Steady Flow Viscosity Research Articles

Correlation of Dynamic and Steady Flow Viscosities of Food Materials

AbstractEight commercial foods representing a wide range of viscosities (i.e. honey, condensed milk, mayonnaise, tomato ketchup, cream cheese, yogurt, process and Mozzarella cheeses) were investigated. Their steady shear viscosity and dynamic complex viscosity were determined by rheological measurements at two temperatures using a Bohlin-CVO rheometer. Based on experimental data, shear rate dependence of steady flow apparent viscosity and frequency dependence of dynamic viscosity was established and compared. It was determined that for condensed milk, tomato ketchup and mayonnaise, a modified Cox-Merz relation could be established. For cream cheese, a generalized Cox-Merz relation was proposed; and for yogurt, a deviation from the Cox-Merz rule was found. For Mozzarella and process cheeses a sharp drop in steady shear viscosity was noticed between 1~10 s-1 shear rate range. The Cox-Merz rule was not applicable for these cheese samples.

Temperature and Shear Rate Dependence of Small Angle Neutron Scattering from Semidilute Polymer Solutions

We use small angle neutron scattering to study the effect of shear on a polymer solution (polystyrene, PS, in dioctyl phthalate, DOP) being in the entangled part of the semidilute regime, in a large range of temperatures and shear rates. The scattering of the induced structure, in the first stages of the flow effect, gives butterfly patterns, i.e., contours constituted of two lobes along the v direction. In later stages, as the shear is increased at constant temperature or the temperature is decreased at constant shear rate, the scattering becomes stronger, having greater dependence on q, and contours tend finally to have an elliptical shape. This means that the objects created by flow are larger. The temperature effect is not only due to the slowing down of the dynamics of the system at lower T, since after correction of the latter, using a time−temperature superposition (determined using oscillatory low strain), the influence of the vicinity of the cloud point on the flow-induced structure remains important. Conversely, steady flow viscosity measured under the same conditions can be corrected using such time−temperature superposition. Some of our results indicate that entanglements are not mandatory to obtain the butterfly effect and that the shear effect can lead to irreversible demixing for solutions closer to the dilute regime.

RHEOLOGICAL STUDY ON HYALURONIC ACID AND ITS DERIVATIVE SOLUTIONS

ABSTRACT Rheological measurements were performed on Hyaluronic acid (HA) and its derivative solutions to evaluate steady flow viscosity and dynamics response with the aim to correlate the materials properties to the concentration, molecular weight and chemical structure. At low molecular weight and concentration, the HA solutions behaved as viscous liquid, whereas a soft-gel response was evident at higher molecular weight and concentration due to chains entanglement. Increasing the molecular weight was more effective than increasing concentration in promoting entanglement of molecular chains of HA. Comparing the behavior of HA solutions with that of Hyaluronic acid derivatives, it is showed that it is possible to modulate the rheological properties of HA based solutions by chemical modification preserving the bio-compatibility of the materials. The results of the rheological analysis provide a valuable tool to properly design optimal substitutes for specific biomedical application.

An instrument for precise measurement of viscoelastic properties of low viscosity dilute macromolecular solutions at frequencies from 20 to 500 kHz

A high-frequency torsional rod apparatus (HFTRA) has been developed for measurements of moderately high-frequency viscoelastic properties of dilute, low viscosity polymer solutions. It employs a long cylindrically shaped resonating element driven by an X-cut (torsional mode) quartz piezoelectric crystal. Up to 11 different normal modes are employed, resulting in 11 discrete frequencies, ranging from approximately 20 to 500 kHz. Measurements are made in free decay; a key feature of the apparatus is the method for high precision measurements of damping coefficients and eigenfrequencies. The instrument is suitable for liquids with 0.003P<‖η*‖<5P and η′≥1.33η″. Typically, η′ has a relative uncertainty of ±2% or less, with the relative uncertainty for η″ being about 4% for liquids with η″ greater than 0.01P. Values of η′ obtained in the HFTRA for low viscosity liquids with small η″ show excellent agreement with the known steady flow viscosities. Measurements of the viscoelastic properties of polymer solutions employing the HFTRA and two other instruments capable of higher precision measurements show excellent agreement, demonstrating that the HFTRA is sufficiently precise for dilute-solution viscoelasticity studies; the working frequency range is such that most of the polymer relaxation time spectrum can be probed for many polymer/solvent combinations.

