Showing papers in "Rheologica Acta in 1993"

A nonlinear regularization method for the calculation of relaxation spectra

Abstract: It is well known that the relaxation spectrum characterizing the linear viscoelastic properties of a polymer melt or solution is not directly accessible by an experiment. Therefore, it must be calculated from data for a material function. With Tikhonov regularization the relaxation spectrum in the terminal and plateau region can be calculated from data for a material function in the corresponding region. Serious difficulties arise however, if the spectrum should be determined in a larger range. These difficulties are caused by the considerably different contributions at short and long relaxation times. We show that these difficulties can be avoided by a nonlinear regularization method.

Concentration dependence of the critical viscoelastic properties of gelatin at the gel point

Abstract: Gelatin gel properties have been studied through the evolution of the storage [G′(ω)] and the loss [G″(ω)] moduli during gelation or melting near the gel point at several concentrations. The linear viscoelastic properties at the percolation threshold follow a power-law G′(ω)αG″(ω)αωΔ and correspond to the behavior described by a rheological constitutive equation known as the Gel Equation. The critical point is characterized by the relation: tan δ = G″/G′ = cst = tan (Δ · π/2) and it may be precisely located using the variations of tan δ versus the gelation or melting parameter (time or temperature) at several frequencies. The effect of concentration and of time-temperature gel history on its variations has been studied. On gelation, critical temperatures at each concentration were extrapolated to infinite gel times. On melting, critical temperatures were determined by heating step by step after a controlled period of aging. Phase diagrams [T = f(C)] were obtained for gelation and melting and the corresponding enthalpies were calculated using the Ferry-Eldridge relation. A detailed study of the variations of A with concentration and with gel history was carried out. The values of Δ which were generally in the 0.60–0.72 range but could be as low as 0.20–0.30 in some experimental conditions, were compared with published and theoretical values.

On the damping function of shear relaxation modulus for entangled polymers

Abstract: Published data of the damping function of the shear relaxation modulus, h(γ), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, γ, to that at the limit of γ = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h(γ) is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h(γ) = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material.

Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance

Abstract: We describe a recursive computer algorithm which generates line spectra from relaxation modulus or creep compliance data without producing negative spectrum lines. We apply the algorithm here to data read from mathematical models for the relaxation modulus. Since these data were thus free of the usual experimental error, we could use a relatively simple form of the basic algorithm that is applicable also to smoothed data. The spectra faithfully reproduced the input functions and may serve for data storage as well as for predicting other experimental responses.

The rheology of layered liquids : lamellar block copolymers and smectic liquid crystals

Abstract: The frequency-dependence of the viscoelastic shear modulus at low frequencies in a lamellar polystyrene-polyisoprene block copolymer is qualitatively identical to that measured in small-molecule smectics, namely, the rod-like 4-cyano-4′-octylbiphenyl and the flexible n-nonyl-1-O-β-D-glucopyranoside All three materials were studied after quenching from the isotropic state, and during and after alignment by large-amplitude oscillatory shearing The kinetics of aligning, as measured by changes in moduli during shearing, are similar, despite great differences in molecular characteristics These moduli and the aligning process are evidently controlled by smectic fluctuations and defects, the dynamics of which have universal features

A note on estimating mastercurves

Abstract: There are several quantities in theology which show a scaling behavior. One well known example is the time-temperature superposition principle of material functions characterizing the linear viscoelastic properties of polymer melts. We propose a mathematical shift procedure for the calculation of mastercurves and the corresponding scaling factors from experimental data which show such a scaling behavior. In order to demonstrate the applicability of the shift procedure mastercurves and scaling factors are determined for material functions of several polystyrene melts and for the specific viscosity of polyisobutylene in cyclohexane.

Generating line spectra from experimental responses. Part II: Storage and loss functions

Abstract: A computer algorithm is described which allows the determination of a discrete distribution of relaxation times from simulated or smoothed storage or loss modulus data, or of retardation times from simulated or smoothed storage or loss compliance data. The distributions faithfully reproduce the input data and are suitable for data storage as well as for generating any other response curves.

A specific slit die rheometer for extruded starchy products. Design, validation and application to maize starch

Abstract: A novel in-line rheometer, called “Rheopac”, has been designed and built in order to study the rheological behaviour of starchy products or, more generally, of products sensitive to a thermomechanical treatment. It is based on the principle of a twin channel, using a balance of feed rate between each of them, in order to make local shear rate vary in the measuring section without changing the flow conditions into the extruder. A wide range of shear rate could be reached and measurements were performed more swiftly than with a classical slit die. The viscous behaviour of maize starch was studied by taking into account the influence of the thermomechanical history, which modified the starch degradation and thus led to important variations in the viscosity. Experimental results were satisfactorily compared to previously published models.

