Comparison of different shear rheometers with regard to creep and creep recovery measurements

The performance of two shear rheometers with regard to creep and creep recovery measurements is investigated. The first one is a commercially available stress-controlled rheometer that uses an air bearing, and the second one is a magnetic bearing torsional creep apparatus that was built at the Institute of Polymer Materials in Erlangen. The creep and creep recovery measurements were performed in the linear-viscoelastic regime of two polyethylene melts at a temperature of 150°C. The creep compliances of the polyethylenes measured by both rheometers are in excellent agreement. The recoverable compliances of both polyethylene melts, however, have lower values in the case of the commercial rheometer than in the case of the magnetic bearing rheometer. The experimental parameters of creep recovery experiments and the features of the two bearings that are responsible for the different results of the two rheometers are discussed. The influence of the level of the applied shear stress on the short time behavior is investigated as well as the residual torque of the bearings which influences the long time region of the recoverable compliances. Also addressed are the influence of the momentum of inertia of the rotor and the bearing friction which is different for the two rheometers.     

Measuring device for precise evaluation of torsional creep and recovery data

An apparatus has been designed and built up to determine the shear creep compliance and viscosity with high accuracy in a wide range of temperature and time. The characteristic feature of this apparatus is the possibility to measure directly the recoverable compliance and to determine the steady state recoverable complianceJ _e . Disturbing instrumental forces are minimized by use of a magnetic bearing. The torque is applied inductively by a modified three phase asynchronous motor. The torsional angle is measured with a laser beam reflected from a mirror to an electro-optical measuring device. Sample thermostating is performed by radiation in a heating chamber, which allows observation of the specimen during measurement.First results of creep and creep recovery measurements are reported, which were carried out on a technical polystyrene above the glass rubbery transition.Dedicated to Prof. Dr. H. Janeschitz-Kriegl on the occasion of his 60th birthday.     

Influence of molecular structure on rheological properties of polyethylenes

Elastic properties of melts of a long-chain branched low density polyethylene (LDPE) with a broad molecular mass distribution and a short-chain branched linear low-density polyethylene (LLDPE) with a more narrow molecular mass distribution were investigated by creep recovery measurements in shear. The results obtained by means of a magnetic bearing torsional creep apparatus in the linear-viscoelastic region, showed that the steady state recoverable compliance of the LLDPE is greater by a factor of two than that of the LDPE. In the short-time region up to 1000 s, however, the time-dependent recoverable compliance of the LDPE is higher than that of the LLDPE. The retardation times for the LLDPE are considerably longer than for the LDPE. For the LDPE the temperature dependence of the entanglement transition is consistent with that of the terminal zone of the creep compliance. The activation energy of 58 kJ/mole lies in the typical range for long-chain branched polyethylenes. In the case of the LLDPE the creep compliances can be shifted to give a mastercurve with an activation energy of 34 kJ/mole, whereas the recoverable compliances do not follow the time-temperature superposition principle. The molecular characterization using TREF showed that the LLDPE has a bimodal branching structure. In addition to a short-chain branched component, a low percentage of a linear constituent with high molecular mass was found. It is postulated that this linear component forms a dispersed phase in the matrix of the short-chain branched constituent. The resulting interfacial tension could be the reason for the long retardation times, the high steady state recoverable compliance and the fact that the time-temperature superposition principle is not fulfilled in the case of the LLDPE investigated. Received: 1 July 1997 Accepted: 12 November 1997     

Creep recovery behavior of metallocene linear low-density polyethylenes

The rheological behavior of two metallocene linear low-density polyethylenes (mLLDPE) is investigated in shear creep recovery measurements using a magnetic bearing torsional creep apparatus of high accuracy. The two mLLDPE used are homogeneous with respect to the comonomer distribution. The most interesting feature of the two mLLDPE is that their molecular mass distributions are alike. Therefore, as one of the mLLDPE contains long-chain branches, the influence of long-chain branching on the elastic properties of polyethylene melts could be investigated. It was found that long-chain branches increase the elasticity of the melt characterized by the steady-state recoverable compliance. The long-chain branched mLLDPE has a flow activation energy of 45 kJ/mol which is distinctly higher than that of the other mLLDPE. The shear thinning behavior is much more pronounced for the long-chain branched mLLDPE. A discrepancy between the weight average molecular mass M _w calculated from size exclusion chromatography measurements by the universal calibration method and the zero shear viscosities of the two mLLDPE was observed. These observations are discussed with reference to the molecular architecture of the long-chain branched mLLDPE. The rheological properties of the long-chain branched mLLDPE are compared with those of a classical long-chain branched LDPE. It is surprisingly found that the rheological behavior is very much the same for these two products although their molecular mass distributions and presumedly the branching structures differ largely. Received: 15 February 1999 Accepted: 10 June 1999     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Influence of long-chain branches in polyethylenes on linear viscoelastic flow properties in shear

