Volume 58, Issue 4, July 2014

The interfacial stress rheometer (ISR), uses the oscillations of a magnetic needle suspended on an interface to characterize the dynamic moduli of thin films. Mathematical theories to interpret the device have developed slowly because of the strong coupling between the stresses in the surface and the bulk subphase. In this work, we simplify the equations of motion by introducing new length scales and reinterpreting the dimensionless numbers. Several Green's functions are developed for typical ISR geometries, leading to a set of boundary element methods for the full numerical solution of the equations of motion. Using Taylor series, a multipole expansion is extracted from the boundary integral equations, and we show that both numerical methods converge in under five elements. Analytical theories are developed for the cases of small and large interfacial stress, proving that the finite size of the needle has an O(1) effect and reinforcing the physics behind the length scales and dimensionless groupings. We directly compare our numerical and analytical solutions to published interfacial velocity data, showing good agreement, and discuss the implications of our results.

A critical gel fluid with high extensibility: The rheology of chewing gum
View Description Hide DescriptionChewing gum provides an excellent everyday example of viscoelastic behavior, and understanding its rheological properties is important for application purposes. Here, we compare the rheological behavior of selected commercial chewing gums and bubble gums. Small amplitude oscillatory shear, shear creep, and steady shear demonstrated that both chewing and bubble gums behave like powerlaw critical gels in the linear regime. Nonlinear viscoelastic behavior was investigated using large amplitude oscillatory shear, shear creep, and startup flows (in shear and uniaxial extension). Bubble gums showed more pronounced strain hardening and greater stresses to break in startup of steady uniaxial extension than chewing gums. We argue that this combination of rheological signatures is sufficient to provide a new robust definition of chewing gum that is independent of specific molecular composition. There are potentially many different formulations and design routes that can achieve this distinctive rheological fingerprint.

A spring model for suspended particles in dissipative particle dynamics
View Description Hide DescriptionThis paper is concerned with the use of oscillating particles instead of the usual frozen particles to model a suspended particle in the dissipative particle dynamics (DPD) method. A suspended particle is represented by a set of basic DPD particles connected to reference sites by linear springs of very large stiffness. The reference sites, collectively modeling a rigid body, move as a rigid body motion calculated through their NewtonEuler equations, using data from the previous time step, while the velocities of their associated DPD particles are found by solving the DPD equations at the current time step. In this way, a specified Boltzmann temperature (specific kinetic energy of the particles) can be maintained throughout the computational domain, including the region occupied by the suspended particles. This parameter can also be used to adjust the size of the suspended and solvent particles, which in turn affect the strength of the shearthinning behavior and the effective maximal packing fraction. Furthermore, the suspension, comprised of suspended particles in a set of solvent particles all interacting under a quadratic soft repulsive potential, can be simulated using a relatively large time step. Several numerical examples are presented to demonstrate attractiveness of the proposed model.

High strain extensional rheometry of polymer melts: Revisiting and improving the Meissner design
View Description Hide DescriptionA new extensional rheometer limited in achievable strain only by sample rupture is presented. The rheometer is based on the Meissner design of two pairs of counterrotating rollers pulling a sample of fixed length but is small enough to fit inside the oven of a standard rotational rheometer and thus is dubbed the Meissner Extensional Rheometry Accessory (MERA). The true strain rate is calculated by visually accessing the sample during deformation using a highspeed digital camera. Extensional experiments were performed on three materials representing a wide range expected rheological behavior, a styrenebutadiene rubber blend, a linear polystyrene, and a branched lowdensity polyethylene. The MERA was able to accurately replicate the results of the wellknown Sentmanat extensional rheometer (SER) design in terms of onset of strainhardening and absolute transient extensional viscosity values. However, due to its design, it was possible to achieve homogeneous extensional flow up to real Hencky strains in excess of 8, which corresponds to a linear stretch in excess of 3000. By comparison, the SER is limited to one drum revolution, which corresponds to a Hencky strain of 3.5–4.0 or a maximum linear stretch of approximately 50. Previously the highest Hencky deformations reported in the literature are for the filament stretching extensional rheometer and Rheometric Scientific RME apparatus and in both cases approach 7, which corresponds to a linear stretch of approximately 1000.