Mapping the stiffness-temperature-moisture relationship of solid biomaterials at and around their glass transition

Abstract: Mechanical changes in biomaterials at and around their glass transition are key factors in their functionality and/or stability. They are described in terms of a relationship betwen a relative stiffness R(T,M) defined as the ratio between a modulus or storage modulus at a temperature T, and moisture M, and its magnitude in the glassy state. The relationship, in turn, is expressed by the model R(T,M) = 1/[1+exp [{T-Tc,(M))/a(M)]} where Tc(M) is a critical temperature identifying the transition temperature range and a(M) a constant representing the relationship's slope. The proposed model correctly accounts for the downward concavity of the stiffness vs temperature relationship at the transition onset. Published data on biosolids indicate that Tc(M) can be described by a single exponential decay term, and so most probably also a(M). Incorporation of these terms into the model enables the creation of realistic three-dimensional maps of the relative stiffness-temperature-moisture relationship at and in the neighborhood of the glass transition region. In principle, the same method can also be used to describe the effect of plasticizers other than water if their influence on Tcand the steepness parameter can be formulated as an algebraic expression.

Rheological properties of poly(vinyl alcohol)/sodium borate aqueous solutions

Abstract: Rheological properties were studied for aqueous solutions of poly(vinyl alcohol) containing sodium borate. The solution exhibited a marked shear thickening at a certain critical rate of shear, γ c and the flow was unstable at higher rates of shear. The loss modulus exhibited a maximum and the angular frequency corresponding to the maximum, ωMAX, was approximately equal to $$\dot \gamma _C $$ . These features were common to several measurements including various molecular weights and concentrations of polymer and various temperatures. Possible mechanism of shear thickening was discussed based on a temporary network model composed of crosslink points of a finite lifetime.

Rheology of polydisperse polymers: relationship between intermolecular interactions and molecular weight distribution

Abstract: An expression of the relaxation function of linear polydisperse polymers is proposed in terms of intermolecular couplings of reptative chains. The relaxation times of each molecular weight are assumed to be shifted according to a tube renewal mechanism accounting for the diffusion of the surrounding chains. The subsequent shift is applied to the relaxation function of each molecular weight obtained from an analytical expression of the complex compliance J*(ω). Therefore the complex shear modulus G*(ω) is derived from the overall relaxation function using the probability density accounting for the molecular weight distribution and four species-dependent parameters: a front factor A for zero-shear viscosity, plateau modulus G N 0 , activation energy E and characteristic temperature T∞. All the main features of the theology of polydisperse polymers are described by the proposed model.

Peristaltic motion of a third-order fluid in a planar channel

Abstract: In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.

The effect of pH, ionic strength, and temperature on the rheology and stability of aqueous clay suspensions

Abstract: The effect of pH level, ionic strength, and temperature on the theology and stability of aqueous suspensions of attapulgite clay was systematically investigated. A Rheometrics Mechanical Spectrometer with cone and plate fixtures was used to measure the steady shear viscosity of the system. The edge charges of the clay particles can be adjusted by changing the pH level of the suspending medium so as to influence the flocculation state and, consequently, the rheological behavior of the suspension. This pH effect may be counteracted by the ionic strength effect at both very high and very low pH levels where the ionic strength is high enough to cause flocculation of the electrostatically stabilized suspension. The temperature effect study indicates that the relative contribution of Brownian motion and shear flow to the viscosity is dependent on the flocculation state of the suspension.

On the admissibility criteria for linear viscoelasticity kernels

Abstract: In a series of recent papers, the discrepancy of the admissibility requirements currently in use for linear viscoelasticity was noted, between the ones associated with the kernels of linear integral models and the ones resulting from the spring-dashpot representation. It is shown here that additional criteria can be obtained from the fading memory principle which completely remove the observed discrepancies between these two different representations.

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

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

On the time-dependency of the flow-induced dynamic moduli of a liquid crystalline hydroxypropylcellulose solution

Abstract: Some unusual rheological features of a liquid crystalline solution of hydroxypropylcellulose (HPC) in water have been investigated Measurements have been performed by using a variety of different apparatuses with cone and plate geometries Particular attention has been devoted to the experimental procedures, including the use of different sealing techniques, which are necessary to avoid solvent evaporation during the very long transients Shear fracture effects, and their dependence on the type of sealing agents have also been studied In steady shear, the HPC solution shows some rheological features which are common to other lyotropic systems, such as a three-region viscosity curve, and a double sign change in the first normal stress difference vs shear rate curve The structural changes which take place after cessation of shear flow have been investigated by following the evolution of the dynamic moduli as a function of the time elapsed after the shear flow is stopped It was found that the rate of the previously applied shear strongly affects both the kinetics and the asymptotic, long time values of the dynamic properties Possible explanations for such behavior in terms of microstructure evolution are presented and discussed

Fourier transform mechanical spectroscopy of the sol-gel transition in zirconium alkoxide ceramic gels

