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     

Effects of polymer–fiber interactions on rheology and flow behavior of suspensions of semi-flexible fibers in polymeric liquids

Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.     

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 rheology of suspensions of porous zeolite particles in polymer solutions

We present data and predictive models for the shear rheology of suspended zeolite particles in polymer solutions. It was found experimentally that suspensions of zeolite particles in polymer solutions have relative viscosities that dramatically exceed the Krieger–Dougherty predictions for hard sphere suspensions. Our investigations show that the major origin of this discrepancy is due to the selective absorption of solvent molecules from the suspending polymer solution into zeolite pores. The effect raises both the polymer concentration in the suspending medium and the particle volume fraction in the suspension. Consequently, both the viscosity of the polymer solution and the particle contribution to the suspension viscosity are increased. We propose a predictive model for the viscosity of porous zeolite suspensions by incorporating a solvent absorption parameter, α, into the Krieger–Dougherty model. We experimentally determined the solvent absorption parameter by comparing viscosity data for suspensions of porous and nonporous MFI zeolite particles. Our results are in good agreement with the theoretical pore volume of MFI particles.     

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.     

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 relaxation of concentrated polymer solutions

The focus of this paper is on the viscoelastic properties of concentrated polymer solutions and polymer melts. Dynamic mechanical measurements were performed on various polystyrene/ethylbenzene solutions with polymer concentrations ranging from 40% up to 100% and temperatures from Tg+30°C up to 70°C (230°C for polymer melts). The basis polymers are two commerical grade polystyrenes (BASF) with M _W = 247 kg/mol and 374 kg/mol, respectively. To avoid solvent loss due to evaporating during the measurements, a special sealing technique was used.A phenomenological model which describes quantitatively the relaxation spectrum of concentrated polymer solutions from the flow regime up to the glass transition regime is developed. The relaxation data of the respective polymer melt and the glass transition temperature of the solution are the only input parameters needed. The temperature dependence is described by a universal, concentration invariant WLF-equation. The relaxation spectra are divided into two parts accounting for the entanglement and the segmental relaxation modes, respectively. The relaxation strength related to the flow and entanglement regime scale with c ^2.3, whereas the segmental relaxation strength does not alter with concentration. All relaxation times change with concentration proportional to c ^3.5. Flow curves can be calculated from these relaxation spectra and thus, our results are useful for engineering applications.Roman Symbols a _T Time temperature superposition shift - factor - a _c Time concentration superposition - shift factor in the flow regime - a _c Time concentration superposition - shift factor in the glassy regime - b _T Modulus temperature superposition - shift factor - b _c Modulus concentration shift factor - in the flow regime - b _c Modulus concentration shift factor - in the glassy regime - B Virial coefficients - c Polymer mass fraction kg/kg - c ₁ WLF-parameter - c2 WLF-parameter K - g Relaxation strength of a relaxation Pa mode - G(t) Relaxation modulus Pa - G Storage modulus Pa - G Loss modulus Pa - GN Plateau modulus of linear flexible Pa polymers - (x) Delta function: (0) = 1, - (x<>0)=0 - h() Damping function - H() Relaxation spectrum Pa - J ₀ ^N Recoverable compliance Pa^–1 - m Mass kg - M _c Critical molecular weight kg/mol - M _e Entanglement molecular weight kg/mol - M _w Weight average molecular weight kg/mol - M Number of datapoints - n Scaling exponent - N Number of discrete relaxation modes - T Temperature °C - T _g Glass transition temperature °C - V Volume 1 Greek Symbols Scaling exponent - _f Thermal expansion coefficient K^–1 - Scaling exponent - Shear deformation - Shear rate s^t–1 - Relaxation time s - _c Characteristic relaxation time of thes Cross model - _e Entanglement relaxation time s - Viscosity Pa s - ₀ Zero shear viscosity Pa s - ₀ First normal stress coefficientPa s2 - Segmental friction coefficient - Frequency rad/s Indices f Flow and entanglement regime - g Glass transition regime - i Count parameter - p Polymer - ref Reference state - s Solvent 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     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001     

Molecular orientation in non-Newtonian flow of dilute polymer solutions around spheres