Glass transition behaviour of Zr- and Ti-based binary amorphous alloys

A study has been made to investigate the effects of free-volume fraction, steady state viscous flow temperature and viscosity on the glass transition and viscous flow behaviour of Cu x Zr 100− x ( x = 40, 50 and 60), Ni x Zr 100− x ( x = 40 and 50) and Cu x Ti 100− x ( x = 40 and 50) amorphous alloys. It was observed that the displacement at T x increases in the order Cu 40Zr 60 > Ni 40Zr 60 > Cu 40Ti 60. We found that this order can be explained by the free-volume fraction and maximum displacement rate at T vs. The relationship between viscosity and free-volume fraction below T x is consistent with Doolittle's empirical formula for the CuZr, CuTi and NiZr systems. It is presumed that the kinetics of free-volume production and annihilation are involved in the thermal stability and glass transition temperature.

Effect of sugars on the physicochemical properties of W/O/W emulsions

A study was made of the influence of a series of sugars (i.e., ribose, xylose, fructose, glucose, sucrose, and maltose) on the steady-flow viscosity of W/O/W emulsions in relation to the migration of water between the two aqueous phases of inside and outside of the dispersed vesicular globules permeating through the oil layer. Fluxes of sugar molecules across the oil layer were also compared with each other in the light of molecular weight and the number of equatorial-OH (e-OH) groups in a sugar molecule. Changes in the viscosity could be observed for a span of time after the preparation on either side of increase or decrease with W/O/W emulsions containing an equimolar concentration of the different sugars separately in the two aqueous phases due to the migration of water. It was found that the flux of water tends to the aqueous phase dissolving one of the sugars possessing less e-OH groups than another sugar existing in the other under an apparently isotonic condition between the two aqueous phases. The water permeation coefficient of the oil layer increased from 5.97 × 10 −4 to 8.89 × 10 −4 cm/s with increasing number of e-OH groups from about two (ribose) to about seven (maltose), while molar flux of sugars across the oil layer decreased with increasing number of e-OH groups in a molecule ranging from 9.83 × 10 −1 to 3.99 × 10 −2 μ M/g of emulsion per hour.

Dynamic melt rheology. I: Re‐examining dynamic viscosity in relationship to the steady shear flow viscosity

AbstractSince 1950's, theoretical as well as experimental efforts have been made to explain the similarity between the shear rate dependence of the steady flow apparent viscosity and the frequency dependence of the dynamic viscosity. The literature points out agreements, as well as occasional disagreements, between the two viscosity terms, depending on the polymer system. In this manuscript, some critical results are presented which suggest that the strain rate dependence of the two viscosities, has entirely different origins and that it is only a coincidence that these data happen to be closer for the common polymers. A time‐temperature dependence of viscoelastic parameters is brought into the discussion to argue the observed pseudo‐plasticity in dynamic melt rheology and to demonstrate, in principle, that the strain rate dependence of the dynamic and steady flow viscosities should be different. Nevertheless, we must mention that the dynamic and steady flow measurements have their own merits and these techniques can complement each other very well.

Viscoelastic and rheological properties of concentrated solutions of proteoglycan subunit and proteoglycan aggregate

The oscillatory and steady shear rheological properties of concentrated solutions of proteoglycan subunit (PGS) and aggregate (PGA) from bovine articular cartilage have been studied using a Rheometrics fluids spectrometer. At comparable concentrations in the physiological range tan delta increases from 0.5 to 1.0 for PGA as the oscillation frequency (omega) increases from 10(-1) to 10(2) rads/s, compared to a decrease from 40 to 5 for PGS. Thus PGA solutions exhibit predominantly elastic response whereas those of PGS exhibit primarily viscous behavior. PGA solutions show pronounced shear-thinning behavior at all shear rates (gamma) in the range 10(-2) less than gamma (s-1) less than 10(2), whereas PGS solutions exhibit predominantly Newtonian flow. For PGA, the small-strain complex viscosity eta* (omega) is substantially smaller than the steady-flow viscosity eta(gamma) at comparable values of omega and gamma. These observations indicate that the presence of proteoglycan aggregates leads to formation of a transient or weak-gel network. Since aggregation leads to a large increase in molecular hydrodynamic volume and hence in the relaxation times for macromolecular rotation, it appears that role of aggregate formation is to shift the linear viscoelastic response from the terminal viscous flow into the plateau elastomeric regime of relaxational behavior. Normal or pathological changes that produce a decrease in aggregation will result in a loss of elastomeric behavior of the proteoglycan matrix.

