerically. The temperature distribution is presented for various viscosity variational parameters and the number is related to the Frank-Kamenetskii parameter. The criticality and disappearance of criticality (transition) of physical parameters and the competing effects of viscous dissipation, viscosity variational number, heat generation and non-Newtonian are discussed.     

A three-parameter model describing the behaviour of a viscoelastic liquid in a tangential annular flow

A three-parameter model describing the shear rate-shear stress relation of viscoelastic liquids and in which each parameter has a physical significance, is applied to a tangential annular flow in order to calculate the velocity profile and the shear rate distribution. Experiments were carried out with a 5000 wppm aqueous solution of polyacrylamide and different types of rheometers. In a shear-rate range of seven decades (5 10^–3 s^–1 < < 1.2 10⁵ s^–1) a good agreement is obtained between apparent viscosities calculated with our model and those measured with three different types of rheometers, i.e. Couette rheometers, a cone-and-plate rheogoniometer and a capillary tube rheometer. a physical quantity defined by:a = {1 – ( / ₀)}/ ₀ (Pa^–1) - C constant of integration (1) - r distancer from the center (m) - r ₁,r ₂ radius of the inner and outer cylinder (m) - v _r local tangential velocity at a distancer from the center (v _r = _r r) (m s^–1) - v ₂ local tangential velocity at a distancer ₂ from the center (m s^–1) - shear rate (s^–1) - local shear rate (s^–1) - ₁ wall shear rate at the inner cylinder (s^–1) - dynamic viscosity (Pa s) - _a apparent viscosity (_a = / ) (Pa s) - _a1 apparent viscosity at the inner cylinder (Pa s) - ₀ zero-shear viscosity (Pa s) - infinite-shear viscosity (Pa s) - shear stress (Pa) - _r local shear stress at a distancer from the center (Pa) - ₀ yield stress (Pa) - ₁, ₂ wall shear-stress at the inner and outer cylinder (Pa) - _r local angular velocity (s^–1) - ₂ angular velocity of the outer cylinder (s^–1)     

Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity

The flow of fluid-solid mixtures in a pipe can be treated as non-Newtonian fluids of third grade. Depending upon the fluid viscosity, entropy generation in the flow system varies. In the present study, flow of third grade fluid in a pipe is considered. The Vogel model is introduced to account for the temperature-dependent viscosity. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that increasing viscosity parameter A reduces the entropy generation number and opposite is true for increasing viscosity parameter B.