 This contribution presents a survey on the influence of long-chain branching on the linear viscoelastic properties zero shear-rate viscosity and steady-state recoverable compliance of polyethylene melts. The materials chosen are linear and slightly long-chain branched metallocene-catalyzed polyethylenes of narrow molecular mass distribution as well as linear and highly long-chain branched polyethylenes of broad molecular mass distribution. The linear viscoelastic flow properties are determined in shear creep and recovery experiments by means of a magnetic bearing torsional creep apparatus. The analysis of the molecular structure of the polyethylenes is performed by a coupled size exclusion chromatography and multi-angle laser light scattering device. Polyethylenes with a slight degree of long-chain branching exhibit a surprisingly high zero shear-rate viscosity in comparison to linear polyethylenes whereas the highly branched polyethylenes have a much lower viscosity compared to linear samples. Slightly branched polyethylenes have got a higher steady-state compliance in comparison to linear products of similar polydispersity, whereas the highly branched polyethylenes of broad molecular mass distribution exhibit a surprisingly low elasticity in comparison to linear polyethylenes of broad molecular mass distribution. In addition sparse levels of long-chain branching cause a different time dependence in comparison to linear polyethylenes. The experimental findings are interpreted by comparison with rheological results from literature on model branched polymers of different molecular topography and chemical composition. Received: 12 July 2001 Accepted: 30 October 2001     

Rheological properties of peanut butter

The rheological properties of two types of commercial peanut butter have been studied. Both products are concentrated suspensions, and differ by the presence of additives. The first type, referred to as “100% peanuts,” is an unstabilized suspension consisting of solid peanut particles in peanut oil which is a Newtonian fluid. The second type, referred to as “smooth,” consists of the same suspension stabilized with a vegetable oil and contains other ingredients such as salt and sugar in very small quantities. A mean volume particle diameter of 6.6 μm has been determined, the particle diameter distribution was found to be narrow, and the solids volume fraction was estimated to be 0.6. Slip encountered in rheometry was greatly reduced by gluing sandpaper to the parallel plates of the rheometer. Both samples behaved like plastic materials and apparent yield stresses of 24 Pa and 370 Pa have been determined for the unstabilized and the stabilized suspensions, respectively. No linear domain was found for both suspensions and the non-linearity was confirmed by deformed Lissajous curves and higher odd harmonics in the output signal of small amplitude oscillatory shear experiments. The stabilized suspension behaved more like a solid, the elastic modulus being larger than the loss modulus and almost independent of the frequency. This solid-like behavior is supposedly caused by strong repulsive (steric) forces induced by the stabilizing agent. Received: 29 September 1999 Accepted: 9 August 2000     

Determination of yield stress fluid behaviour from inclined plane test

The aim of this paper is to determine precisely under which conditions an inclined plane can be used as a rheometer, which could represent a practical and rapid technique for various types of industrial or natural viscoplastic coarse suspensions. We first examine its efficiency and relevancy for determining fluid yield stress in a straight way by measuring the deepest fluid layer able to stay on the inclined plane. We have made experiments with different materials (clay-water suspensions) whose yield stress ranged from 35 to 90 Pa, using 1 m long open rectangular channels with a slope ranging from 10 to 30° and a width ranging from 5 to 25 cm. Our procedure involved measuring the final fluid depth far from edges a long time after the end of the slow gravity-induced emptying of a dam placed upstream. The fluid yield stress was also estimated independently by fitting a Herschel-Bulkley model to simple shear rheometry data obtained within a relatively wide shear rate range. A good agreement between inclined rectangular channel tests and independent usual rheometrical tests is obtained even for aspect ratios (flow depth to channel width ratio) as large as 1 when one assumes that, when the fluid has stopped, the side and bottom wall shear stresses are equal to the fluid yield stress. These results prove the efficiency of the inclined plane test for determining yield stress when appropriate experimental precautions are taken for both tests. In addition we examine the possibility of determining the simple shear flow curve of a mud suspension from fluid depth, velocity and discharge measurements of different steady flows in a wide open channel (8 m long; 60 cm wide) equipped with a recirculating system. The results obtained from inclined plane tests are in good agreement with independent rheometrical data (with torsional geometries). However it is technically difficult to cover a wide shear rate range from the inclined plane technique since this requires a rather wide channel flow rate range.     