Viscoelastic properties of solutions of ovine submaxillary mucin

The linear viscoelastic and rheological properties of high molecular weight ovine submaxillary mucin (OSM) solution have been investigated in terms of the Newtonian steady-flow viscosity [eta(gamma)], the complex oscillatory viscosity [eta*(omega)], and the storage and loss shear moduli [G'(omega) and G"(omega)]. It was observed that tau(gamma), eta*(omega), and G'(omega) are always higher when OSM is dissolved in 0.1M NaCl than when at the same concentration in 6M GdnHCl. This is consistent with previous observations that submaxillary mucins self-associate in 0.1M NaCl to form large aggregates, which are disrupted in 6M GdnHCl. As the OSM concentration increases, the appearance of a plateau shear modulus indicates the formation of a gel network in both solvents. The results suggest gelation involves specific intermolecular interactions, perhaps due to hydrophobic forces between interdigitated oligosaccharide side chains. The viscoelastic behavior of OSM solution at high concentration is thus similar to that reported in the literature for porcine gastric mucin (PGM). However, the OSM gels are mechanically weaker, having moduli that are an order of magnitude lower than those for PGM gels of comparable concentration. The oligosaccharide side chains of OSM consist of only 1-2 sugar units compared to 10-15 for PGM, but it appears that this is sufficient to allow for intermolecular interaction and the formation of weak gels.

On the hydrodynamic braking flow of a viscoelastic fluid

This paper considers the flow of a viscoelastic fluid between two parallel plates. The bottom plate slides in its own plane and the top plate moves normal to its own plane. The flow is thus a combination of shearing and squeeze-film flow, and mimics a hydrodynamic braking action. The computation includes not only the flow between the plates but also the inlet and outlet regions which contribute to the load and greatly increase the difficulty of the problem. There does not seem to have been any previous attempt to include this feature. The fluid model adopted is a differential-type viscoelastic constitutive equation, which predicts a decreasing (Carreau-type) viscosity in steady state simple shear flow, and overshooting, oscillatory behaviour in the starting-up of a simple shear flow. The problem is solved by a decoupled boundary element method, adapted to solve non-linear transient flow problems. The program treats non-linear terms as pseudo-body forces in the repeated solving of a set of linear problems. The numerical results point to the existence of strong vortices at the inlet and outlet of the bearing in the viscoelastic case, and they show an increase in both the normal and the tangential forces as the product of the relaxation time and the squeeze rate (Weissenberg number) rises. There is also an increase as the sliding velocity increases. The frictional coefficient, however, is nearly the same as the newtonian value. The results form an explanation for the increased resistance to squeezing found in viscoelastic films.

Blood modeling using polystyrene microspheres

The steady flow viscosity at shear rates 0 to 120 sec-1 and dynamic viscoelasticity at frequencies 0.02 to 0.8 Hz were determined for aqueous suspensions of uniform polystyrene microspheres of 1.0 micron diameter. Rheological properties of the microsphere suspensions were Newtonian for particle concentrations up to 32%. By introducing dextran and calcium chloride into the particle suspensions, non-Newtonian behavior was produced similar to that observed for human blood. The cooperative effects of dextran and calcium ions promoted aggregation of particles at a concentration as low as 12%. Thus, a suspension of uniform sized spherical polystyrene particles in aqueous solution of dextran may be made to mimic blood by controlling the surface charge on the polystyrene spheres using addition of calcium ions to the medium.

A characterization of shear flow in continuous fibre thermoplastic laminates

The viscoelastic response of some continuous fibre thermoplastic composites has been investigated dynamically. The contribution of the number and direction of laminate ply layers and fibre type, together with the geometry, have been explored in relation to the matrix polymer. An interpretation in terms of an apparent Maxwell viscosity is in agreement with steady shear flow viscosity, and approximates to a large strain dynamic viscosity. A yield stress of the order of 1 kPa is implied by the Maxwell interpretation together with a high stress viscosity more than 10 times the viscosity of the matrix polymer. The use of model laminates leads to the prediction of both interply and intraply polymer flow in continuous fibre thermoplastic composites.