The general lowfrequency prediction for asymptotically nonlinear material functions in oscillatory shear
View Description Hide DescriptionWe use a fourthorder fluid expansion to make general predictions for asymptotically nonlinear material functions in oscillatory shear, a characterization protocol sometimes known as mediumamplitude oscillatory shear. The calculation applies to any viscoelastic fluid in the terminal regime defined by the limit of Deborah number much less than one. Two viscous nonlinearities appear at third order, with shear stress scaling as ω ^{3}, and are interrelated by a constant multiplicative factor. Two elastic nonlinearities appear at fourth order, with shear stress scaling as ω ^{4}, and are also interrelated by a constant multiplicative factor. These nonlinear measures are decoupled from the linear material functions G′ and G″ because they depend on different expansion coefficients. Experimental measurements are presented for all four asymptotic shear material functions using a linear and wellentangled homopolymer of polyisoprene. The experimental observations are consistent with both the predicted frequency scaling and the predicted interrelations in the terminal regime. Signs and magnitudes cannot be universally predicted, leaving these as free parameters that depend on the specifics of the material microstructure or constitutive model. These general results explain previous observations involving different materials and constitutive models, and provide an important reference for future experiments, analytical results, and numerical computations of these rheological fingerprints.

Stressgradient induced migration of polymers in corrugated channels
View Description Hide DescriptionWe study the flow of a dilute polymer solution in a wavy channel under steadystate flow conditions by employing the nonequilibrium thermodynamics twofluid model [Mavrantzas and Beris, Phys. Rev. Lett. 69, 273–276 (1992)], allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finiteelement method. We present numerical results for polymer concentration, stress, velocity, and fluxes of polymer as a function of the nondimensional parameters of the problem (the Deborah number , the Peclet number , the Reynolds number , the ratio of the solvent viscosity to the total fluid viscosity , and the constriction ratio of the channel width ). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length scale, expressed by the ratio of / , increases. The migration is more pronounced for macromolecules characterized by longer relaxation times and takes place toward the expanding part of the channel or toward the centerplane. Migration is also enhanced by the width variability of the channel: The more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymerdepleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as for the concentration.

Material properties of the shearthickened state in concentrated near hardsphere colloidal dispersions
View Description Hide DescriptionReversible shear thickening is common in concentrated dispersions of Brownian hardspheres at highshear rates. We confirm the existence of a welldefined colloidal shearthickened state through experimental measurements of the shear stress and the first and second normal stress differences in the shearthickened state as a function of the particle volume fraction for a model dispersion of near hardspheres. The shear stress and normal stress differences are observed to grow linearly with the shear rate in the shearthickened state and both normal stress differences are observed to be negative. Our experimental results show the shearthickened state of colloidal dispersions can be described by three material properties—the shear viscosity and first and second normal stress difference coefficients—that are a function of the volume fraction. All three material properties are found to diverge with a power law scaling as close to maximum packing, , which is found to be 0.54 ± 0.01. We find r,sts > 2,sts > 1,sts. These results are consistent with theoretical predictions for shear thickening by hydrocluster formation and quantitatively comparable to Stokesian Dynamics simulations. We further postulate and show that these material properties are consistent with those measured for nonBrownian suspensions.

Large amplitude oscillatory shear and Fourier transform rheology analysis of branched polymer melts
View Description Hide DescriptionIn this paper, the predictions of the Pompom constitutive model in medium and large amplitude oscillatory shear (LAOS) are examined using Fourier transform rheology (FTR). FTR is commonly used in combination with small amplitude oscillatory shear to fit linear Maxwell parameters to dynamic moduli, and in this paper, this process is expanded to larger strain amplitudes and to further terms in the Fourier series. For both small and large amplitudes, these higher harmonics are dependent on the nonlinear Pompom parameters and the Pompom parameter space is explored to see how experimental oscillatory shear data can infer molecular detail. In the regime of small and medium strain amplitude, there exists an asymptotic solution to the Pompom equations which depends only on the ratio of the orientation and stretch relaxation times, and . This asymptotic solution is found to be accurate up to strains of order unity and the branching priority, q, only affects the stress response at larger strains. The Pompom parameters fitted to extensional data are compared to LAOS data for three materials; two lightly branched metallocene catalyzed high density polyethylenes and a densely branched low density polyethylenes. In general, the Pompom model performs well in LAOS but tends to over predict experimental results at high strain amplitudes.