Comparison of viscous and elastic properties of polyolefin melts in shear and elongation

Viscous and elastic properties of a linear polypropylene (PP) and a long-chain branched low-density polyethylene (LDPE) have been investigated by creep and creep–recovery experiments in shear and elongation. The data obtained verify the ratios between the linear values of the viscosities and the steady-state elastic compliances in shear and elongation predicted by the theory of linear viscoelasticity. In the nonlinear range, no simple correlation between the viscous behaviour in shear and elongation exists. The elongational viscosity of the PP decreases with increasing stress analogously to the shear thinning observed; the linear range extends to higher stresses in elongation than in shear, however. The LDPE shows thinning in shear and strain hardening in elongational flow. For the LDPE, a linear steady-state elastic tensile compliance corresponding to one third of the linear steady-state elastic compliance in shear was determined. For the PP, this theoretically predicted value is approximately reached. Analogous to the viscous behaviour, the linear range extends to higher stresses in elongation than in shear. For both materials, the steady-state elastic compliances in the nonlinear range decrease with increasing stress in shear as well as in elongation. However, the decrease in elongation is more pronounced.     

A new eccentric-cylinder rheometer

A new eccentric-cylinder rheometer with guard-ring equipment was constructed as an auxiliary set-up to a Rheometrics Mechanical Spectrometer, type 7200, which enables measurements with the eccentric disk technique. Experimental tests with Newtonian fluids and polymer solutions of relatively low viscosity show that this instrument yields reliable plots of shear viscosity and first normal-stress coefficient over several decades of the effective average shear rate. These coincide very well with plots from a commercial cone-and-plate rheometer even for higher relative eccentricities (up to 0.75). However, no systematic effects of eccentricity, to be expected for higher shear rates, could be observed with these fluids, so that supplementary tests applying fluids with more pronounced viscoelastic properties are to be carried out.     

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.     

Direct measurement of static yield properties of cohesive suspensions

A technique of yield stress investigation based upon the combined use of two devices (an applied stress rheometer and an instrument for measuring the propagation velocity of small amplitude, torsional shear waves) is described. Investigations into the low shear rate rheological properties of illitic suspensions are reported for shear rates, typically, in the range 10^–4— 10^–1 s^–1 under applied stresses in the range 0.01 — 10 Nm^–2 and involving shear strains between 10^–1 and 10^–4. Results are presented which demonstrate that the technique does not invoke the excessive structural disruption of material associated with applied shear rate based methods (direct and otherwise) and the widely encountered problem of wall slip at the surface of rotational measuring devices is avoided using miniature vane geometries. Results are compared with those obtained using smooth-walled cyclindrical measuring devices in both applied stress and applied shear rate instruments.Yield measurements are considered in relation to the structural properties of the undisturbed material state and shear moduli obtained by studying the propagation of small amplitude (10^–5 rad), high frequency (~ 300 Hz) torsional shear waves through the test materials are reported. Experimental techniques and instrument modifications to permit these measurements are described.     

Rheology of pulp suspensions using ultrasonic Doppler velocimetry

Conventional rheometry coupled with local velocity measurements (ultrasonic Doppler velocimetry) are used to study the flow behaviour of various commercial pulp fibre suspensions at fibre mass concentrations ranging from 1 to 5 wt.%. Experimental data obtained using a stress-controlled rheometer by implementing a vane in large cup geometry exhibits apparent yield stress values which are lower than those predicted before mainly due to existence of apparent slip. Pulp suspensions exhibit shear-thinning behaviour up to a high shear rate value after which Newtonian behaviour prevails. Local velocity measurements prove the existence of significant wall slippage at the vane surface. The velocimetry technique is also used to study the influence of pH and lignin content on the flow behaviour of pulp suspensions. The Herschel–Bulkley constitutive equation is used to fit the local steady-state velocity profiles and to predict the steady-state flow curves obtained by conventional rheometry. Consistency between the various sets of data is found for all suspensions studied, including apparent yield stress, apparent wall slip and complete flow curves.     

