Shear viscosity of suspensions of aligned non-Brownian fibres

We report on the steady-state shear viscosity of suspensions of fibres dispersed in Newtonian fluids, in a wide range of volume fractions throughout the dilute and semi-dilute regimes. We show that the apparent shear-thinning behaviour, which is sometimes observed in the semi-dilute regime at intermediate shear rates, is an experimental artefact due to the presence of transient clusters of entangled fibres in the suspensions. At high shear rates, the fibres are aligned and the suspensions exhibit Newtonian behaviour. In this regime, the viscosity is a function of volume fraction and fibre aspect ratio only. The data can be rescaled onto a universal curve using a variable that accounts for the average contribution of the particles to the bulk stress. All these results are discussed in relation to recent theories. Received: 19 January 1999 Accepted: 17 June 1999     

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.Originally presented at the Annual European Rheology Conference 2003, AERC 2003     

Study of semidilute fibre suspension rheology with lattice-Boltzmann method

A hybrid lattice-Boltzmann numerical simulation method is undertaken to study the rheology of non-colloidal, rigid fibres in sheared, semidilute Newtonian suspension. The viscosity and the first normal stress difference are calculated with the combined use of numerical fibre orientation information and a corrected form of the slender body theory of Batchelor (J Fluid Mech Digit Arch 46(4):813–829, 1971). The corrections make the theory applicable in semidilute suspension flow (Shaqfeh and Fredrickson, Phys Fluids A: Fluid Dyn 2(1):7–24, 1990) with fibres of finite aspect ratio. The corrected theory within its framework, based on spacing among fibres in semidilute suspension, only considers hydrodynamic interactions among fibres and inferences that the effect of actual fibre–fibre mechanical contacts on rheological properties of such suspension systems remains inconsequential. To investigate this issue, the rheological properties of semidilute suspension were calculated directly from the numerical simulation. This approach accounted for both hydrodynamic and mechanical interactions among fibres. This direct measurement proved that the mechanical interactions increase both the relative shear viscosity and the first normal stress difference in the semidilute suspension to values which are larger than permissible within the framework of Batchelor’s theory.     

Fibre suspension rheology: effect of concentration, aspect ratio and fibre size.

Viscosity data for fibre suspensions are produced using cone-and-plate geometry of enhanced dimensions for the reduced influence of fibre-wall interactions. Semi-concentrated suspensions of monodisperse polyamide fibres in silicone oil, with a variety of fibre concentrations (2, 5 and 8%), lengths and diameters, were studied. The suspension viscosity was measured in a range of shear stress in order to study the stress dependence. The study here focuses on the nature of the forces and interactions that contribute to the suspension viscosity. The results show that at sufficiently high stress levels, the suspension viscosity tends to reach a steady-state. At very low stress levels the suspension viscosity increases over time, most likely due to structures formed by adhesive forces. At higher concentrations, the viscosity depends on the absolute size of the fibres, again indicating the presence of non-hydrodynamic interactions.     

Shear behaviour of biopolymer suspensions with spheroidal and cylindrical particles

The rheological behaviour of suspensions is influenced by many parameters, one of which is the particle shape. For rigid particle suspensions a number of studies demonstrate the effects of the particle aspect ratio. Indeed, fibres are widely used as rheology modifiers in different materials such as synthetic polymers. This work is concerned with testing the hypothesis that regularly shaped particles with aspect ratios larger than one that are made of gelled biopolymers could be used as rheology modifiers for biopolymer solutions. Biopolymers, and mixtures thereof are a widely used ingredient in foods and other products with structure functionality. Tailoring rheology modifiers by morphology offers an alternative to using different biopolymers. It is demonstrated how biopolymer suspensions with regular spheroidal, or cylindrical particle shapes can be produced by gelling the droplet phase of a liquid two phase biopolymer mixture in a shear field. Biopolymers were chosen such that gelation is initiated by cooling. Shear-cooling at constant stresses leads to the formation of ellipsoidal particles. Cylindrical particles can be generated by stepping up the shear stress prior to gelation, i.e., stretching the droplet phase into fibrils, and trapping the shape prior to break-up through gelation. Morphologies and steady shear rheological data for suspensions of the two biopolymers gellan and κ-carrageenan with an internal phase volume of 0.2 are reported. The influence of particle shape on relative viscosity is pronounced. At high shear stresses particle orientation leads to decreased viscosity with increasing particle aspect ratio. In the low shear region, higher aspect ratio suspensions show higher viscosities. Additionally, the material properties, including the interfacial tension, which influence the suspension morphology are reported. Received: 3 March 2000 Accepted: 22 August 2000     

