The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table     

The rheology of strongly-flocculated suspensions

The rheology of strongly-flocculated dispersions of colloidal particles has been investigated at particle concentrations where a continuous network is formed rather than a collection of discrete flocs. Such networks are shown to possess a true yield stress in both shear and in uniaxial compression (as realised in a centrifuge). Properties measured as a function of particle concentration and particle size include the yield stresses in shear (σ_y) and compression (P_y); the limiting and strain-dependent, instantaneous shear moduli G_O and G(γ); the elastic recovery at finite strains, and the rate of centrifugally-driven compaction. The yield stresses and moduli appear to show a power-law dependence on particle concentration with G_O and P_y, having the same power-law index and σ_y a somewhat lower one. The data are in part consistent with predictions based on the idea that the networks have a heterogeneous structure comprising a collection of interconnected fractal aggregates. The behaviour as a function of particle size and concentration is however not completely scaleable as might be expected on this basis. Thus, whereas the shear yield stress could be scaled to remove its dependence on particle radius a and volume fraction φ (over the measured range 0.25 μm ⩽ a ⩽ 3.4 μm; 0.05 ⩽ φ ⩽ 0.25) as could the strain dependent modulus (0.25 ⩽ a ⩽ 1.3 μm; 0.08 ⩽ 0.25), the particle-size and concentration dependence of P_y and G_O could only be scaled for particles with radii between 0.16 and 0.5 μm, smaller and larger particles having different and much higher power-law index in respect of their concentration dependencies. In the case of the smaller particles the failure of the scaling is thought to be due to an anomaly since these particles distort significantly under the influence of the strong van der Waals forces and this causes the aggregates to be more compact then they otherwise would be. The reasons for the failure at larger sizes is not clear.     

Computer simulation of the rheology of concentrated star polymer suspensions

We use particle-based computer simulations to study the rheology of suspensions of high-functionality star polymers with long entangled arms. Such particles have properties which are intermediate between those of soft colloidal particles and entangled polymer chains. In the simulations, each star polymer is coarse-grained to a single particle. In order to faithfully reproduce dynamical properties, it is very important to not only include time-averaged interactions (potentials of mean force) but to also account for transient interactions induced by entanglements between the arms of different star polymers. Using a model which has all these features, it is found that, for sufficiently high shear rates, the start-up shear stress displays an overshoot. With increasing concentration, the core interactions increasingly dominate the initial stress response, leading to a maximum in the stress overshoot at relatively low strain values (0.1 to 0.5). Transient forces start to dominate after this initial stage. In a simulated experiment in which the shear rate is suddenly stepped-down from a high to a lower value, the stress shows a clear undershoot, with the minimum stress again at a relatively low strain value (based on the new shear rate). Finally, it is shown that a stress plateau develops in the flow curve. This plateau is absent when the transient forces between the polymer stars are not taken into account.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

Kinetic theory and rheology of dilute polymer solutions

Summary A summary is given of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results.With 1 table     

An elastohydrodynamic theory for the rheology of concentrated suspensions of deformable particles

The equations which govern thin films of a Newtonian liquid confined between deformable solid surfaces are applied to the regions of near contact in a concentrated suspension of deformable particles.For the case of slightly deformable elastic particles, one obtains the socalled “elastohydrodynamic” equations of lubrication theory.The appropriate asymptotic solution of these equations yields estimates for the viscosity, of a form proposed earlier by Frankel and Acrivos [1] for rigid particles, as well as a relaxation time for a suspension of near spheres. The present method, which goes beyond the dissipation calculation of Frankel and Acrivos to a derivation of the full stress tensor, yields the same form of dependence of viscosity on particle concentration. However, there is an as yet unexplained difference between the methods in the value of a numerical coefficient determined by the assumed packing of the spheres.While further work is needed on the kinetic theory for fluid suspensions, the methods employed here for the derivation of the stress tensor should have direct utility for certain solid dispersions, where it is possible to specify a priori the particle-packing in the system.     

The rheology of suspensions of vinylon fibers in polymer liquids. I. Suspensions in silicone oil

Summary The steady shear flow properties of suspensions of vinylon fibers in silicone oil were measured by means of a cone-plate type rheometer. Three kinds of vinylon fibers used had no distributions of length and were more flexible than glass fibers and the like. The content of the fibers ranged from 0 to 7 wt.%. Shear viscosity, the first normal-stress difference, yield stress, and relative viscosity were discussed. Shear viscosity and relative viscosity increased with the fiber concentration and the aspect ratio, and depended upon the shear rate. The applicability of Ziegel's equation of viscosity for fiber suspensions was investigated. The first normal-stress difference increased with the fiber concentration, aspect ratio, and shear rate and its relative increase was much larger than for shear stress and viscosity depending on the properties of the characteristic time, The yield stress could be determined by Casson plots for large aspect ratio fiber suspensions even in low concentration comparing with the suspensions of spherical particles or powder. The influence of the flexibility of the fibers for the rheological properties of the fiber suspensions can not be ignored.With 12 figures and 2 tables     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

The main purpose of this study was to examine the viscous and elastic properties and capillary flow of fiber suspensions in Newtonian fluids as well as in polymer solutions. The fillers used were glass, carbon, nylon and vinylon fibers. Glycerin was used as a Newtonian suspending medium and HEC and Separan solutions as viscoelastic suspending media. The viscosity and the first normal-stress difference were measured using a coaxial cylindrical rotating viscometer and a parallel-plate rheogoniometer respectively. The influence of the concentration, aspect ratio, diameter and flexibility of the fibers on the viscous and elastic properties of the fiber suspensions was investigated. Empirical equations were obtained for the relative viscosity and first normal-stress difference for the fiber suspensions in glycerin. The capillary flow of these suspensions is discussed in part II.     