A novel approach is presented to study the benchmark problem of flow around spheres in model dilute solutions of monodisperse samples of atactic polystyrene in di-octyl phthalate. Spheres are held stationary on flexible cantilevers of known spring-constant, k, while the polymer solutions are pumped past at controlled flow rates, allowing access to a wide range of Deborah number. In this way the non-Newtonian forces experienced by the spheres can be measured as a function of Deborah number, while detailed observations and measurements of birefringence are made, enabling assessment of macromolecular strain and orientation. In addition the flow field around a sphere has been measured in an a-PS solution. Experiments have been performed on a single sphere and on two spheres axially aligned in the direction of flow. The extensional flow around the downstream stagnation point of the single sphere is found to play a pivotal role in the development of molecular strain and stress, resulting in flow modification and subsequent non-Newtonian behaviour. The flow birefringence in the wake is found to modify severely the flow around a second, downstream, sphere, affecting the non-Newtonian forces encountered by the second sphere. This provides an explanation for the time interval dependent terminal velocity often observed when two spheres follow the same path through viscoelastic liquids.     

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.     

A rheo-optical study of shear-thickening and structure formation in polymer solutions. Part II: Light scattering analysis

Light scattering calculations based on Anomalous Diffraction Theory (AD), Rayleigh spheroids, and flexible macromolecules are used to propose a phenomenological explanation for the relationship between shear-thickening and structure formation in polymer solutions. Quantitative comparisons are made to experimental data for the rheo-optical behavior of fractionated polystyrene solutions presented in part I of this paper. Results from the ADA calculations suggest that the viscosity and dichroism behavior can be attributed to the production and growth of micron-size, optically isotropic structures during flow. The saturation dichroism behavior exhibited by the solutions which shear thin can be attributed to the formation of entanglement regions which achieve a fixed size and act as Rayleigh spheroids in their scattering behavior. The magnitude and shear rate dependence of the observed birefringence can be accounted for on the basis of the non-linear, flexible macromolecule model, implying that birefringence is governed by the polymer chains remaining in solution which do not take part in the structure formation. The latter result is consistent with the experimental observation that the birefringence dependence on shear rate is the same whether the solution exhibits shear thickening or shear thinning in its viscosity behavior.     

On-line measurement of elasticity and viscosity in flowing polymeric liquids

A new slit-die rheometer (the Stressmeter) for on-line and sample measurement of the viscosity, , and the first normal stress difference, N ₁, in steady shear flow for molten polymers and other high-viscosity liquids is described. Two liquid-filled transverse slots, located in one die wall near the center station, give pressures P ₂ and P ₃ from whose difference the wall shear stress is calculated. In the other die wall at a location opposite the center of the P ₂ slot is a flush-mounted transducer, giving a pressure P ₁. N ₁ is calculated from the hole pressure P ^* = P ₁–P ₂. A metering pump, used to measure the flow rate Q, is supplied with melt either from an extruder (online mode) or from a pressurized sample cylinder (sample mode). The wall shear rate is calculated from Q and ; the Weissenberg-Rabinowitsch correction and a new small-viscous-heating-correction algorithm (affecting ) are used. Viscous heating corrections are small; entrance and exit errors are negligible. The instrument is tested by comparing its results with those obtained from cone-plate and capillary rheometers. Measurement ranges extend to = 200 kPa, = 3000 s^–1, and temperature = 250°C.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     

A rheo-optical study of shear-thickening and structure formation in polymer solutions. Part I: Experimental

Simultaneous measurements of the optical and theological response of solutions of highly fractionated polystyrenes have been made, in-situ, to ascertain the connection between flow-induced structure formation and the phenomenon of shear-thickening. Transient and steady state viscosity, dichroism, birefringence and the associated orientation angles were measured in decalin and bromobenzene in the semi-dilute region using a couette device capable of shear rates up to 8,000 s^–1. A one-to-one correlation has been found between the occurrence of maxima in the dichroism and minima in the viscosity. While the size and shape of the shear-thickening structures could not be directly determined, results suggest they are intermediate in size between a cluster of entangled chains and a completely phase-separated liquid. For solutions exhibiting shear-thinning alone, no maximum in dichroism was observed, the signal instead showed a saturation behavior at high shear rates. Birefringence was found to be insensitive to the structure formation and attributable to that of the dissolved chains or entanglement regions. The kinetics of the structuring process leading to shear-thickening are instantaneous and completely reversible and there is a concentration window, above and below which only shear-thinning occurs.     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999