Abstract: The gelation of a ceramic precursor, zirconium alkoxide, has been studied using dynamic oscillatory measurements. The gelation time is controlled by varying the concentrations of zirconium propoxide, hydrolysis with water, and acetylacetone concentration which acts as a chelating ligand. Gelation times were varied from minutes to months. The gelation time varied with zirconium concentration to the −10 power, hydrolysis to the −7 power, and ligand concentration of the −17 power. The sol-gel transition was monitored using the criteria of Winter in which G′∼G″∼ω n and tan (δ) = tan $$\tan (\delta ) = \tan \left( {\frac{{n\pi }}{2}} \right)$$ . It is shown that the use of multiple superimposed sinusoidal waves to simultaneously measure the moduli at several frequencies is faster than using individual frequency sweep experiments. The selection of rate and strain criteria for brittle network gels is discussed in detail.

The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra

Abstract: The discretization of linear viscoelastic spectra is valuable as a starting point for non-linear viscoelastic modeling. However, obtaining the parameters of the generalized Maxwell model from linear viscoelastic experiments with naive least squares procedures is known to be an ill-posed problem. A novel technique, the Pade-Laplace method was recently elucidated (Fulchiron et al., 1993) for robustly extracting the parameters of the generalized Maxwell model from stress relaxation experiments, without any a priori assumption about the number of Maxwellian modes. We extend this method for obtaining the Maxwellian modes from dynamic data and discuss the relationship between continuous viscoelastic spectra and the Maxwellian modes obtained by this procedure. Furthermore, the applicability of this method with experimental data in limited time/frequency windows is clarified. Finally, a procedure for assembling the discretized spectrum with the Pade-Laplace method applied to both stress relaxation and dynamic data with typical experimental time/frequency cutoffs is developed.

Rheological behavior of a semi-crystalline polymer during isothermal crystallization

Abstract: The theological behavior of a molten semi-crystalline polymer, namely, a high density polyethylene (HDPE), was investigated during isothermal crystallization from the melt, using dynamic oscillatory experiments at 1 tad/s in a parallel plates rheometer. The theological results were compared with those obtained from differential scanning calorimetry in the same conditions. During the crystallization, the molten and crystallizing polymer provides a useful model for filled polymers, the crystalline phase being the filler and the liquid phase being the matrix. In most cases, the filler can be considered to be spherical shaped (spherulites). Owing to the amorphous phase linking liquid and crystallites, the adhesion between matrix and filler in this system is perfect. The filler content increases continuously during the crystallization. This model might be used to test laws relating the theological parameters to the volume fraction of filler. Problems related to the rheometry for such systems are discussed and the key parameters insuring reproducibility and accuracy in the measurements are pointed out. The relative sensitivity of the various theological parameters (storage and loss moduli, loss angle) to structural changes of the liquid has been out forward. Some preliminary equations relating the variation of these parameters to the volume fraction of filler, through the use of simple fractal exponents have been derived and discussed in comparison with laws provided by various authors.

Shear rheometry of polydimethylsiloxanes. Master curves and testing of Gleissle and Yamamoto relations

Abstract: This study concerns the shear rheometry of a series of nine silicone fluids, all linear or branched polydimethylsiloxanes (PDMS), with varying mass distributions.

Flow-induced concentration fluctuations in polymer solutions: Structure/property relationships

Abstract: Mechanical and optical rheometric measurements are reported on solutions of polystyrene dissolved in dioctyl phthalate, a solution that can undergo an apparent phase separation upon the application of shear. Solutions prepared using three molecular weights ranging from one to four million were studied. Time-temperature superposition was observed to apply for these solutions up to and including the onset of an apparent shear thickening of the steady shear and first normal stresses. Optical measurements employing turbidity and scattering dichroism determined that concentration fluctuations were enhanced by flow and grew parallel to the vorticity axis below the critical velocity gradient for the onset of the apparent shear thickening effect. Prior to the onset of thickening, the fluctuations were observed to rearrange and orient parallel to the flow direction. Second normal stress difference measurements indicate these solutions have a negative ratio of the second to the first normal stress differences. It is interesting to point out that the ratio tends to zero in the vicinity of the shear rate range at which shear thickening occurs.

