Steady Shear Rate Research Articles

An asymptotic expansion for the high-frequency superposed dynamic viscosity of the Doi-Edwards fluid

It has been observed that when small oscillations are superposed on a steady shearing flow of a polymer fluid, the superposed dynamic viscosity becomes independent of the underlying steady shear rate at high frequencies of oscillation. Previous predictions of such behavior from the BKZ theory depended on the assumption that the linear shear modulus, G( t), can be continued analytically across the imaginary axis in the complex t-plane. It is shown that this cannot be done for a Doi-Edwards fluid and, therefore, that the previous arguments do not apply to this fluid. Nevertheless, a new derivation establishes that the observed high-frequency behavior of the superposed dynamic viscosity is, indeed, predicted by the Doi-Edwards fluid. An asymptotic expansion of the dynamic viscosity is also obtained.

Constitutive Behavior of Semi-Solid Metal Alloy Slurries

AbstractThe constitutive flow behavior of semi-solid metal alloy slurries has been modeled using an internal variable framework. The formulation represents the primary flow response of these materials: history dependence (thizotvopy), steady state shear rate thinning (pseudoplasticity) and constant internal structure shear rate thickening (dilatancy). The flow response at any given structure has been decoupled from structure-dependent response in carefully controlled rapid transient experiments done on a computer-controlled, high temperature, Couette geometry rheomneter. The data for Sn-15wt%Pb correlates well with the model.

Viscoelastic properties of aqueous solutions of an exocellular polysaccharide from cyanobacteria

The viscoelastic properties of aqueous solutions of the exocellular polysaccharide of Cyanospira capsulata have been studied, over a wide range of polymer concentrations, using small deformation oscillatory, steady and transient shear methods. The viscoelastic spectra generally resemble those of an entangled network, although notable deviations can be observed in the low frequency dependence of G′ and G″. At higher polymer concentrations, the viscoelastic spectrum shows solid-like behaviour over a wide range of frequencies. The superposition of η ∗(ω) and η(γ) curves occurs only at low frequencies, at higher frequencies the slope of η ∗(ω) is lower than that of η(γ). By studying the time evolution of shear stress after the inception of a steady shear rate (stress overshoot), the recovery of non-linear properties after steady shearing flow is seen to occur after times of c. 10 3 s (in the case of 1·1% w/v solutions). The overall viscoelastic properties appear original in comparison with those of the two structurally limiting types of polysaccharide, the ‘ordered’ chain xanthan and the ‘random coil’ guar. A rationale for this ‘anomalous’ viscoelastic behaviour can be tentatively proposed in terms of flickering intermolecular cross-interactions between semi-flexible segments, which occur in addition to the usual topological constraints.

Decay of a shear-induced phase transition on a micellar solution measured by time-dependent small-angle neutron scattering

Transient small-angle neutron scattering (SANS) experiments on sheared aqueous surfactant solutions of trimethyl(tetradecyl)ammonium salicylate (TTMA-Sal) are reported. A 0.005 M solution without shear shows a weak correlation peak. For steady shear rates above a threshold value of Γ = 50 s−1 the scattering pattern shows an abrupt increase in anisotropy which is related to a shear-induced structure transition. The analysis of the anisotropic pattern reveals the existence of two types of micelle: short rodlike micelles which are weakly aligned and very long rodlike aggregates which are strongly aligned and which are only present for Γ above the threshold value. We report results on transient SANS measurements in which the shear rate was changed stepwise from a value of 400 s−1 to zero. It is found that the smaller micelles are randomized in orientation, whereas the longer ones do not change orientation at all but their concentration vanishes. The number of surfactant molecules bound in the smaller micelles (type I) increases with time, whereas the number of surfactants bound in the larger ones (type II) decreases. The sum of both remains constant. The number of surfactant molecules bound in type II micelles decays exponentially with a half life of T1/2 = 1.7 (1) s.