Measurement of Torsionally Induced Shear Stresses in Shrink-Fit Assemblies

Shear stresses along the shaft/hub interface in shrink-fit components, generated by torsional loads, can drive premature failure through fretting mechanisms. It is difficult to numerically predict these shear stresses, and the associated circumferential slip along the shaft/hub interface, due to uncertainties in frictional behaviour and the presence of steep stress gradients which can cause meshing problems. This paper attempts to provide validation of a numerical modelling methodology, based on finite element analysis, so the procedure may be used with confidence in fitness-for-purpose cases. Very few experimental techniques offer the potential to make measurements of stress and residual stress interior to metallic components. Even fewer techniques provide the possibility of measuring shear stresses. This paper reports the results of neutron diffraction measurements of shear stress and residual shear stress in a bespoke test specimen containing a shrink-fit. One set of measurements was made with a torsional load ‘locked-in’. A second set of measurements was made to determine the residual shear stress when the torsional load had been applied and removed. Overall, measurement results were consistent with numerical models, but the necessity for a small test specimen to allow penetration of the neutron beam to the measurement locations meant the magnitude of shear stresses was at the limits of what could be measured experimentally.     

Rheological properties of disperse systems at low shear stresses

Three-dimensional network structures can be built up in disperse systems due to long-range colloidal interactions between the dispersed particles. The rheological behaviour of such coagulation structures has been studied by means of creep and recovery experiments at low shear stresses, i.e. by measuring the shear strain as a function of time under constant stress and after removal of stress. Measurements of this type give insight into the elastic and viscous deformations and the retardation times necessary to reach equilibrium or steady-state conditions.Results obtained with dispersions of pigments in polymer solutions and with monodisperse polymer latexes indicate the existence of an equilibrium state at low shear stresses with a predominant elastic deformation and a high viscosity suggesting that the disperse systems investigated do not behave exactly as rigid gels but apparently exhibit a dynamic equilibrium of structural break-down and formation under applied stress. This behaviour is approximately described by a 4-parameter-model with an instantaneous and a steady-state compliance, one retardation time, and a viscosity.At higher shear stresses thixotropic structural break-down occurs resulting in a transition from the rheological behaviour described here to a liquid-like state with a comparatively low viscosity. In this stress range the viscoelastic properties become strongly time-dependent.These measurements give evidence of the presence of two types of deformation: an instantaneous, purely elastic deformation attributable to the unperturbed coagulation structure and the creep-recovery behaviour of an elastic liquid apparently related to the breaking and re-forming of bonds.     

Rheometry on magnetorheological (MR) fluids

Test fixtures of a commercial concentric cylinder rheometer (Physica Rheolab MC 20) were modified to enable measurements under magnetic inductions up to 0.5 Tesla in a shear rate range of 0.1 up to 1000 s ^–1 and temperatures 0° to 150°C. In the 2 x90°-cups only two 90° sectors of the stationary part of the double concentric cylinder arrangement are submitted to the magnetic field which is created outside the test tools by an electromagnet. A prototype of a 360°-cup contains the electromagnet within the cup and avoids the correction necessary for the sector geometry. Measurements are shown for a carbonyl iron MR fluid and two nano MR fluids. An encouraging comparison of the viscosity function and MR effect (shear stress changes due to the field) measured by using the various cups is presented. The detailed investigation of the magnetic field distribution in the tools yields a distinct radial field gradient and also stray fields that make the quantification of the effective field in the gap difficult. The change of the field when the gap is filled with MR fluid is addressed. MR effects up to 13 000 Pa have been found, the limited torque range of the rheometer making it necessary to use relatively small gap dimensions which introduce errors due to edge effects. Shear rates up to 40000 s^–1 as typical for the application in dampers were investigated by a piston-driven capillary rheometer making use of a thermostated rectangular slit with superimposed magnetic field. A satisfactory agreement of the magnetorheological data with the concentric cylinder results is found in the overlapping shear rate range.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Extensional rheology of a shear-thickening cornstarch and water suspension

A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.     

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.     

Characterization of the non-linear response of asphalt mixtures using a torsional rheometer

There is sparse documentation of the large normal stresses that develop in asphalt mixtures subjected to shear, a typical characteristic of non-linear materials. In this study, we continue our initial investigations of using a torsional rheometer for measuring the normal stresses developed in asphalt mixtures when subjected to torsion. Samples of sand-asphalt mixture are subjected to rotation rates as low as one revolution in ninety minutes. This study provides further clear evidence of significant development of normal stresses due to shearing and emphasizes the need for the development of models that can describe such a phenomenon.