Boundary conditions for contacts lines in coextrusion flows

Abstract: A bicomponent coextrusion process is modelled using a 3-D finite element formulation. The layer uniformity problem in coextrusion is addressed by examining the effects of the polymer melt/polymer melt/die wall contact line boundary condition. It has been observed that the less viscous polymer layer will tend to displace the more viscous polymer layer near the die wall. The behaviour of the contact lisle is considered to be either a “stick” or “slip” boundary condition. In the “stick” boundary condition, the contact line does not move from its original position after the two polymer layers meet, A slip boundary condition allows the contact line to move along the die wall. The calculated interfaces which result from different contact line assumptions are determined. Results show that if a “stick” boundary condition is appropriate for a given fluid/fluid/solid contact line, then a very thin entrained layer of the more viscous polymer melt will be trapped between the less viscous polymer melt and the die wall. Slip boundary conditions would allow complete displacement of the contact line along the die wall. Both slip and stick boundary conditions produce similar interface profiles far away from the die wall for small viscosity ratios. In certain eases, the displacement of the more viscous material by the less viscous material will cease and a static interface structure is produced regardless of die length. Experimental work with polycarbonate melts is compared with the numerical simulations.

Free oscillatory shear measurements : an interesting application of constant stress rheometers in the creep mode

Abstract: A constant stress rheometer in the creep mode was used to perform free oscillatory shear measurements on soft solids. The results obtained are in good to excellent agreement compared to forced oscillatory shear measurement data. Depending on the rheologic properties of the sample and the moment of inertia of the rotating device of the measurement system, free oscillations are suited to confirm or supplemented forced oscillatory measurement results.

An investigation of possible mechanisms of heterogeneous drag reduction in pipe and channel flows

Abstract: When concentrated polymer solutions are injected into the core-region of a turbulent pipe or channel flow, the injected polymer solution forms a thread which preserves its identity far beyond the injection point. The resulting drag reduction is called heterogeneous drag reduction.

Rheology of low viscosity, high concentration brown coal suspensions

Abstract: The paper describes how the theology of low concentration brown coal suspensions can be exploited to produce high concentration, low viscosity suspensions which are attractive as a potential coal-water fuel. Brown coal suspensions with solid concentrations approaching those of bituminous black coal have been prepared. The high inherent water content (≈ 60 wt %) and macroporosity of the brown coal have been reduced by thermal and chemical means. The hydrophobicity of the coal surface has been increased sufficiently to reduce the tendency for swelling and water uptake. This, together with densification, has allowed the solids content to be progressively improved from 30 wt % solids with raw coal to 65 wt% solids with modified coals while maintaining the viscosity of the suspension at a low level. The high solid concentration was achieved without additives.

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

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

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Abstract: Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.

Experimental estimation of wall slip for filled rubber compounds

Abstract: The phenomenon of wall slip during flow of rubber compounds through capillaries is investigated for a typical styrene-butadiene elastomer with carbon black. It was found that at low temperature (110°C) the dependencies of slip velocity V c on shear stress are described by the power law but, additionally, V c depends on radius of a channel. At high temperatures there is a critical shear stress below which sliding is absent. Sliding appears only at higher shear stresses where, again, V c depends on shear stress and the radius of a channel.

An experimental study of the first normal stress difference — shear stress relationship in simple shear flow for concentrated shear thickening suspensions

Abstract: For many polymeric solutions in a simple shear flow a plot of the logarithm of the first normal stress difference N 1 against the logarithm of the shear stress σ, for a range of temperatures results in a linear relationship. For such polymer solutions these plots yield a straight line of slope very close to 2 when measured at low shear rates. This relationship is tested against a polymer solution (polyacrylamide in a 50/50 mixture of glycerol/water), a polymer melt (polyethylene), and three concentrated suspensions. These are Superclay (supplied by English China Clays, Cornwall, U.K.) in water, polyvinylchloride in dioctylphthalate and polystyrene latex in water, at volume concentrations of 40% 48%, and 60%, respectively. It was found that the log N 1 — log σ relationship is applicable to the polymer solution and melt over a significant range of shear rates and temperatures. In the cases of concentrated suspensions the relationship holds to the point of onset of the shear thickening behaviour. Beyond this point a different relationship exists, however, flow instabilities are apparent. A comment on the contribution of N 1 and N 2 to the flow instabilities is made.

Orientation tensors in simple flows of dilute suspensions of non-Brownian rigid ellipsoids, comparison of analytical and approximate solutions

Abstract: General analytical solutions are obtained for the planar orientation structure of rigid ellipsoid of revolutions subjected to an arbitrary homogeneous flow in a Newtonian fluid. Both finite and infinite aspect ratio particles are considered. The orientation structure is described in terms of two-dimensional, time-dependent tensors that are commonly employed in constitutive equations for anisotropic fluids such as fiber suspensions. The effect of particle aspect ratio on the evolution of orientation structure is studied in simple shear and planar elongational flows. With the availability of analytical solutions, accuracies of quadratic closure approximations used for nonhomogeneous flows are analyzed, avoiding numerical integration of orientation distribution function. In general, fourth-order orientation evolution equations with sixth-order quadratic closure approximations yield more accurate representations compared to the commonly used second-order evolution equations with fourth-order quadratic closure approximations. However, quadratic closure approximations of any order are found to give correct maximum orientation angle (i.e., preferred direction) results for all particle aspect ratios and flow cases.