Scaling analysis and mathematical theory of the interfacial stress rheometer
View Description Hide DescriptionThe interfacial stress rheometer (ISR), uses the oscillations of a magnetic needle suspended on an interface to characterize the dynamic moduli of thin films. Mathematical theories to interpret the device have developed slowly because of the strong coupling between the stresses in the surface and the bulk subphase. In this work, we simplify the equations of motion by introducing new length scales and reinterpreting the dimensionless numbers. Several Green's functions are developed for typical ISR geometries, leading to a set of boundary element methods for the full numerical solution of the equations of motion. Using Taylor series, a multipole expansion is extracted from the boundary integral equations, and we show that both numerical methods converge in under five elements. Analytical theories are developed for the cases of small and large interfacial stress, proving that the finite size of the needle has an O(1) effect and reinforcing the physics behind the length scales and dimensionless groupings. We directly compare our numerical and analytical solutions to published interfacial velocity data, showing good agreement, and discuss the implications of our results.

Dissipative particle dynamics simulation of dilute polymer solutions—Inertial effects and hydrodynamic interactions
View Description Hide DescriptionWe examine the accuracy of dissipative particle dynamics (DPD) simulations of polymers in dilute solutions with hydrodynamic interaction (HI), at the theta point, modeled by setting the DPD conservative interaction between beads to zero. We compare the first normalmode relaxation time extracted from the DPD simulations with theoretical predictions from a normalmode analysis for theta chains. We characterize the influence of bead inertia within the coil by a ratio L m/R g, where L m is the ballistic distance over which bead inertia is lost, and R g is the radius of gyration of the polymer coil, while the HI strength per bead h* is determined by the ratio of bead hydrodynamic radius (r H) to the equilibrium spring length. We show how to adjust h* through the spring length and monomer mass, and how to optimize the accuracy of DPD for fixed h* by increasing the friction coefficient (γ ≥ 9) and by incorporating a nonlinear distance dependence into the frictional interaction. Even with this optimization, DPD simulations exhibit deviations of over 20% from the theoretical normalmode predictions for high HI strength with h* ≥ 0.20, for chains with as many as 100 beads, which is a larger deviation than is found for Stochastic rotation dynamics simulations for similar chains lengths and values of h*.

Letter to the Editor: Sufficiently entangled polymers do show shear strain localization at high enough Weissenberg numbers
View Description Hide DescriptionThis Letter concludes that the recent data of Li et al. [J. Rheol. 57, 1411–1428 (2013)] are entirely consistent with the previous observations of the occurrence and absence of shear banding during startup shear and nonquiescent relaxation after large stepwise shear. In other words, based on the linear viscoelastic characteristics of these solutions depicted in Fig. 5(a) of Li et al., we find their results to follow from the previous analysis: One insufficiently entangled solution naturally exhibited homogeneous shear under the explored conditions. The two more entangled solutions did not exhibit shear banding and nonquiescent relaxation, because the samples appear to have significant polydispersity in the molecular weight distribution and because the applied shear rates were much lower than those needed to produce shear banding. Thus, the observations of Li et al. support rather than refute the existing knowledge concerning nonlinear rheological responses of entangled polymer solutions to startup and stepwise shear.

Response to: Sufficiently entangled polymers do show shear strain localization at high enough Weissenberg numbers”
View Description Hide DescriptionIn response to the Letter Wang et al. (2014) challenging the results of Li et al. (2013), the present letter addresses the specific concerns in the order that they are raised. (1) Whether the material properties (molecular weight, concentration, and polydispersity index) of the samples used in [Li et al. (2013)] agree with Table I in the same paper? (2) What is the true shear banding phase diagram, if any? (3) Are the shear cessation tests carried out by Li et al. (2013) in the regime where nonquiescent relaxation is expected? (4) How to minimize edge effects? (5) How would other factors, such as location of particle tracking velocimetry observation, plastic film on meniscus, misalignment, and surface treatment, affect the velocity profiles?

Erratum: “Convective constraint release (CCR) revisited” [J. Rheol. 58, 89–102 (2014)]
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