A constitutive equation for a dilute solution of Hookean dumbbells with approximate hydrodynamic interaction

In a recent series of papers, Öttinger's consistently averaged hydrodynamic interaction has been shown to yield shear-rate dependent viscosity and normal stress coefficients in steady shear flow for dilute solutions of elastic dumbbells and chains. Even more recently, Fan has numerically solved the diffusion equation for the Hookean dumbbell with complete hydrodynamic interaction and he has compared his results with those of the Öttinger model. In this paper, a new approximation 1 1 Note to proofs: H.C. Öttinger has pointed out that he and J. Honerkamp had suggested and model in this paper in J. Chem. Phys., 84 (1986) 1028, a paper of which the author was previously unaware. for the Oseen—Burgers tensor is proposed where the configuration-dependent terms are replaced by appropriate averages rather than averaging the Oseen—Burgers tensor as a whole as in the Öttinger model. The proposed model leads to a differential constitutive equation which at low shear rates is similar to the Giesekus constitutive equation for a Hookean dumbbell with anistropic drag and anisotropic Brownian motion. The steady shear viscosity and normal stress coefficients for the proposed model are shear-rate dependent and are in close agreement with Fan's numerical calculations. Elongational viscosity for both positive and negative elongation rates are calculated.

Interaction of the fibrinogen-binding tetrapeptide Gly-Pro-Arg-Pro with fine clots and oligomers of alpha-fibrin; comparisons with alpha beta-fibrin.

AbstractThe tetrapeptide Gly‐Pro‐Arg‐Pro(GPRP) was introduced by diffusion into fine unligated clots formed from human fibrinogen at pH 8.5 and ionic strength 0.45 by batroxobin (αβ‐fibrin) and by thrombin (α‐fibrin). The α‐fibrin clots were essentially liquefied at GPRP concentrations above 1 mM and αβ‐fibrin clots above 15 mM, and the degree of polymerization of the resulting oligomers decreased progressively with increasing GPRP concentration as shown by γ‐γ ligation with factor XIIIa and subsequent gel electrophoresis. Much smaller concentrations of GPRP, when introduced into unligated clots by diffusion, were sufficient to modify their mechanical properties profoundly. The shear modulus of elasticity G25 measured 25 s after imposition of stress fell, for example, by a factor of 0.4 at 0.1 mM GPRP in α‐fibrin and at 1.1 mM in αβ‐fibrin. The rate of shear creep under constant stress and the proportion of irrecoverable deformation also increased enormously. This behavior, and the corresponding decrease in steady flow viscosity, may be interpreted in terms of competition of GPRP with A sites on the E domains of fibrin monomers for bidning to “a” sites on the D domains, resulting in a moderate increase with increasing GPRP concentration of the average proportion of severed network strands and an enormous increase in the rate at which all strands dissociate and reassociate. Reassociation of severed strands in new configurations is a necessary corollary since the differential modulus or compliance remains constant during creep and creep recovery. The greater susceptibility of α‐fibrin clots to interaction with GPRP is attributed to stabilization of contacts between monomer units by Bb associations in αβ‐fibrin. Ligated clots, with or without GPRP, exhibited essentially no time‐dependent creep and no irrecoverable deformation, corresponding to an absence of any severance of network strands.

Steady Flow Viscosity and Rigidity of Colloidal Spheres in Deionized Suspensions

AbstractSteady‐flow viscosities of colloidal spheres, i.e., colloidal silica (8–45 nm in diameter) and monodisperse polystyrene latices (diam. 85 to 780 nm), are measured in deionized suspensions and in the presence of a small amount of NaCl. The plots of shear stress (S) of the crystal‐like structure of the colloids against shear rate (q) show the following features: (1) at very small values of q (smaller than 0.1 s−1), S increases very sharply with increasing q. The S – q curve is S‐shaped, and the rigidity (G) of the colloidal crystal is evaluated from the plots of S against qt/2 (shear strain), where t is time. The G‐values are between 20 and 3000 Pa, which are consistent with those reported hitherto, and increase as the sphere's concentration increases. (2) The sharp increase in S ceases above the critical q value, from which the yield stress of the crystal‐like structure is evaluated to be between 0.1 to 2 Pa. (3) The log (viscosity, η) vs. log q plots shows non‐Newtonian flows: η increases as q decreases and then η reachs a constant value. Furthermore, log η begins to increase linearly as log q decreases with a slope of −1, which supports the crystal‐like nature of the suspensions.

