Index of content:
Volume 57, Issue 3, May 2013

Edge fracture hampers the measurement of the two normal stress differences N1 and N2 in a conepartitioned plate rheometer with two partitions (CPP2). A third nonmeasuring partition has therefore been added, solely to shield off edge fracture (CPP3). The partial normal forces on the inner two partitions are much better balanced than on the CPP2. The new partitioned plate rheometer cell has been downsized to fit an MCR300. Potentially, N1 and N2 can now be obtained for all rheometric tests that can be performed with that rheometer. This publication reports on the technical features of the CPP3 cell. Step shearrate tests in the range 0.1 < Wi < 3 and a strain of γ = 40 have been performed with a poly(dimethyl siloxane) (PDMS) standard to proof the rheometric functionality. The characteristic relaxation time of the PDMS is comparable to the axial response time, in spite of a cone angle of 0.15 rad. This means that transient normal force data are affected by instrument compliance. Steady state N1 and N2 however are measured correctly. N1 compares with data from a CPP2 and the MCR300, but can be determined with much less polymer. The scattering of the steady state second normal stress difference N2 is substantially reduced compared to the CPP2. A critical evaluation of the pros and cons of the CPP3 is given, based on the results of this study.

Strong squeeze flows of yieldstress fluids: The effect of normal deviatoric stresses
View Description Hide DescriptionThis work aims to study squeeze flows when the lubrication approximation does not necessarily hold. Strong squeeze flows are defined as the cases in which a sample is compressed by a disk with the initial speed of 40 cm/s, whereas weak squeeze flows are realized when the disk is softly released manually to avoid any impact of the sample at the beginning of compression. Strong and weak squeeze flows of yieldstress materials are studied experimentally and theoretically. In the experiments, disklike constantvolume samples of Carbopol solutions and bentonite dispersions are compressed between two approaching disks being subjected to constant forces. In addition, experiments with shear flows in parallelplate and vane viscometers are conducted. Using visualization through the transparent wall of the squeezing apparatus, it is demonstrated that the noslip conditions hold. It is also demonstrated that during the fast stage of strong squeeze flows, the material response can be explained by deviatoric normal stresses, which elucidates the link of strong squeeze flows to elongational flows. The analysis of the data in the framework of the Newtonian and Herschel–Bulkley models shows that in the present case the nonlinearity of the rheological response at the fast stage of strong squeeze flows is not very significant, and a strainrateindependent viscosity can be used as a reasonable approximation. On the other hand, at the final stage of squeeze flows, when samples spread significantly under the action of a constant squeezing force, the compressive stresses become small enough, and the dominant role is played by the yield stress. No significant signs of thixotrophy were observed. It is shown that strong squeeze flow in the squeezing apparatus is a convenient tool useful for the measurement of viscosity and the yield stress of complex soft materials.

A discrete model for the apparent viscosity of polydisperse suspensions including maximum packing fraction
View Description Hide DescriptionBased on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, noncolloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process, appearing to be the first model consistently describing polydisperse volume fractions and maximum packing fraction within a single approach. In that context, the consistent inclusion of the maximum packing fraction into effective medium models is discussed. Furthermore, new generalized forms of the wellknown Quemada and Krieger–Dougherty equations allowing for the choice of a secondorder Taylor coefficient for the volume fraction ( coefficient), found by asymptotic matching, are proposed. The model for the maximum packing fraction as well as the complete viscosity model is compared to experimental data from the literature showing good agreement. As a result, the new model is shown to replace the empirical Sudduth model for large diameter ratios. The extension of the model to the case of small size ratios is left for future work.

