Volume 52, Issue 5, September 2008
Index of content:
52(2008); http://dx.doi.org/10.1122/1.2957699View Description Hide Description
According to tube model ideas, chain stretch at deformation rates below the inverse Rouse time of the chain, is only possible for polymertopologies with two or more branch points. The basic topologies, which embody this idea, are the H molecule with two side chains, and the pom-pom molecule with side chains at each end of the backbone. According to the pom-pom hypothesis, maximum chain stretch of the backbone is limited by branch point withdrawal, i.e., the side chains are drawn into the tube of the backbone as soon as the relative tension in the backbone reaches a value of . This hypothesis, which has never been verified before, can now be tested by considering recent elongational experiments by Nielsen et al. [Macromolecules39, 8844–8853 (2006)] on a nearly monodisperse polystyrene pom-pom melt with . The analysis presented is based on the original integral version of the pom-pom model, and on the molecular stress function (MSF) model with strain-dependent tube diameter. The material strain measure determined from the experiments is found to be consistent with a constant maximum stretch, independent of the elongation rate, which is, however, significantly larger than . To achieve quantitative agreement between experiment and modeling, (1) dynamic dilution of the backbone, which increases the tube diameter of the backbone and reduces equilibrium tension in the backbone, (2) finite extensibility effects, (3) stretch relaxation causing a transition from chain stretch to tube squeeze at lower strain rates, and (4) the dynamics of branch point withdrawal need to be considered. Integrating all of these features in a MSF stretch evolution equation with multiple time scales, the fundamental pom-pom hypothesis is confirmed.
Time-dependent tube flow of compressible suspensions subject to pressure dependent wall slip: Ramifications on development of flow instabilities52(2008); http://dx.doi.org/10.1122/1.2955508View Description Hide Description
A mathematical model developed earlier for the time-dependent circular tube flow of compressible polymer melts subject to pressure-dependent wall slip [Tang and Kalyon, J. Rheol52, 507–525 (2008)] was applied to the tube flow of polymericsuspensions with rigid particles. The model relies on the apparent slip mechanism for suspensionflow with the additional caveat that the polymeric binder slips at the wall according to a pressure-dependent wall slip condition. The numerical simulations of the tube flow of concentrated suspensions suggest that steady flow is generated when the flow boundary condition at the wall is a contiguous strong slip condition along the entire length of the tube wall. The findings of the simulations are consistent with the experimental flow curves and flow instability data collected on suspensions of a poly (dimethyl siloxane), which itself exhibits wall slip, compounded with rigid and hollow spherical particles in the 10–40% by volume range. Increasing the concentration of rigid particles gives rise to the expansion of the range of flow rates over which the flow remains stable, as consistent with the experimental observations.
52(2008); http://dx.doi.org/10.1122/1.2952510View Description Hide Description
By using simultaneously rheometry and a multiple light scattering technique, diffusing wave spectroscopy (DWS), we have studied the steady flows of three-dimensional aqueous foams. A number of parameters—the surfactants, the liquid volume fraction, and the roughness of the rheometer surfaces—are widely varied in order to determine which quantities have an impact on the macroscopic flow behaviors. By comparing to previous theoretical and experimental results, we show that flow regimes can either be slip or shear dominated. Two opposite slip regimes are identified; the transition from one to the other is obtained either by changing the surfactant or the liquid fraction, and we quantitately discuss which regime is selected for any given foamproperties. Similarly, different shear regimes are also found, and we discuss the link between the macroscopic rheometrymeasurements, the nature of the flow, and the interfacial microscopic properties. Despite the occurrence of slip, we show how we can recover the actual shear rate by DWS, and how we can quantitatively explain the measured slip velocities.
52(2008); http://dx.doi.org/10.1122/1.2965473View Description Hide Description
Diffusing wave spectroscopy’s (DWS) sensitivity to local shear rate has been used to investigate the nonlinear rheology of (1) a dopedshear thinning, semidilute polymer solutionmeasured in the cone-plate and parallel-plate geometries and of (2) dopedshear banding wormlike micellessolutionsmeasured in the cylindrical-Couette geometry. DWS measurements of the semidilute polymer solution in the cone-plate geometry under stress controlled conditions were used to construct a flow curve for the material, the expected radial dependence of the local shear rate being demonstrated in the parallel-plate geometry. The method is shown to be sensitive to shear banding in semidilute wormlike micelles in the cylindrical-Couette geometry under strain controlled conditions, and DWS correlation functions were quantitatively interpreted using a heterogeneous shear flow model. Flow curves and shear rate profiles were inferred from these measurements.