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.     

Extensional flow of polymer solutions through porous media

The flow behaviour of various polymer solutions of non-hydrolyzed polyacrylamide, hydrolyzed polyacrylamide, polyox and Xanthan was investigated in a plexiglass column having a succession of enlargements and constrictions, and compared with the flow behaviour and mechanical degradation of a solution of non-hydrolyzed polyacrylamide in a packed column of non-consolidated sand. The flow behaviour of this solution was found to be very similar in both the sand pack and plexiglass pore.Apart from the Xanthan solution, all other polymer solutions showed a viscoelastic behaviour in the plexiglass pore. The onset of viscoelastic behaviour, which has previously been defined using the shear rate ( ), stretch rate ( _s ) and Ellis number (E ₁), could be more precisely evaluated using a modified stretch rate (S _G). The pressure losses across the plexiglass pore for different polymer solutions of the same type were found to follow a unique curve provided the suggested group (S _G) was used, a situation which was not achieved with the other rheological parameters.The multipass mechanical degradation of the non-hydrolized polyacrylamide was tested through the sand pack against the suggested group (S _G) and Maerker's group (M _a). It was found that the loss of the solution viscoelasticity due to multipass mechanical degradation was better represented usingS _G thanM _a. A cross-sectional area (cm²) - C ^* critical concentration of polymer (ppm) - d plexiglass pore enlargement diameter - D average sand grain diameter (cm) - e equivalent width for the plexiglass pore - E ₁ Ellis number (a Deborah number) - F _R resistance factor - F _Ri resistance factor at the first pass - h height of the flow path of the plexiglass pore - K power-law constant - K _h,K _w effective permeability to hydrocarbon and water, respectively (10^–8 cm²) - M _a Maerker's group for a given porosity (s^–1) - M _ai value ofM _a at the first pass - N _D Deborah number - n power-law index - Q flow rate (cm³/s) - R capillary radius (cm) - R _g radius of gyration - S _G suggested group of rheological parameters representing a modified maximum stretch rate (s^–1) - S _Gi value ofS _G at the first pass - T _R,t characteristic time for the fluid (s) - t _s residence time (s) - V ₀ superficial velocity (cm/s) - V mean velocity of flow through a porous medium (cm/s) - average axial velocity in the enlargement section of the plexiglass pore (cm/s) - V ₁,V ₂ maximum velocity at a plexiglass enlargement neck and centre - [] intrincis viscosity - viscosity (mPa s) - _r relative viscosity (ratio of the viscosity of the polymer solution to that of the solvent) - shear rate (s^–1) - _s stretch rate (s^–1) - characteristic time for the polymer solution (s)     

Shear rheology of carbon nanotube suspensions

The shear rheology of carbon nanotube suspensions is reviewed from the perspective of colloid and polymer science. In the semi-dilute to concentrated regimes, the nature of the equilibrium or quiescent state is often dominated by nanotube entanglement and strong attractive inter-particle interactions that favor the formation of a disordered network or gel. The strength of this network with respect to the applied stress dictates the development of mesoscale structural anisotropy, first through a global yield stress and then through a critical stress for homogenization. For concentrated suspensions, the nematic liquid-crystalline order anticipated for high-aspect-ratio rigid rods has been observed in a few select scenarios. The opportunity for deeper theoretical insight is emphasized and intuitive physical arguments are offered that might serve as a foundation for future study.     

The rheology of a smectic main-chain polymer

The rheology of a smectic main-chain polymer shows that the activation energy is high (275 kJ mol^–1) and that the viscosity is more than two orders of magnitude higher than in the isotropic phase. The recoverable strain in the smectic phase is largely due to the reformation of the smectic layers after cessation of shear.     