Der Einfluß der elastischen Eigenschaften des Trägermediums auf das Fließverhalten von Kugel- und Fasersuspensionen

The influence of the elastic properties of the suspending medium on the flow of viscoelastic glass bead and glass fibre suspensions through flat orifices was investigated. The results are discussed by contrasting the flow behaviour of the viscoelastic suspensions with that of corresponding suspensions in a Newtonian suspending medium. For the suspensions in a Newtonian oil linear relationships were always found between the pressure loss and the effective velocity gradient in orifice flow. Thus it can be concluded that in this case the influence of the filler on the flow behaviour is independent of the imposed strain. Increasing the filler content or using more anisotropic particles led to higher viscosities and thus to larger pressure losses. It is well known that viscoelastic polyisobutene solutions show strain rate dependent flow behaviour. Due to the increasing influence of elasticity with increasing strain rate, the apparent flow curves can be divided into characteristic regions with different slopes. The addition of filler to such solutions altered the shape of the flow curves and it was found that the onset of “flow hardening” occurred at lower imposed strains. In addition, characteristic changes in the hardening behaviour and flow stability were observed; these were most pronounced for the fibre suspensions, even at low concentrations. For the fibre suspensions, these phenomena could be related to the influence of the fibres on the undisturbed flow field near the orifice, leading, in general, to higher strain velocities between the fibres. On the other hand, enhanced extensional strains are induced at the ends of the fibres and, at the same time, shear flow occurs along the fibres. These two effects counteract each other with respect to the hardening behaviour of the polymer. Similar effects may also occur in the glass bead suspensions, although they would certainly be less pronounced.     

Shear influence on fibre orientation

The purpose of this experimental work was to study the influence of shear close to a solid boundary on the fibre orientation in suspensions with different fibre aspect ratios and concentrations. We have studied a laminar suspension flow down an inclined plate. The fibre orientation in different wall parallel planes were measured. We applied an index-of-refraction (IR) matching method together with particle tracking techniques to obtain the fibre motion. The fibre orientation was extracted using a two-dimensional wavelet transform. The shear flow resulted in fibres perpendicularly oriented to the streamwise direction (“rollers”) in the near wall region. These rollers were observed in the experiment to perform a rolling-sliding motion down the inclined plate around a stable perpendicular orientation. As the distance to the wall increased the number of rollers decreased and the fibre orientation was unaffected from its initial streamwise orientation. As the aspect ratio increased the influence of shear on the fibre orientation decreased for all measured wall parallel planes. This was also the case for higher fibre concentrations. The purpose of this study was to contribute to the development of the capacity to control the sheet network structure in papermaking. KTH-Biofibre Materials Centre (BiMaC), FaxenLaboratoriet KTH-Mechanics for supporting this study. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Lubricated compression and X-ray microtomography to analyse the rheology of a fibre-reinforced mortar

In this work, the microstructure and the rheology of a glass-fibre-reinforced fresh mortar were studied. Various fibre contents and aspect ratios and two types of fibrous reinforcement, i.e. slender fibre bundles and fibres, were tested. The microstructure was analysed by using X-ray microtomography. It is shown that the non-deformed mortar is a porous granular suspension, the porous microstructure of which is not influenced by the presence of fibres, which in turn display a 2D planar random fibre orientation. The rheology was investigated by subjecting samples to constant axial strain rate and lubricated compression. The roles of the actual strain, the mortar resting time, the fibre content and aspect ratio on recorded stress levels are emphasised. Besides, for the investigated strain rate and material parameters, the mortar flow is quasi-incompressible and does not affect significantly the porous microstructure nor the fibrous one. Lastly, the stress increase which is induced by the addition of fibre bundles is similar to that predicted by Newtonian models of semi-dilute fibre suspensions.     