Nonlinear viscoelasticity of polymer nanocomposites under large amplitude oscillatory shear flow
View Description Hide DescriptionIn this study, the nonlinear response of polymer nanocomposites under large amplitude oscillatory shear (LAOS) flow was investigated. We first investigated polycaprolactone (PCL)/multiwall nanotube (MWNT) composites under LAOS flow using different analyzing methods including Lissajous plot analysis, stress decomposition, and Fourier transform rheology (FTrheology). The nonlinear parameter Q was obtained from the FTrheology as a function of strain amplitude, and the zerostrain nonlinearity Q 0 ( ) was also calculated. We compared the linear and nonlinear viscoelastic properties as we increase MWNT concentration ( ). It was found that the zerostrain nonlinearity (Q 0) was more sensitive to detect the effect of MWNT concentration than the linear viscoelastic properties. We also investigated the effect of particle shape on nonlinear viscoelastic properties of the polymer composites containing particles of different shape, e.g., PCL/MWNT (onedimensional thread shape), PCL/organomodified montmorillonite (twodimensional plate shape), PCL/precipitated calcium carbonate (threedimensional cubic shape). Furthermore, we introduced a new parameter, nonlinear–linear viscoelastic ratio, to compare linear and nonlinear viscoelasticity.

Effects of moderate elasticity on the stability of co and counterrotating Taylor–Couette flows
View Description Hide DescriptionRecently, we explored the effects of weak fluid elasticity (El ≪ 1) on the stability of co and counterrotating Taylor–Couette (TC) flows [Dutcher and Muller, J. Rheol. 55(6), 1271–1295 (2011)], where accessible flow states were primarily governed by the dominant inertial forces, yet modified by the weaker elastic forces. Here, the study of the inertial–elastic TC problem is expanded to El near unity, illuminating the effects of increasing the elastic forces on the inertially driven instabilities. A polyethylene oxide solution was carefully chosen to have optimal rheological properties and exhibit limited shear and oxidative degradation. The sequence of transitions to turbulence found here is notably different from that observed previously for either Newtonian or lowelasticity fluids. As El approaches order 1, laminar and turbulent flows are separated by only two coherent flow states: Standing vortices and disordered rotating standing waves. In contrast to our experiments at lower El, we also observe flow state hysteresis. In addition, the final turbulent flow state was not turbulent Taylor vortices (TTV) as seen with Newtonian and weakly elastic fluids, but rather a state we refer to as elastically dominated turbulence, which occurs at a significantly lower Reynolds number than TTV. Stability mappings involving rotation of the outer cylinder show that the flow states and transitions depend on the amount of counter or corotation. As the degree of counter rotation increased, greater deviations from Newtonian and low El behavior were found, due to the presence of a nodal surface that changes the characteristic length scale of the flow.

Rheology of viscoelastic suspensions of spheres under small and large amplitude oscillatory shear by numerical simulations
View Description Hide DescriptionThe dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by threedimensional direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspension. A fictitious domain method is used to manage the particle motion. After the stress field is computed, the bulk properties are recovered by an averaging procedure. The numerical method is validated by comparing the computed linear viscoelastic response of Newtonian and nonNewtonian suspensions with previous theories and simulations. The numerical predictions are in very good quantitative agreement with experimental data for the Newtonian case, whereas deviations are found with respect to some sets of experiments for semidilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggregates in the bulk of the suspension is examined. The simulations show that the presence of structures significantly alters the loss modulus. Such an effect is more pronounced as the volume fraction increases. In this light, the above mentioned disagreement between simulations and data (and among experimental data themselves) can be rationalized, as its origin can be attributed to inhomogeneous particle configurations. For increasing strain amplitudes, both loss and storage moduli depart from the linear viscoelastic values. Although the deviations are qualitatively similar to the large amplitude response of the unfilled suspending matrix, our results for dilute and semidilute suspensions show that the decrease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, a higher concentration of solid particles reduces the value of strain amplitude such that the nonlinear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Finally, the effect of fluid elasticity on the particle motion is analyzed. The particles are found to move away from their starting positions and the average distance, computed at the beginning of each cycle with respect to the initial configuration, linearly increases with the number of cycles. The change in the microstructure is attributed to the longrange hydrodynamic interactions mediated by fluid viscoelasticity.