Bulk rheology of dilute suspensions in viscoelastic liquids

A theoretical relation is derived for the bulk stress in dilute suspensions of neutrally buoyant, uniform size, spherical drops in a viscoelastic liquid medium. This is achieved by the classic volume-averaging procedure of Landau and Lifschitz which excludes Brownian motion. The disturbance velocity and pressure fields interior and exterior to a second-order fluid drop suspended in a simple shear flow of another second-order fluid were derived by Peery [9] for small Weissenberg number (We), omitting inertia. The results of the averaging procedure include terms up to orderWe ². The shear viscosity of a suspension of Newtonian droplets in a viscoelastic liquid is derived as $$\eta _{susp} = \eta _0 \left[ {1 + \frac{{5k + 2}}{{2(k + 1)}}\varphi - \frac{{\psi _{10}^2 \dot \gamma ^2 }}{{\eta _0^2 }}\varphi f_1 (k, \varepsilon _0 )} \right],$$ whereη ₀, andω ₁₀ are the viscosity and primary normal stress coefficient of the medium,ε ₀ is a ratio typically between ?0.5 and ?0.86,k is the ratio of viscosities of disperse and continuous phases, and \(\dot \gamma \) is the bulk rate of shear strain. This relation includes, in addition to the Taylor result, a shear-thinning factor (f ₁ > 0) which is associated with the elasticity of the medium. This explains observed trends in relative shear viscosity of suspensions with rigid particles reported by Highgate and Whorlow [6] and with drops reported by Han and King [8]. The expressions (atO (We ²)) for normal-stress coefficients do not include any strain rate dependence; the calculated values of primary normal-stress difference match values observed at very low strain rates.     

The crossover between linear and non-linear mechanical behaviour in polymer solutions as detected by Fourier-transform rheology

 The application of oscillatory shear strain leads, in the non-linear regime, to the appearance of higher harmonic contributions in the shear stress response. These contributions can be analyzed as spectra in Fourier space, with respect to different frequencies, amplitudes and phase angles. In this article, we present an application of this new characterization method to a solution of the linear homopolymer polyisobutylene. The degree of non-linear response during oscillatory shear is quantified using the normalized intensity of the third harmonic contribution. We were able to show experimentally on polyisobutylene that there is an immediate onset of the non-linear response even for very small shear strain amplitudes. Received: 21 June 1999/Accepted: 21 August 1999     

Shear rheology of polymer solutions near the critical condition for elastic instability

The use of constant viscosity, highly elastic polymer solutions, so called Boger fluids, has been remarkably successful in elucidating the behavior of polymeric materials under flowing conditions. However, the behavior of these fluids is still complicated by many different physical processes occurring within a narrow window of observation time and applied shear rate. In this study, we investigate the long-time shear behavior of an ideal Boger fluid: a well characterized, athermal, dilute, binary solution of high molecular weight polystyrene in oligomeric polystyrene. Rheological measurements show that under an applied steady shear flow, this family of polymer solutions undergoes a transient decay of normal stresses on a timescale much longer than the polymer molecule's relaxation time. Rheological and flow visualization results demonstrate that the observed phenomenon is not caused by polymer degradation, phase separation, viscous heating, or secondary flows from elastic instabilities. Although the timescale is much shorter than that associated with polymer migration in the same solutions (MacDonald and Muller, 1996), the appearance of this phenomenon only at the rates where migration has been observed suggests that it may be a prerequisite for observing migration. In addition, we note that through sufficient preshearing of the sample, the normal stress decrease suppresses the elastic instability. These results show that there is considerable uncertainty in choosing the appropriate measure of the fluid relaxation time for consistently modeling the critical condition for the elastic instability, the decay of normal stresses, and the migration of polymer species.     

The physical interaction of spherical particles in suspensions

Summary An experimental examination of the interaction between a falling sphere and an aqueous suspension of nonsettling spheres through which it is passing is described. It is shown that if theReynolds number is small the falling speed of a sphere is unaffected by the size of the suspended spheres, provided that the volume concentration of the suspension is unchanged. This is shown to be true even when the falling sphere is of the same size as the suspended spheres. At highReynolds numbers, however, the falling speed of a sphere diminishes as its size approaches that of the suspended particles. The significance of these results to the theory of the viscosity of suspensions is discussed.     

The pseudoturbulent diffusion of particles in homogeneous suspensions

The effective diffusion coefficients for suspended particles caused by their pseudoturbulent pulsations, are treated. Derivatives of the dynamic variables which determine the average motion of the locally homogeneous suspension are neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, January–February, pp 67–72, 1970.     

Extensional flow behavior of polymer solutions and particle suspensions in a spinning motion

Mechanical spinning of fluid filaments was used to generate an extensional flow, in which rheological measurements were obtained for a Newtonian fluid, two aqueous polymer solutions, and two fluid suspensions of rod-shaped particles. The tensile stress was determined by measuring the tensile force of the fluid filament while the kinematics were determined from photographic measurement of the filament profile and the assumption of a flat velocity profile. The measured tensile stresses for the Newtonian fluid matched predicted stresses, thereby confirming the validity of the experimental technique.The spinning behavior of each polymer solution could be correlated as stress versus extension rate. The apparent “spinning viscosity” increased with increasing rate of extension, in contrast to shear-thinning behavior in viscometric flow. For the fluid suspensions, the presence of rod-shaped particles increased the apparent viscosity far more in extensional flow than in shear. Tensile stresses calculated from a theoretical formula for suspensions proposed by Batchelor agreed rather well with experiment. Some general criteria for the interpretation of the spinning experiment are proposed, and some microrheological implications of the present findings are discussed.