Index of content:
Volume 45, Issue 1, January 2001
45(2001); http://dx.doi.org/10.1122/1.1332787View Description Hide Description
Different software packages are available commercially which can be applied to oscillatory shear data to recover an estimate of the relaxation spectrum of the viscoelastic material tested. The underlying algorithms, based on some form of regularization, are indirect and technically involved. Davies and Anderssen [J. Non-Newtonian Fluid Mech. 73, 163–179 (1997)] have derived exact sampling localization results for the determination of elastic moduli from (exact) storage and loss moduli. It is now shown how their results can be exploited to construct simple and explicit moving-average formulae which recover estimates of the relaxation spectrum from oscillatory shear data, with realistic observational errors. Explicit moving-average formulae are presented which experimentalists can apply immediately to appropriately sampled oscillatory shear measurements. The given formulae are validated on noisy data obtained from synthetic relaxation spectra.
Rheology and nuclear magnetic resonance measurements under shear of sodium dodecyl sulfate/decanol/water nematics45(2001); http://dx.doi.org/10.1122/1.1332387View Description Hide Description
We report on the rheology and deuteron nuclear magnetic resonance (NMR) measurements performed on the nematic lyotropic system sodium dodecyl sulfate, decanol, and water. For total surfactant and cosurfactant concentrations of about 30% by weight, we prepared nematic calamitic and nematic discotic solutions. We have studied the flow behavior of the and phases in terms of the transient shear stress using different rheological histories. In flow-reversal experiments, the transient response exhibits nonperiodic oscillations in the region of small deformations which is followed by a long-lasting relaxation toward the stationary state. In the pseudo-Newtonian regime of the viscosity, we have found that the stress, when normalized to its long term value and plotted versus deformation, is shear-rate independent. measurements at rest and under shear were performed on nematic calamitic and discotic solutions prepared in At rest, the NMR spectra exhibit well-resolved doublet structures, which indicate an alignment of the director along the axis of the magnetic field. At shear rates large enough alignment is achieved with respect to the flow velocity. One finds alignment angles of 12 ° and 105 ° for the directors of the calamitic and discotic phase, respectively. Combining the results obtained by rheology and by NMR, we provide strong evidence that the and nematics of the sodium dodecyl sulfate / decanol system are textured nematics of the flow-aligning type.
45(2001); http://dx.doi.org/10.1122/1.1332385View Description Hide Description
In this paper we present new experimental evidence indicating that the presence of adsorbed polymer chains in the die exit region of a slit die is a necessary feature in the production of sharkskin on the extrudate. Specifically, we use a flow birefringence technique to visualize the level of molecular deformation in the die exit region. By varying the applied shear stress level, we are able to find the critical molecular deformation in the die exit to produce sharkskin when the no-slip boundary condition prevails. We then perform the same experiment on a slit die with the slip boundary condition in the die exit. It is observed that no sharkskin roughening of the extrudate occurs even at a much higher level of retardance.
45(2001); http://dx.doi.org/10.1122/1.1332384View Description Hide Description
Nonlinear step shear relaxation moduli in a series of entangled polystyrene/diethylphthalate solutions are studied using mechanical rheometry and birefringencepolarimetrymeasurements. We pose the question: Is the step shear damping function universal for fluids in the class entangled liquids? The experimental results provide a clear answer in the negative, and in fact show that the damping functions in entangled polymer liquids continuously vary with polymer molecular weight and concentration. In weak to moderately entangled solutions, experimental results are in accord with the Doi–Edwards theoretical prediction, (type A damping). At higher entanglement densities, however, damping functions become progressively softer than particularly at low strains (type C damping). The transition from type A to type C damping behavior is accompanied by the appearance of a complex time-dependent crossing pattern in experimental plots at variable shear strain. Using a simple tube model analysis, we show that both experimental observations can be explained in terms of coupled relaxation of polymer segment orientation and tube equilibration following step shear.
An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids45(2001); http://dx.doi.org/10.1122/1.1332388View Description Hide Description
Following development of a filament-stretching extensional rheometer at Monash University, similar rheometers have been designed and built in other laboratories. To help validate the basic technique, a collaborative program was undertaken to compare results from several instruments. First, three test fluids prepared at the University of California at Berkeley were characterized in steady and transient shear flows there and at the Massachusetts Institute of Technology (M.I.T.), and then tested in extensional rheometers at M.I.T., Monash and the University of Toronto. Each fluid is a constant-viscosity solution of narrow-molecular-weight-distribution polystyrene dissolved in oligomeric polystyrene. The solute molecular weights are 2.0, 6.5, and 20 million g/mol, and the polymer concentration in each fluid is 0.05 wt. %. From linear viscoelasticmeasurements, the Zimm relaxation times of the fluids are found to be 3.7, 31, and 150 s, respectively. The scaling of relaxation times with molecular weight indicates better-than-theta solvent quality, a finding consistent with independent intrinsic viscometry measurements of equilibrium coil size. Each fluid was tested in the three filament stretching rheometers at similar Deborah numbers. Despite variations in instrument design and the general difficulty of the technique, transient Trouton ratios measured in the three instruments are shown to agree quantitatively.