Applicability of the Leonov Model to Steady Shear Flow and Stress Relaxation after Cessation of the Flow for Concentrated Polymer Solutions and Melts

Applicability of the Leonov constitutive model was investigated based on reliable experimental data on steady shear flow and stress relaxation after cessation of the flow for several concentrated polymer solutions and polymer melts. The following conclusions were obtained :(1) Analytical solutions for stress components in steady shear flow and stress relaxation after cessation of the flow were derived from basic equations of the Leonov model in different ways from those of Leonov et al.(2) Discrete relaxation time spectra were determined based on the dynamic viscoelastic data, assuming constant ratio τn/τn+1 for adjacent relaxation times and variable relaxation strength Gn.(3) When the discrete relaxation time spectra were determined properly in wide range of time scales, the Leonov model could predict quantitatively the shear stress and the first normal stress difference in steady shear flow for all samples investigated.(4) When the steady shear rate was high, the Leonov model gave much smaller stresses than experimental data at long time end of the stress relaxation. Since the first normal stress difference is underestimated in stress relaxation process, evaluation of flow birefringence and molecular orientation should be very careful when it is made based on the predicted stresses.

A novel sliding plate rheometer for molten plastics

AbstractA novel sliding plate rheometer has been developed that is suitable for use with molten plastics, concentrated polymer solutions, raw elastomers, and other viscoelastic or thixotropic materials. It can generate steady shear rates from 0.05 to 500 s−1 and can also be used to measure linear viscoelastic properties. In addition, it can be used to measure a broad spectrum of nonlinear viscoelastic properties such as the nonlinear relaxation modulus and the shear stress growth coefficient. In order to measure these nonlinear properties it is necessary to generate large, uniform, transient deformations Involving high strain rates. Rotational and capillary melt rheometers are not capable of generating this type of deformation, and until now it was not convenient to use sliding plate rheometers for this type of application. However, the recent development of a reliable and robust shear stress transducer makes it very convenient to use the sliding plate geometry to carry out all of these tests. The new rheometer is described, and examples of the types of data it can generate are shown.

Viscoelasticity of carp actomyosin solution during heating.

The steady and dynamic shear rate behaviors of carp actomyosin solution were measured during incubation at 40°C. The maximum steady shear viscosity was observed around 35 min, while the maximum dynamic rigidity was observed around 2h. The hysteresis loop area increased for 2h, and thereafter it remained almost unchanged till 6h where the dynamic rigidity decreased. Therefore we deduce that during the incubation, the network structure would develop also in the carp actomyosin solution as in the hen or rabbit myosin solution, but the network structure of carp actomyosin solution would be so weak as to be broken down even during the repeated measurements of dynamic behaviors. The actomyosin solution at pH 5.8 exhibited the lowest viscoelasticity. The solution at pH 6.8 exhibited the highest dynamic rigidity. The solution at pH 7.8 exhibited the highest stress in the shear rate scan measurement. These results were explained by the fact that the actomyosin solution at pH 5.8 existed near the isoelectric point, and the network structure at pH 6.8 would be different from the network structure at pH 8.8. In the temperature scanning experiment the dynamic rigidity began to increase around 40°C the maximum was observed around 61°C, The peak value around 61°C was high at pH 5.8 and pH 6.8, and low at pH 7.8.

Polymer coatings with a destabilizing action on suspensions

The rheological behaviour of concentrated suspensions of spherical glass particles can be influenced drastically by surface pretreatment of the particles. This treatment consisted of silanization with mono- or difunctional organo-silicon compounds. Results from ESCA, IR and SEM analysis strongly suggest that silanization with the reagent dimethyldichlorosilane (DMDCS) results, depending on the processing, in a more or less homogeneous layer of oligomer and/or polymer. The particles were suspended in an apolar (DOP) and in a polar liquid (glycerol/water). All suspensions exhibited perfect or nearly Newtonian behaviour except DMDCS-coated glass in glycerol/water. With the latter, under oscillatory shear conditions, behaviour of a continuous coagulation network structure was found: dynamic moduli are hardly dependent on frequency while network structure breakdown occurred already at the lowest accessible deformation (10 −3). Under steady shear rate conditions pseudoplastic behaviour was found, with relative differential viscosities at high shear rates (10 2 s −1) approaching the value of equivalent suspensions of uncoated spheres. Results are interpreted with the giant floc model, according to which macroscopic shear is understood as microscopic slip along shear planes between coagulated domains. The origin of coagulation in these systems is not in van der Waals forces because bond strengths as judged from rheology are too high. Polymer bridging between coating polymers is suggested as flocculation mechanism.

