Index of content:
Volume 55, Issue 6, November 2011
55(2011); http://dx.doi.org/10.1122/1.3625559View Description Hide Description
A cone-partitioned-plate fixture for the ARES rheometer (TA instruments, DE) has been designed, implemented, and validated. This geometry allows measuring the nonlinear shear flow properties of samples, which display edge fracture in regular cone-and-plate geometries, such as polymer melts and concentrated solutions. Reliable bulk shear flow data can be obtained with these systems at high rates and strains, using very small sample quantities. Measurements can be performed at temperatures ranging from at least − 50 °C up to over 200 °C in a controlled nitrogen environment. An extensive set of start-up shear measurements on moderately entangled linear monodisperse polyisoprene (60 kg/mol) and polystyrene (182 kg/mol) melts to validate the design are presented and discussed with focus on the Cox–Merz rule and the characteristics of the stress overshoot. With this new geometry, the range of artifact-free data is extended by a decade in Weissenberg number (Wi D ). It is shown that the obtained results compared well with the limited experimental data available from the literature on monodisperse polymer melts. Furthermore, we show that, for the investigated range of Wi D in start-up shear, the two monodisperse linear polymers of different chemistry with nearly the same number of entanglements, scale identically.
Hard vs soft constraints in the full field reconstruction of incompressible flow kinematics from noisy scattered velocimetry data55(2011); http://dx.doi.org/10.1122/1.3626411View Description Hide Description
High quality flowkinematics reconstruction from noisy and spatially scattered data requires the use of regularization techniques but remains a challenge. We set out to test the effect and practical relevance of additional incompressibility constraints. To this end, we present two methods for reconstructing smooth velocity and velocity gradient fields from such data in an incompressible two-dimensional complex flow. One is based on a generalized Tikhonov regularization combined with a finite element approximation and uses a stream function formulation, which enforces incompressibility (hard constraint). This approach is compared to that in which incompressibility is asymptotically achieved by adding a divergence penalty term in the regularization expression (soft constraint). The methods are compared on synthetic velocity data, obtained for an incompressible Oldroyd–B fluid in a cross-slot channel with added noise. For such data sets, both methods are seen to lead to essentially identical results. However, for a given grid size, the stream function formulation uses a single regularization parameter and less degrees of freedom to provide the required continuity of the gradient fields. The fidelity of the reconstruction is investigated in terms of the quality of the streamlines and velocity gradient history. Incompressibility constraints turn into significant and valuable improvement for applications as we demonstrate by analyzing the stress and optical signal fields obtained by applying a constitutive equation to the reconstructed flow fields.
55(2011); http://dx.doi.org/10.1122/1.3626414View Description Hide Description
Effect of the addition of polymeric fine fibers on the rheological properties is studied employing poly(lactic acid) PLA as a matrix. Fine fibers of poly(butylene terephthalate) PBT, whose melting point is higher than that of PLA, is prepared in a PLA matrix by melt-stretching with rapid cooling. Then, the rheological properties of the composites are evaluated at the temperature between melting points of PLA and PBT. It is found that only 1 wt. % of PBT fibers greatly enhances the elongational viscosity, although shear viscosity is hardly changed. In particular, the composite shows strain-hardening behavior, which has not been detected for polymer composites with rigid fibers. Elastic deformation of network composed of flexible PBT fibers, leading to bending of fibers and/or friction between fibers, will be responsible for the strain-hardening. The marked elasticity is also detected for a composite of silicone oil containing the PBT fine fibers.
55(2011); http://dx.doi.org/10.1122/1.3621521View Description Hide Description
Edge fracture occurs frequently in non-Newtonian fluids. A similar instability has often been reported at the free surface of fluids undergoing shear banding and leads to expulsion of the sample. In this paper, the distortion of the free surface of such a shear banding fluid is calculated by balancing the surface tension against the second normal stresses induced in the two shear bands, and simultaneously requiring a continuous and smooth meniscus. We show that wormlike micelles typically retain meniscus integrity when shear banding, but in some cases can lose integrity for a range of average applied shear rates during which one expects shear banding. This meniscusfracture would lead to ejection of the sample as the shear banding region is swept through. We further show that entangled polymer solutions are expected to display a propensity for fracture because of their much larger second normal stresses. These calculations are consistent with available data in the literature. We also estimate the meniscus distortion of a three-band configuration, as has been observed in some wormlike micellar solutions in a cone and plate geometry.