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     

Analysis of periodic 3D viscous flows using a quadratic discrete Galerkin boundary element method

A discrete Galerkin boundary element technique with a quadratic approximatión of the variables was developed to simulate the three-dimensional (3D) viscous flow established in periodic assemblages of particles in suspensions and within a periodic porous medium. The Batchelor's unit-cell approach is used. The Galerkin formulation effectively handles the discontinuity in the traction arising in flow boundaries with edges or corners, such as the unit cell in this case. For an ellipsoidal dilute suspension over the range of aspect ratio studied (1 to 54), the numerical solutions of the rotational velocity of the particles and the viscosity correction were found to agree with the analytic values within 0.2% and 2% respectively, even with coarse meshes. In a suspension of cylindrical particles the calculated period of rotation agreed with the experimental data. However, Burgers' predictions for the correction to the suspension viscosity were found to be 30% too low and therefore the concept of the equivalent ellipsoidal ratio is judged to be inadequate. For pressure-driven flow through a fixed bed of fibres, the prediction on the permeability was shown to deviate by as much as 10% from the value calculated based on approximate permeability additivity rules using the corresponding values for planar flow past a periodic array of parallel cylinders. These applications show the versatility of the technique for studying viscous flows in complicated 3D geometries.     

Shear flow rheological properties of vinylon- and glass-fiber reinforced polyethylene melts

Shear viscosity, shear stress and first normal-stress difference have been investigated for glass- and vinylon-fiber filled polyethylene melts over a wide range of shear rate by means of three kinds of instruments. The influence of fiber content and fiber properties on the rheological properties is discussed. The viscosity increases with increasing aspect ratio and fiber content, and the influence of these parameters on the flow properties is evident at low shear rates. The first normalstress difference increases more rapidly with increasing glass fiber content, especially at low shear stresses. The influence of vinylon fibers on the first normal stress-difference vs. shear-stress relationship is different from that of glass fibers.     

Study of geometry effects in torsional rheometry of fibre suspensions

This work concerns the problem of measuring the viscosity of a suspension of fibres that are not short compared to the dimensions of the measurement device. We have examined various geometry effects in shear using parallel-plate and cone-and-plate configurations. Steady state viscosity, transient viscosity and first normal stress difference have been studied. Silicone oil with milled glass fibres at 8 vol.% was used as a model fibre suspension. The conventional parallel-plate geometry exhibits a significant gap dependence of the apparent viscous response. Too small gaps constrain the fibre rotations, thus lowering the initial stress peak and delaying the development of steady state. Too large gaps lead to a loss of liquid at the sample perimeter, which reduces the apparent steady state viscosity. The steady state response, however, seems to be correct for gaps in the range 1–2 mm when the maximum fibre length is 1.5 mm. The cone-and-plate geometry is less sensitive to large gaps. Too small a gap at the (truncated) cone apex leads to anomalous response due to bridging of the gap by fibres. The use of unusually large plates (100 mm diameter) and different cone angles and truncations was explored. It was shown that cone-and-plate configurations of large diameter and large truncation can effectively decrease the geometry disturbances both due to fibre bridging at the cone apex and loss of liquid at the edge.     

Flow and breakup characteristics of elliptical liquid jets

This paper presents the results of an experimental study on liquid jets discharging from elliptical orifices into still ambient air. The experiments were conducted with a set of elliptical orifices of approximately same area of cross section but varying orifice aspect ratio using water and water–glycerol mixture as experimental fluids. The flow behavior of liquid jets was analyzed using their photographs captured by an imaging system. The measurements obtained for the elliptical liquid jets were compared with the circular liquid jets discharging from a circular orifice of the same area of cross section. Elliptical geometry of the orifice results in a flow process by which the emanating liquid jet periodically switches its major and minor axes as it flows downstream of the orifice. In this paper, we attempt to characterize the axis-switching process through its wavelength and amplitude. For a given elliptical orifice, the axis-switching process is dominantly seen in a particular range of flow conditions. The effects of the orifice aspect ratio and liquid viscosity on the axis-switching process are revealed through this study. The experimental results on jet breakup show that axis-switching process has a destabilizing effect on elliptical liquid jets within a particular range of flow conditions and it results in shorter breakup lengths compared to the circular jet. The extent to which axis-switching destabilizes the jet is dictated by the viscosity of liquid. An increase in orifice aspect ratio destabilizes elliptical liquid jets with low viscosity like water; however, this behavior seems to get obscured in water–glycerol mixture elliptical jets due to high viscosity.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