Non-linear behaviour of asphalts in steady and transient shear flow

Steady-state and transient shear stress and normal stress data were obtained for four asphalts with a modified Weissenberg Rheogoniometer. Interest was specially related to non-linear behaviour at high shear-rates. The time-temperature superposition principle was found to hold in non-linear behaviour. Moreover, steady-state and transient data could be plotted as master curves irrespective of the nature of the asphalts. In particular, the master curve of steady-state viscosity could be extended to results published in the literature. In the nonlinear region the shear stress relaxation after cessation of a steady shear rate\(\dot \gamma\) becomes a function of\(\dot \gamma\)t only and is related to the primary normal-stress coefficient, as predicted by the Yamamoto equation. In the shear stress growth experiment an overshoot is obtained at a constant strain close to 1.5, independent of the rate of strain.

Viscoelastic fluid flow exhibiting hysteritic phase changes

In the present paper a mathematical theory is given for a viscoelastic fluid exhibiting a hysteresis loop in the shear stress versus shear rate plane. The main rheological idea is to introduce a constitutive equation of rate type whose steady shear stress versus shear rate locus is nonmonotone. The main mathematical idea is to use a local shock structure theory to pick out the admissible solutions in loading and unloading of the applied driving force.

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic cast results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10–100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.

Behaviour in shear flow of monodisperse polystyrene solutions: analysis and correlations for steady flow and shear stress relaxation

Stress relaxation experiments have been performed from a steady shear rate on monodisperse polystyrene solutions with molecular weight Mw ranging from 1.3 × 105 to 1.6 × 106 and concentration C ranging from 0.05g ml−1 to 0.4g ml−1.Tangential stress data are analysed using a long relaxation time, τ2 and a short one τ1. At long times, relaxation curves η− are parallel so that τ2 is shear-rate independent. The behaviour of τ1 shows the same features as the viscosity and normal stress functions: i.e. a constant value τ10 at low shear rates and a power-law behaviour at high shear rates. Furthermore τ2 and τ10 ∼ M3.4wC4.The initial rate of relaxation defines an elastic parameter [dη−/dt]0. In the limit of low shear rate, we obtain −[dη− /dt]0 ⋍2/Je0. In contrast to the elastic compliance Je, [dη− /dt]0 is found to be shear-rate independent. In contrast to earlier assertions, we found Je0 to be slightly dependent on molecular weight: Je0 ∼ -1 /[dη− /dt]0 ∼ M0.5wC−1.5. Two rheological relations between steady normal stress values and transient tangential stress measurements were tested. Only Yamamoto's equation was found to be consistent with data obtained on the samples of lowest molecular weight (Mw <106. Neither Yamamoto's equation nor the test for the BKZ model were found to be valid for the sample of highest molecular weight (Mw = 1.3 × 106) at concentrations above 0.1 g ml−1.

Rheology of Pharmaceutical Systems: Oscillatory and Steady Shear of Non-Newtonian Viscoelastic Liquids

A comparative analysis of oscillatory and steady shear rate measurements was made on carboxymethylcellulose solutions of two concentrations and two viscosity grades. In the oscillatory methods, the material is examined under nearly quiescent equilibrium conditions. Steady shear, conversely, produces large deformations and may yield false results, often interpreted as thixotropy, if the shear rate experiment is not conducted properly. Solutions of carboxymethylcellulose at concentrations ordinarily used in drug product formulations were examined by oscillatory and steady shear methods at low shear. Viscoelastic properties of pharmaceutical materials were measured using a newly developed oscillometric instrument. Mathematical expressions, formulated on the basis of a generalized Maxwell model for viscoelasticity and viscosity in steady shear, were correlated using these two rheological test methods. The results showed large increases in viscosity and relaxation time with increasing carboxymethylcellulose concentrations as well as with increasing molecular weights of the polymeric solute. The behavior of carboxymethylcellulose under both oscillatory and steady shear agreed with theory, linking the two methods of testing. Applications in pharmacy to this rheological analysis are presented. The present investigation attempted to bridge the gap between oscillatory and steady shear methods, demonstrating how both can find appropriate use in the analysis of non-Newtonian materials of pharmaceutical importance.