45(2001); http://dx.doi.org/10.1122/1.1332389View Description Hide Description
We study the elasto-capillary self-thinning and ultimate breakup of three polystyrene-based ideal elastic fluids by measuring the evolution in the filament diameter as slender viscoelastic threads neck and eventually break. We examine the dependence of the transient diameter profile and the time to breakup on the molecular weight, and compare the observations with simple theories for breakup of slender viscoelastic filaments. The evolution of the transient diameter profile predicted by a multimode FENE-P model quantitatively matches the data provided the initial stresses in the filament are taken into account. Finally, we show how the transient uniaxial extensional viscosity of a dilute polymer solution can be estimated from the evolution in the diameter of the necking filament. The resulting “apparent extensional viscosity” profiles are compared with similar results obtained from a filament stretching rheometer. Both transient profiles approach the same value for the steady state extensional viscosity, which increases with molecular weight in agreement with the Rouse–Zimm theory. The apparent discrepancy in the growth rate of the two transient curves can be quantitatively explained by examining the effective stretch rate in each configuration. Filament thinning studies and filament stretching experiments thus form complementary experiments that lead to consistent measures of the transient extensional viscosity of a given test fluid.
45(2001); http://dx.doi.org/10.1122/1.1332788View Description Hide Description
The rheology of modelsuspensions has been characterized by standard experiments and predicted from Stokesian dynamics (SD) computer simulations.Suspensions of spherical monodisperse polystyrene latex particles (average diameter 0.45 μm) are prepared in aqueous solutions of carboxymethyl cellulose (CMC) at different concentrations and molecular weights. The rheological measurements are compared with viscosity predictions of a SD model that includes electrostatic and van der Waals forces. A new method is proposed to include boundary roughness in the SD model. The model is able to predict the correct steady shear viscosity as a function of shear rate, CMC concentration, and molecular weight. The degree of shear thinning, given by the slope of the viscosity curves, is well predicted by the model. Good quantitative agreement can be obtained if the model results are shifted along the shear rate axis by a factor of 50. The microstructural mechanisms responsible for the shear thinning are shown and described. Normal stress predictions are similar to those presented by others. The potential and limitations of the technique at the present status of its development are outlined and discussed.
45(2001); http://dx.doi.org/10.1122/1.1332997View Description Hide Description
We outline a model to describe the rheology and the nonlinear response of layered materials. Explicitly, the focus is on cases wherein the system possesses internal states whose relative populations undergo a change upon the application of a stress. The objective of the model is to describe the mutual interplay between stress-induced transformations and the macroscopic rheological response of the materials. We focus on the specific case of multiblock copolymers, wherein the bridge and loop conformations of the chain constitute the internal states. The numerical results of our model for different polymeric architectures and different rheological constraints indicate a rich variety of phenomena including strain localization and shear banding. We derive an explicit constitutive equation that explains the origin of the inhomogeneous rheological response of the model.
The linear viscoelastic behavior of highly filled polydimethylsiloxane measured in shear and compression45(2001); http://dx.doi.org/10.1122/1.1332386View Description Hide Description
The frequency and time dependent moduli of up to 60% glass bead filled polydimethyl siloxane (PDMS) were studied for four different molecular weight materials with a rotational, compressional, and lubricated squeezing flow rheometer. Measurements of the storage and loss modulus taken with a conventional rotational instrument show good qualitative and quantitative agreement with those taken with a newly developed oscillatory compressional rheometer for PDMS of the lowest molecular weight studied, and show trends similar to those reported previously for similar materials. The agreement between the two instruments is better for both unfilled and 35% filled material of a higher molecular weight. Good agreement was also observed between measurements of the relaxation modulus in lubricated squeezing flow and measurements of the storage modulus with the new compressional device for a high molecular weight PDMS at all filler levels. The modulus derived from oscillatory measurements showed good quantitative agreement with that measured in lubricated squeezing flow for identical materials. The effect of polymer molecular weight on the relative behavior of the loss and storage modulus with increasing filler content was also studied. It was shown that as the polymer molecular weight increases, the ratio of the loss to storage modulus becomes nearly independent of the filler volume fraction over the frequency range studied. The effect of an increase in filler amount on the elasticity of the material was shown to depend both on the polymer molecular weight and the frequency, and is explained in terms of the influence of the filler on the Deborah number of the system.