A conepartitioned plate rheometer cell with three partitions (CPP3) to determine shear stress and both normal stress differences for small quantities of polymeric fluids
View Description Hide DescriptionEdge fracture hampers the measurement of the two normal stress differences N1 and N2 in a conepartitioned plate rheometer with two partitions (CPP2). A third nonmeasuring partition has therefore been added, solely to shield off edge fracture (CPP3). The partial normal forces on the inner two partitions are much better balanced than on the CPP2. The new partitioned plate rheometer cell has been downsized to fit an MCR300. Potentially, N1 and N2 can now be obtained for all rheometric tests that can be performed with that rheometer. This publication reports on the technical features of the CPP3 cell. Step shearrate tests in the range 0.1 < Wi < 3 and a strain of γ = 40 have been performed with a poly(dimethyl siloxane) (PDMS) standard to proof the rheometric functionality. The characteristic relaxation time of the PDMS is comparable to the axial response time, in spite of a cone angle of 0.15 rad. This means that transient normal force data are affected by instrument compliance. Steady state N1 and N2 however are measured correctly. N1 compares with data from a CPP2 and the MCR300, but can be determined with much less polymer. The scattering of the steady state second normal stress difference N2 is substantially reduced compared to the CPP2. A critical evaluation of the pros and cons of the CPP3 is given, based on the results of this study.

Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere–wall and sphere–sphere interactions
View Description Hide DescriptionAxisymmetric sphere–wall and twosphere interactions were examined in a viscoelastic solution composed of polyisobutylene polymer in tetradecane. The Reynolds and Stokes numbers were small, so that inertia played at most a minor role, while the Deborah numbers De were in the range 0.4 < De < 3.5. When single spheres fell away from the solid top of the containing vessel, or toward the bottom, the range of the sphere–wall interaction was reduced in the viscoelastic fluid relative to a Newtonian fluid. The reduced range was more pronounced at higher settling speeds. In addition, the interaction in the viscoelastic fluid was reversible, in that the effect of the wall on a sphere moving away from it was the same as that on a sphere moving toward it. In the experiments with two equal spheres sedimenting along their lineofcenters, the spheres moved together until they touched. The rate at which they moved together was measured for sphere–sphere separations ranging from contact to many diameters, and for separations greater than 2 diameters was in fair agreement with analytic predictions. The average sedimentation rate of the two spheres increased as they moved together, by an amount that was in good agreement with the Newtonian solution at low Reynolds number.

Validity of the modified molecular stress function theory to predict the rheological properties of polymer nanocomposites
View Description Hide DescriptionThe transient shear and extensional properties of ethylene vinyl acetate nanocomposites containing two geometrically different nanoparticles (spheres of CaCO3 and platelet of clay) were investigated experimentally and the data were compared to the rheological predictions of the modified molecular stress function (MSF) theory as recently proposed by Abbasi et al. [Rheol. Acta 51, 163–177 (2012)]. While good agreement was obtained for spherical particles, deviations were observed for platelet particles at concentrations higher than 2.5 wt. %. The limitation of MSF theory for such compositions was related to the domination of the linear rheological response by the presence of particle nanonetworks over polymeric chains' contribution. This particle network contribution was also found to increase nonlinearity under large deformation, a phenomenon which was quantified via Fourier transformed rheology on data obtained under large amplitude oscillatory shear.

Rheology and morphology of model immiscible polymer blends with monodisperse spherical particles at the interface
View Description Hide DescriptionWe show that the addition of solid particles to droplet–matrix blends of immiscible polymers induces massive changes in the rheology and the flowinduced structure even at loadings as low as 0.1 vol. %. Experiments were conducted using blends of polyethylene oxide (PEO, dispersed phase), polyisobutylene (PIB, continuous phase), and 470 nm monodisperse silica particles with two different surface wettabilities. Rheological experiments were conducted under molten conditions, while the morphology was characterized at room temperature using scanning electron microscopy. We are able to image the morphology at both lengthscales: The >20 μm lengthscale of the dispersed phase, as well as the submicron lengthscale of the particles. Rheological experiments along different trajectories in the ternary particle/PEO/PIB composition diagram reveal that addition of ∼1 vol. % particles that are preferentially wetted by the PIB induces a large increase in steady shear viscosity, severe shearthinning, and yieldlike behavior. However if the particles are equally wetted by PEO and PIB, these effects are greatly diminished. Remarkably, addition of very low loadings (∼0.1 vol. %) of particles reduces the viscosity under some conditions regardless of wettability. These rheological changes are interpreted in terms of three observations from morphological studies: That particles greatly enhance coalescence at low volume loadings, that particles jam the interface at higher loadings, and that particles bridge across drops and glue them together into large clusters. The first two of these effects occur regardless of particle wettability, whereas the last occurs only with particles that are preferentially wetted by the continuous phase.