DYNAMIC AND STEADY SHEAR RATE ASPECTS OF MINCED MEAT ‘SETTING’

ABSTRACT Dynamic and time‐dependent steady shear rate properties of minced chicken meat were studied immediately after preparation and following a 24 hr low temperature incubation. Incubation at 3d̀ C resulted in a significant increase in the storage moduli and a relatively constant decrease in the loss tangent over the range of strain amplitude (0.010‐0.126; at an angular frequency of 0.299 s ‐1. The stress relaxation behaviour was retarded and the equilibrium shear stress value was 30% higher when compared with the untreated samples. Time‐dependent studies of hysteresis loop areas revealed a significant increase in structure breakdown after incubation. The effects observed after low temperature incubation were ascribed to an intermolecular interaction between myosin A and F‐action.

Flow of polyethylene melts with steadystate and recurrent deformation

Results are presented of studies on melts of batches of polyethylene differing in overall molecular weight and branching. For high-density polyethylene, unlike the low-density material, the ratios between the tangential and normal stresses and between the constituents of the composite dynamic shear modulus are independent of temperature. A close agreement has been found between the total and net viscosity with cyclic vibration frequencies equal to the steady shear rate.

Time-dependent shear flows of a suspension of particles with weak Brownian rotations

A dilute suspension of rigid axisymmetric particles in a time-dependent shear flow is considered in circumstances where the shear flow alignment of the particles dominates small but not unimportant Brownian disorientations. Three cases are studied: stress relaxation on the cessation of a steady shear, the sudden application of a steady shear from a state of rest and the sudden change from one steady shear rate to another. The rheology exhibits effects on two basic time scales provided that the particle aspect ratio r is not extreme: oscillatory features with a frequency proportional to the shear rate γ which are due to the rotation of the particles about their Jeffery orbits, and an exponentially fading memory due to Brownian diffusion with a characteristic time praportional to the inverse diffusion rate D−1. When the particle aspect ratio r becomes large, the oscillation frequency is reduced to γ/r while the diffusion rate is enhanced to Dr2 for some features and to Dr4 for others.

Modifications of an R-16 Weissenberg Rheogoniometer

In the course of our work on the characterization of materials by our kinetic interpretation of non-Newtonian flow, it had become desirable to make measurements other than at steady state constant shear rate and the sudden application of a steady shear. The present paper describes four modifications we have made and used: (1) a torque detection system to eliminate upper cone motion during transient and oscillatory measurements; (2) measurements under both unsteady and steady state condition in a constant stress field; (3) a versatile and inexpensive oscillatory capability to allow both amplitude and frequency variation of nearly any wave form desired; and, finally, (4) the measurement of the primary normal force difference under any conditions, with essentially no change in gap setting. Examples of typical results on a concentrated polymer solution are presented.

The stability of steady shear flows of some viscoelastic fluids

The stability of steady shear flows of some viscoelastic fluids relative to small perturbations in the initial data is examined. It is shown that all values of the steady shear rate where the flow curve exhibits a zero or negative slope the flow is unstable. This conclusion is corroborated by existing experimental data and bears upon the phenomenon of melt fracture.

Prediction of the first normal stress difference in polymer solutions

AbstractShear stress and first normal stress difference data are presented for several polymer solutions undergoing steady shear rates from 1.0 to 100,000 sec.−1. The steady shear response is divided into three regions as a function of increasing shear rate. These are the diffusion controlled linear region, a moderate shear rate region where shear controls the entanglement‐disentanglement process, and a high shear rate region where aggregation of polymer molecules occurs. The transitions between the three regions are clearly illustrated by using a group designated as the rotation rate function.A molecular model is derived for the shear controlled region that allows prediction of the first normal stress difference from the viscosity function and one additional constant that depends only on the molecular species. The White‐Metzner equation is found to adequately describe the aggregation region at high shear rates.

Influence of superimposed steady shear flow on the dynamic properties of polyethylene melts

AbstractExperiments in which an oscillatory shear flow is superimposed on a steady state shear flow were performed on polyethylene melts by the use of a cone and plate type rheogoniometer. The phase difference between oscillatory shear stress and shear strain increases in all cases and for all frequencies with the increase of the superimposed shear rate. Between ω0, the frequency at which the phase difference is π/2 and the steady shear rate \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document}, as found by Booij for polymer solution, the relation ω0 = 1/2 \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma$\end{document}. holds also for polyethylene melts. The significance of this relation is discussed briefly from the viewpoint that the entanglement density decreases with the increase of the imposed shear rate.