45(2001); http://dx.doi.org/10.1122/1.1332785View Description Hide Description
The effects of long chain branching (LCB) on the viscosity and first normal stress coefficient of metallocene polyethylene (mPE) are described. LCB increased the zero shear viscosity and the susceptibility to shear thinning. The first normal stress coefficient increased with degree of LCB at all rates. The materials with LCB followed the Cox–Merz rule and the Gleissle mirror relations while the linear material followed only the Cox–Merz rule. These results indicate that the behavior of long chain branched mPE in simple shear can be predicted using only linear viscoelastic properties.
45(2001); http://dx.doi.org/10.1122/1.1332786View Description Hide Description
This paper reports for the first time our preliminary findings of a new gas-assisted extrusion process. We have discovered that if gas is injected at a metal die/molten polymerinterface at a low flow rate, it is possible to establish a stable gas layer at the interface, which can give rise to an essentially full slip wall boundary condition. We report experimental optical observations, flowbirefringence data, pressure difference, and die swell data for both a slit and rod geometry extrusion. We also match some of the experimental results with a viscoelastic numerical simulation. The introduction of wall slip induced by the presence of the gas layer has a profound effect on the magnitude of the die swell observed for polyethylene processed using gas-assisted extrusion. The experiments demonstrate, without ambiguity, that wall boundary conditions can play a crucial role in the overall extrusionflow of high viscosityviscoelastic fluids, such as polyethylene.
45(2001); http://dx.doi.org/10.1122/1.1333001View Description Hide Description
In this paper we report an experimental study on the conditions for droplet breakup in concentrated emulsions under simple shear flow. We present a set of experiments where the ratio between drop and matrix viscosity was varied from 0.1 to 22 and the volume fraction ranged from 0% to 70%. It was observed that the critical shear rate for breakup decreased by more than an order of magnitude for the most concentrated emulsions. Further, drops with viscosity ratio of 22 were seen to rupture in simple shear as soon as the emulsion concentration was raised to 40%. All these effects were conveniently explained by means of a mean field model which assumes simply that breakup of a droplet in a concentrated emulsion is determined by the average emulsionviscosity rather than the continuous phase viscosity.
45(2001); http://dx.doi.org/10.1122/1.1333000View Description Hide Description
A calculation method for two-dimensional time-dependent free surface flows is presented. The method extends the capabilities of CONNFFESSIT (calculation of non-Newtonian flows:finite elements and stochastic simulation technique) to transient free surface flows. The macroscopic unknowns are the velocity and the pressure fields together with the shape of the free surface. Particle tracking techniques, one of the main components of CONNFFESSIT, are capitalized upon in order to efficiently track the time evolution of the free surface. The ability of CONNFFESSIT to treat models for which no closed-form constitutive equation can be derived and to yield full molecular information is now enhanced with a technique for the calculation of free surface flows. In order to validate the method, transient, free jet swell calculations for the Oldroyd-B fluid using CONNFFESSIT are compared with continuum-mechanics POLYFLOW calculations.
45(2001); http://dx.doi.org/10.1122/1.1332998View Description Hide Description
The deformation of Newtonian droplets with zero interfacial tension in a Newtonian matrix is studied in simple shear flow for viscosity ratios ranging from 0.095 to 10.29. The experiments use a counter-rotating Couette apparatus driven by independent servo motors, with a control scheme that keeps the droplet centered under a video camera.Dropletdeformation is measured by analyzing the video images, using the method of moments. Both the matrix and the droplet are silicone oils, and the droplet contains a fluorescent dye. Low-viscosity droplets stretch monotonically, while higher viscositydroplets may stretch, wobble, or tumble. The theory of Wetzel and Tucker (2001) for ellipsoidal droplets with zero interfacial tension is compared to the data, by adjusting those portions of the initial shape and orientation that are not observable in the experiment. The agreement is excellent in all cases, requiring only that the initial droplet shape be close to an ellipsoid.
45(2001); http://dx.doi.org/10.1122/1.1332999View Description Hide Description
Exponential shear flows of polymer melts are investigated. These flows are of interest because they share some properties of both planar extension and simple, constant-rate, shear. In particular, embedded points separate exponentially in time, like extensional flows, yet the flow direction and velocity gradient are perpendicular, as for all shear deformations. A comparison between the predictions of the “pom-pom” molecular model of McLeish and Larson [J. Rheol. 42, 81–110 (1998)] in exponential shear and experimental data is presented. The solutions in exponential shear are used to contrast this flow with simple shear and extensional flows and the physical processes driving the solutions are analyzed in each of the three geometries. Accurate quantitative predictions are made using the multimode approach, and the possibility of using exponential shear to obtain the multimode nonlinear spectrum of a melt is explored. It is concluded that although exponential shear is less effective than extensional flows at exposing the influence of the nonlinear parameters of a melt, there are still situations where it is a useful flow for obtaining these parameters.