Wall slip of HDPEs: Molecular weight and molecular weight distribution effects
View Description Hide DescriptionThe slip behavior of several highdensity polyethylenes (HDPEs) is studied as a function of molecular weight (M w) and its distribution for broad molecular weight distribution metallocene and Ziegler–Natta catalyst resins. It is found that slip depends strongly on M w and its distribution. First, the slip velocity increases with decrease of molecular weight, which is expected to decay to zero as the M w approaches a value with characteristic molecular dimension similar to surface asperities. For HDPEs that exhibit stick–slip transition, the slip velocity has been found to increase with increase of polydispersity. The opposite dependence is shown for HDPEs of wider molecular weight distribution that do not exhibit stick–slip transition. A criterion is also discussed as to the occurrence or not of the stick–slip transition which is found to depend strongly on M w and its distribution.

Development of a stochastic constitutive model for prediction of postyield softening in glassy polymers
View Description Hide DescriptionA stochastic constitutive model has been developed that explicitly acknowledges the nanometer size dynamic heterogeneity of glassy materials, where the distribution of the viscoelastic relaxation times emerges naturally as a result of the dynamic heterogeneity. A set of stochastic differential equations for local stresses and entropy describing behavior of a mesoscopic domain are developed, and the observed macroscopic response of the material is obtained as an average of an ensemble of domains. The stochastic constitutive model naturally predicts and provides a mechanism for the postyield stress softening and its dependence on physical aging that is observed during constant strain rate uniaxial deformations.

Shear and dilatational linear and nonlinear subphase controlled interfacial rheology of βlactoglobulin fibrils and their derivatives
View Description Hide DescriptionThis work presents a linear and nonlinear interfacial rheological characterization of viscoelastic protein adsorption layers formed by βlactoglobulin fibrils, βlactoglobulin peptides, and native βlactoglobulin (called monomers) at the water–oil interface at pH 2. The fibril and peptide solution presented a similar surface density, whereas βlactoglobulin monomers lower the interfacial tension more efficiently. The interfacial tension/dilatational rheology response to drop area amplitude sweeps showed pronounced differences, as the βlactoglobulin fibrils and monomer react nonlinear at high frequencies and area strains, an effect not observed for βlactoglobulin peptides. Step strain experiments in combination with frequency sweeps present the material response: In the low frequency regime, βlactoglobulin peptides and βlactoglobulin monomers can be characterized by the behavior of irreversibly adsorbed molecules. At high frequencies, both peptides and monomers behaved like reversibly adsorbed molecules, while βlactoglobulin fibrils showed a mixed behavior at all frequencies. The observed dilatational rheological responses can be described using two different adsorption models, the Maxwell model and a modified Lucassen and van den Temple model. In interfacial shear rheology, the pH increase led to highly nonlinear behavior. A large amplitude oscillatory shear analysis in combination with subphase pH changes showed strain stiffening occurring at the isoelectric point, which was quantified by the strainstiffening index S.

Local mobility and microstructure in periodically sheared soft particle glasses and their connection to macroscopic rheology
View Description Hide DescriptionOscillatory shear is a widely used characterization technique for complex fluids but the microstructural changes that produce the material response are not well understood. We apply a recent micromechanical model to soft particle glasses subjected to oscillatory flow. We use particle scale simulations at small, intermediate and large strain amplitudes to determine their microstructure, particle scale mobility, and macroscopic rheology. The macroscopic properties computed from simulations quantitatively agree with experimental measurements on wellcharacterized microgel suspensions, which validate the model. At the mesoscopic scale, the evolution of the particle pair distribution during a cycle reveals the physical mechanisms responsible for yielding and flow and also leads to quantitative prediction of shear stress. At the local scale, the particles remain trapped inside their surrounding cage below the yield strain and yielding is associated with the onset of large scale rearrangements and shearinduced diffusion. This multiscale analysis thus highlights the distinct microscopic events that make these glasses exhibit a combination of solidlike and liquidlike behavior.