Basic characteristics of uniaxial extension rheology: Comparing monodisperse and bidisperse polymer melts55(2011); http://dx.doi.org/10.1122/1.3626416View Description Hide Description
We have carried out continuous and step uniaxial extension experiments on monodisperse and bidisperse styrene-butadiene random copolymers (SBR) to demonstrate that their nonlinear rheological behavior can be understood in terms of yielding through breakdown of the chain entanglement network and rubberlike rupture via non-Gaussian chain stretching leading to chain scission, respectively. In continuous extension, the sample with bidisperse molecular weight distribution showed greater resistance, due to double-networking, against the yielding-initiated failure. An introduction of 20% high molecular weight (106 g/mol) SBR to an SBR matrix (2.4 × 105 g/mol) could postpone the onset of nonuniform extension by as much as two Hencky strain units. In step extension, the bidisperse blends were also found to be more resistant to elastic breakup than the monodisperse matrix SBR. Rupture in both monodisperse and bidisperse SBR samples occurred when the finite chain extensibility was reached at sufficiently high rates. It is important to point out here that these results along with the concept of yielding allow us to clarify the concept of strain hardening in extensional rheology of entangled polymers.
Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor-Couette flows55(2011); http://dx.doi.org/10.1122/1.3626584View Description Hide Description
This study examines the impact of dilute polymer solutions on the unique isolated secondary flows between concentric, rotating cylinders, namely Taylor-Couette (TC) flow. We mapped the stability of flow states using Newtonian and dilute polyethylene oxide (PEO) solutions over the Reynolds number range of − 100 < Reo < 500 and 0 < Rei < O(103), where subscripts ‘o’ and ‘i’ refer to outer and inner cylinders, respectively. Elasticity number (El) of the PEO fluids, defined as the ratio of elastic to inertial forces, ranges from O(10− 4) to O(10− 2). This work expands on previous studies by (a) significantly expanding the range of Rei, Reo, and El examined, (b) use of a consistent, conservative protocol for reaching flow states, and (c) rheological characterization of the solutions via shear and capillary breakup extensional rheometry. Using spectral analysis of flow visualization of the r-z or z-θ planes, we find the effect of El on the critical conditions for laminar and chaotic axisymmetric and nonaxisymmetric flow states is nonmonotonic and mode-dependent, with greater modification of higher order transitions involving small-scale features. While the critical conditions are modified by low El for all transitions, the flow states vary from those for Newtonian fluids at higher Rei and for the more elastic fluids.
55(2011); http://dx.doi.org/10.1122/1.3626945View Description Hide Description
This paper is focused on the theoretical modeling of the rheological properties of the magnetic suspensions in shear flows under an external magnetic field aligned with the streamlines. The conventional theory postulates that the field-induced aggregates of magnetic particles are highly anisotropic and aligned with the flow direction. Therefore, no substantial variation in suspension viscosity would be expected in the presence of field. However, experiments reveal a strong Bingham rheological behavior of the suspensions with a dynamic yield stress of the same order of magnitude that the one measured in the magnetic fields perpendicular to the flow. We explain the high level of shear stress, generated in longitudinal magnetic fields, by stochastic rotary oscillations of the aggregates caused by many-body magnetic interactions with neighboring aggregates. The interaggregate interactions are accounted for by an effective rotational diffusion process with a diffusion constant proportional to the mean square interaction torque—a net magnetic torque exerted to a given aggregate by all the neighboring aggregates. Using the equations for the orientation tensors coupled with the balance of forces acting on aggregates, we find the orientation distribution and size of the aggregates as function of the magnetic field intensity and shear rate. Our theory, developed for semidilute regime, reproduces the Bingham behavior observed experimentally and fits the experimental data reasonably well in a wide range of particle concentrations. We find that the yield stress increases quadratically with the magnetic field strength and exhibits a cubic growth with respect to the particle volume fraction. A part from resolving a particular rheological problem, the new concept of magnetically induced diffusion reveals the importance of long-range nonhydrodynamic interactions in the rotary diffusion process and could probably contribute to the understanding of this process in other concentrated systems subject to nonhydrodynamic interactions.