Effect of melt viscosity of polypropylene on fibrillation of thermotropic liquid crystalline polymer in in situ composite film

 Various grades of polypropylene were melt blended with a thermotropic liquid crystalline polymer, a block copolymer of p-hydroxy benzoic acid and ethylene terephthalate (60/40 mole ratio). The blends were extruded as cast films at different values of draw ratio (slit width/film thickness). Fibrillation of TLCP dispersed phase with high fiber aspect ratio (length/width) was obtained with the matrix of low melt flow rate, i.e., high viscosity and with increasing film drawing. Melt viscosities of pure components and blends measured using capillary rheometer were found to decrease with increasing shear rate and temperature. Viscosity ratios (dispersed phase to matrix phase) of the systems being investigated at 255 °C at the shear rate ranged from 10² to 10⁴ s⁻¹, were found to lie between 0.04 and 0.15. The addition of a few percent of elastomeric compatibilizers; a tri-block copolymer SEBS, EPDM rubber and maleated-EPDM, was found to affect the melt viscosity of the blend and hence the morphology. Among these three compatibilizers, SEBS was found to provide the best fibrillation. Received: 10 January 2000/Accepted: 24 January 2000     

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     

A note on the extensional viscosity of elastic liquids under strong flows

In this article a parametric study based on a balance between viscous drag and restoring Brownian forces is used in order to construct a nonlinear dumbbell model with a finite spring and a drag correction for a dilute polymer solution. The constitutive equations used are reasonable approximation for describing flows of very dilute polymer solutions such as those used in turbulent drag reduction. We investigate the response of an elastic liquid under extensional flows in order to explore the roles of a stress anisotropy and of elasticity in strong flows. It is found that for low Reynolds numbers, the extensional viscosity of a dilute polymer solution is governed by two parameters: a Deborah number representing the importance of the elasticity on the flow and the macromolecule extensibility that accounts for the viscous anisotropic effects caused by the macromolecule orientation. Two different asymptotic regimes are described.The first corresponds to an elastic limit in which the extensional viscosity is a function of the Deborah number and the particle volume fraction. The second is an anisotropic regime with the extensional viscosity independent of Deborah number but strongly dependent on macromolecule aspect ratio. The analysis may explain from a phenomenological point of view why few ppms of macromolecules of high molecule weight or a small volume fraction of long fibres produce important attenuation of the pressure drop in turbulent flows. On the basis of our analysis it is seen that the anisotropic limit of the extensional viscosity caused by extended polymers under strong flows should play a key role in the attenuation of flow instability and in the mechanism of drag reduction by polymer additives.     

The effect of fibre length on the overall moduli of composite materials

An application of the self-consistent method (s.c.m.) is given to the problem of determining overall moduli for short fibre reinforced composites. It is assumed that the fibres can be considered to be spheroids. For fully-aligned fibres, the numerical results are presented in graphical form and show the dependence of the compliances on aspect ratio and volume fraction. It is shown that an aspect ratio of 100 is essentially infinite. By making use of some (albeit tentative) ideas on how to handle the misalignment of fibres the s.c.m. results are shown to compare favourably with experiment.     

Determination of elongational viscosity of polymer melts by RME and Rheotens experiments

Several linear (LLDPE, HDPE, PS) and long-chain-branched (LDPE, PP) polymer melts were investigated by an elongational rheometer (RME Rheometrics) and by Rheotens (Göttfert). The Molecular Stress Function (MSF) theory is briefly reviewed and used to extrapolate the steady-state elongational viscosity. To evaluate Rheotens experiments, a new process model is introduced which assumes that the elongational viscosity in the Rheotens test is a function of the draw ratio only. The apparent elongational viscosities extracted from Rheotens curves are found to lie in between the steady-state elongational viscosity and three times the shear viscosity.