52(2008); http://dx.doi.org/10.1122/1.2955511View Description Hide Description
We have developed a multi-sample micro-slit rheometer (MMR) which is capable of measurements over a broad range of temperatures, viscosities and shear rates. The instrument is mechanically simple as the flow is generated by external gas pressure and the shear rate is measured through optical tracking of the flow front. In the current implementation, the required volume of each sample is approximately and we measure four samples simultaneously. We demonstrate the performance of the MMR by measurement of the flow curves (viscosity versus shear rate) of three representative polymers: A polydimethylsiloxane melt, a polyisobutylene solution, and a polystyrene melt. We adapt standard data correction methods to account for shear-thinning and entry/flow-front effects. We report a high level of accuracy and precision. This instrument will be particularly useful in cases of multiple samples, limited material quantity, and when optical access is useful.
52(2008); http://dx.doi.org/10.1122/1.2964201View Description Hide Description
An accurate, configuration-based, coarse-grained model for dilute macromolecular solutions is presented. The basic approach relies on exploring the macromolecular configurational diversity present in the flow of dilute polymeric solutions and identifying and partitioning the most frequently observed configurations, e.g., folds, half dumbbells, kinks, dumbbells, coils, and stretched states. The probability of finding any one of these configurations is calculated using a master configuration map that dictates the conditional probability of finding a configuration with a given chain extension. Each configuration class is modeled using a dumbbell description with a suitably modified drag coefficient. The configuration-based model is implemented using a Brownian dynamics simulation and the predictions are compared with the corresponding bead-spring model and finitely extensible nonlinear elastic dumbbell in homogeneous steady shear and uniaxial extension. Finally, prospects for model improvement are discussed.
An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence52(2008); http://dx.doi.org/10.1122/1.2946437View Description Hide Description
Recent experiments suggest that short fibers in concentrated suspensions align more slowly as a function of strain than models based on Jeffery’s equation predict. We develop an objective model that captures the slow orientation kinetics exhibited by short-fiber suspensions. The standard moment-tensor equation of fiber orientation is used to find equations for the change rates of the eigenvalues and eigenvectors of the orientation tensor. As a phenomenological assumption, the growth rates of the eigenvalues are reduced by a constant scalar factor, while the rotation rate expressions for the eigenvectors are unchanged. The eigenvalue/eigenvector equations are then reassembled as a tensor equation. An equivalent kinetic theory is also developed. The new model is tested in a variety of flows, and found to exhibit slower kinetics than the standard model but similar steady-state orientations. The model provides an excellent fit to the shear stress transient in a shear reversal experiment with a 30% glass fiber filled polybutylene terephthalate resin melt, and we show how this experiment can be used to determine the parameters of the model.
52(2008); http://dx.doi.org/10.1122/1.2964199View Description Hide Description
Spurt occurs in the flow of entangled melts in a capillary rheometer in which the driving pressure is controlled. As the driving pressure increases, at a critical value there is a sudden increase in flow rate, often called spurt. This discontinuity is followed by another regime of smoothly increasing flow rate. A phenomenon that may contribute to this instability is a curve of wall shear stress versus slip velocity that has a maximum followed by a minimum, and there are models that predict such behavior. We used a sliding plate rheometer (SPR) to study wall slip for a highly entangled, linear polybutadiene at and at . By varying the plate speed, we were able to explore the entire curve of shear stress versus slip velocity. This curve exhibited a maximum and a minimum in the stress, providing support for theories predicting this behavior and an explanation for the spurt effect in capillary rheometry. The spurt flow of the same polymer was also observed, and slip velocities were estimated and compared with those determined using the SPR. The slip velocities obtained using the two instruments were in good agreement.
52(2008); http://dx.doi.org/10.1122/1.2963135View Description Hide Description
Concentrated suspensions of soft deformable particles, e.g., polymermicrogelpastes and compressed emulsions, display a generic slip behavior [Meeker et al., J. Rheol.92, 18302 (2004a); Meeker et al., J. Rheol.48, 1295–1320 (2004b)]. When sheared with smooth surfaces, they exhibit apparent motion due to slip at the wall. Wall-slip stops at a sliding yield stress the value of which is much lower than the bulk yield stress. The physical mechanism of slip at low stresses and the origin of the sliding yield stress have so far been unresolved issues. We propose that the paste-wall interactions control the wall-slip behavior and determine the occurrence of the sliding yield point. We present experiments performed with different shearing surfaces. Two distinct slip behaviors are identified: depending on whether the interaction between the microgel particles and the wall is attractive or repulsive, wall-slip can be either suppressed or promoted. We provide an extension to the elastohydrodynamic slip model of Meeker and co-workers by incorporating attractive or repulsive interactions between the slipping paste particle and the wall. The interplay of various short range forces due to van der Waals, hydrophobic/hydrophilic, and/or electrostatic interactions and elastohydrodynamics is used to explain the influence of the shearing surface on wall-slip. The model encompasses the different slip regimes observed in our experiments and can predict the slip behavior accurately for well characterized surfaces.