55(2011); http://dx.doi.org/10.1122/1.3630943View Description Hide Description
The viscosity of a non-Brownian suspension in simple shear cannot be theoretically predicted in the limit of the semidilute approximation, since it depends on the initial configuration. Batchelor and Green [J. Fluid Mech.56, 401–427 (1972)] proved that the suspensionviscosity can be expressed in power series of the solid volume fraction and the second order coefficient, b, resulted undetermined. On the contrary, experimentally Pasquino et al. [J. Rheol.52, 1369–1384 (2008)] obtained a single steady state and estimated the value of b. We here numerically show that laminar mixing is able to induce a unique steady state also in the semidilute regime, since it is effective to break the closed orbits that may occur in these suspensions. To this end, we investigated the effect of the initial conditions on the steady state starting from seven different configurations ranging from the fully uniform and ordered one to the agglomerated one, passing through different random distributions. We, finally, numerically predict, via Stokesian dynamics, the coefficient b for the viscosity of a monolayer of rigid spherical particles suspended in a Newtonian fluid, undergoing simple shear flow obtaining b = 6.5 in a good agreement with both the data of Pasquino et al. and the theoretical predictions obtained under the hypothesis of absence of closed orbits [Wilson and Davis J. Fluid. Mech.421, 339–367 (2000)]. It is also shown that the Cox–Merz rule is fulfilled by the suspensions that we have numerically studied, i.e., up to a volume fraction of about 0.17.
55(2011); http://dx.doi.org/10.1122/1.3635384View Description Hide Description
Two tube-based molecular models, the hierarchical 3.0 model and the branch-on-branch model were evaluated for their abilities to predict the behavior of a series of polydisperse, H-shaped, 1,4-polybutadienes. The samples had been synthesized using a novel technique designed to suppress the generation of high molar mass by-products. While size exclusion chromatography data indicated that the samples were monodisperse, low molar mass by-products were later revealed by temperature gradient interaction chromatography. Viscoelastic data were obtained at temperatures ranging from −75 °C to 25 °C, and the samples were found to be thermorheologically simple. Sensitivity and uncertainty analyses revealed that among the model parameters, the value of plateau modulus has the strongest effect on model predictions. As molecular models improve, it will become ever more essential to evaluate them using accurate data on materials whose microstructures have been reliably established. This is especially important for materials that are structurally polydisperse.
Shear-induced phase separation (SIPS) with shear banding in solutions of cationic surfactant and salt55(2011); http://dx.doi.org/10.1122/1.3641517View Description Hide Description
The rheological behavior and microstructure of branched, cationic wormlike micellar (WLM) solutions of 40 mM erucyl bis(hydroxyethyl)methylammonium chloride (EHAC) are studied as a function of added salt (sodium salicylate) concentration, temperature, and shear rate via Rheosmall-angle light scattering (Rheo-SALS). These WLM solutions exhibit shear-enhanced concentration fluctuations leading to shear-induced phase separation (SIPS), manifested as visual turbidity under shear and the appearance of a characteristic “butterfly” scattering pattern in Rheo-SALS experiments. Flow kinematics measurements in a Couette geometry are used to determine the relationship between SIPS and shear banding, i.e., the splitting of the flow into shear bands with different local shear rates.Modeling using the Giesekus constitutive equation aids in discrimination between banding and nonbanding solutions. The combination of Rheo-SALS, dynamic rheology, velocimetry, and constitutive equationmodeling allows detailed exploration of the relationship between SIPS, shear banding, fluid microstructure, and the equilibrium phase behavior.