On the rotational diffusion of rod-like macromolecules in lyotropic-mesomorphic phases

The rotational diffusion of rod-like macromolecules, idealized as monodisperse rods, in concentrated solution is considered. The Doi-Edwards model is modified to explain the experimentally observed increase of the rotational relaxation time with increasing concentration in the lyotropic-nematic phase of rigid rod-like molecules in solution. Our approach consists in (i) reconsidering the original Doi-Edwards model to eliminate unphysical behaviour of the rotational relaxation time at the limit of perfect order, and (ii) including concentration effects on the translational diffusivity of rods in the Doi-Edwards model. Predictions of the corrected model are compared with steady flow viscosity data for poly(n-alkylisocyanates). In the lyotropic-nematic phase a very good qualitative agreement between the theory and experiment is observed. Additionally, the model applied to a highly concentrated isotropic phase explains in a natural way the viscosity behaviour as the concentration is increased towards the criti...

Solvent dependence of the viscous and viscoelastic properties of a high molecular weight polystyrene in moderately concentrated solution

The steady-flow viscosity and viscoelastic behaviour of two solutions of a sensibly monodisperse polystyrene of high molecular weight ( M w = 498 000) have been measured over a temperature range of 100°C for identical concentrations of 20.55 wt.%. Toluene and methyl ethyl ketone were chosen as the two low viscosity solvents having, respectively, good and marginal thermodynamic affinities. Dynamic viscoelastic measurements were made at a frequency of 41 kHz using travelling torsional waves. At this frequency, both solutions exhibit behaviour characteristic of the rubbery region, and the ratio of the dynamic viscosity normalised by dividing by the corresponding solvent viscosity is independent of the solvent until the onset of the glass transition region with decreasing temperature. The storage shear modulus of the toluene solution in the rubbery region is higher than for the MEK solution, indicating a higher entanglement density in the better solvent and a larger polymer radius. Some features of the results in the poor solvent (MEK) appear to indicate that, as the temperature decreases, partial exclusion of the solvent leads to the formation both of stronger entanglements and of macromolecular aggregates or bundles, as suggested by Dreval and others 6–8,11,22.

Application of a constitutive equation to polymer melts

AbstractYamamoto's integral constitutive equation in which the memory function is dependent on the second invariant of the rate of deformation tensor at past times has been found to be successful in predicting many of the nonlinear viscoelastic functions from the linear viscoelastic data for melts of linear polyethylenes, polypropylenes, and polystryene but not for those of branched polyethylenes with high level of long‐chain branching. A specific functional form for the rate‐dependent relaxation spectrum is used and is based on the physical meaning resulting from the molecular entanglement theory of Graessley on steady shearing flow. No arbitrary constant is involved in such an interconversion scheme. The data examined are dynamic storage modulus and loss modulus, steady flow viscosity, first normal stress difference, and parallel superimposed small oscillations on steady shear flow. The theory predicts that in such parallel superimposed experiments, storage modulus G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) divided by the square of frequency shows a maximum under finite shear and that G′(ω,\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm \dot \gamma } $\end{document}) would itself become negative at a frequency whose value is about one third the superimposed rate of shear. The experiments are in line with such predictions. Possible reasons for the failure of the theory for branched polyethylenes are considered, and a possible approach is suggested so that the interconversion scheme may be successful for such resins.

Shear rate dependence of the viscoelasticity of polymer solutions.: II. xanthan gum

The shear rate dependent rheological properties of aqueous solutions of xanthan gum are measured. The steady flow viscosity is non-Newtonian and the oscillatory flow viscoelasticity is strongly dependent upon the amplitude of the shear rate as well as the frequency. A method for characterization and analysis of these nonlinear viscoelastic properties is described. The analysis is based upon a generalized Maxwell model in which the relaxation processes truncate in a manner dependent on the shear rate. The same relaxation processes are responsible for both the steady and the oscillatory flow behavior. With the xanthan gum solution at a concentration of 1000 ppm, the relaxation spectrum can be approximated by three discrete relaxation processes which have relaxation times of 0.531 s, 0.092s, and 0.0066 s. These three processes are sufficient to describe how the viscoelasticity changes with both shear rate and frequency and how the steady flow viscosity changes with shear rate.

Correlation of dynamic and steady flow viscosities of filled polymer systems

Correlation of dynamic and steady flow viscosities of filled polymer systems