Volume 54, Issue 3, May 2010
Index of content:
Non-linear viscoelastic models for semi-flexible polysaccharide solution rheology over a broad range of concentrations54(2010); http://dx.doi.org/10.1122/1.3329746View Description Hide Description
The experimental linear viscoelastic and steady-state shear data over a broad concentration range of several aqueous semi-flexible polysaccharide solutions can be quantitatively predicted by the multimode Phan-Thien Tanner, Giesekus, and extended Pom-Pom non-linear viscoelastic models using a single set of parameters. Experimental data from an aqueous solution of the polysaccharide guar galactomannan , aqueous phosphopolysaccharide “viilian” solution excreted by Lactococcus lactis subspecies cremoris SBT 0495 , and aqueous Propionibacterium acidi-propionici polysaccharide solution are taken from literature. A master curve can be constructed by shifting data from different concentrations over the horizontal and vertical axes. A simple model to describe the concentration dependence of the relaxation time and plateau modulus over the entire concentration range is presented. Transient shear viscosity data are quantitatively and first normal stress coefficient are qualitatively predicted for the guar galactomannan solution. Due to their proven performance in finite element simulations, these non-linear viscoelastic constitutive equations could help us to improve predictive modeling of time-dependent complex flow problems for polysaccharide solutions with variations in concentration and temperature in the spatial domain using only a single set of parameters. However, as a previous step, the performance of additional rheological experiments in simple flows, i.e., transient and steady-state extensional measurements, is recommended.
54(2010); http://dx.doi.org/10.1122/1.3366603View Description Hide Description
A two-phase microstructural constitutive relation is combined with the thin-shell model for the simulation of blown film extrusion. This combination includes equations for momentum conservation, flow-enhanced crystallization, viscoelasticity, and bubble-tube cooling. Consistent with typical blown film operation, the simulations set the bubble air mass and take-up ratio as constants, while treating the machine tension and inflation pressure as dependent variables. In all the simulations performed, the high degree of crystallization, and subsequent system stiffening, located the freeze-line naturally. Bubble geometry, temperature, and crystallinity were fitted to experimental data using material and kinetic parameters mostly obtained by a simpler quasi-cylindrical model. The thin-shell microstructural model was compared to a modified quasi-cylindrical model. The models predict similar responses to operational changes, including axial locked-in stresses at the freeze-line, but have significant differences in the locked-in stresses in the transverse direction, which were attributable to the use of different momentum equations. Either model can be used for data fitting, parameter estimation, and prediction of most process responses to upsets.
54(2010); http://dx.doi.org/10.1122/1.3368729View Description Hide Description
We probed the viscoelastic behavior of polydisperse star/linear polymer blends with varying composition and average arm length. The linear viscoelastic behavior has been investigated over a wide range of frequencies using both oscillatory and long creep/recovery experiments. A method was developed for splitting the molar mass distributions of the blends into the contributions of different architectures. These results were used to implement a time-marching algorithm based on a parameter-free tube model for predicting the linear viscoelastic behavior. The model predictions were successfully validated with the experimental data, opening the route for designing blends with desired rheological properties.
54(2010); http://dx.doi.org/10.1122/1.3372720View Description Hide Description
Linear and nonlinear (in both steady and transient shear flows) rheological properties of polymer/layered silicate nanocomposites prepared by melt mixing of poly(butylene succinate-co-adipate) and organically modified montmorillonite are investigated. Morphology of the nanocomposites is observed by x-ray diffraction and by transmission electron microscopy. Linear viscoelastic measurements in oscillatory shear with small strain amplitude show a low frequency plateau for storage modulus (an indication of a pseudo-solid like structure). A strong shear-thinning behavior for all ranges of shear rates is observed for high clay loading. An unusual behavior is observed for steady state normal stress differences. At low shear rates their values are larger than those observed for pure polymer. An inverse relation is observed at relatively high shear rates. The two models [Eslami, H., M. Grmela, and M. Bousmina, “A mesoscopic rheological model of polymer/layered silicate nanocomposites,” J. Rheol.51, 1189–1222 (2007); Eslami, H., M. Grmela, and M. Bousmina, “A mesoscopic tube model of polymer/layered silicate nanocomposites,” Rheol. Acta48, 317–331 (2009)] that we have developed previously allow us to relate the observed rheological behavior to the physics taking place in the nanocomposites on a mesoscopic level. The models take into account the chain-chain, chain-lamella, and lamella-lamella interactions. With their help, we are also able to separate contributions from the polymer and the nano charge.
54(2010); http://dx.doi.org/10.1122/1.3372837View Description Hide Description
When a fixed volume of a pure viscous fluid is squeezed between two parallel circular plates under a constant force, in the absence of surface tension, the radius of the propagating fluid front increases such that is linear in time in the lubrication limit [Engmann, J., C. Servais, and A. S. Burbridge, “Squeeze flow theory and applications to rheometry: A review,” J. Non-Newtonian Fluid Mech.132, 1–27 (2005)]. However, when the experiment is repeated with a suspension of rigid spheres instead of the pure viscous fluid, the behavior deviates from this vs relationship at a radius . This deviation is followed by the appearance of an instability in the azimuthal direction at the propagating suspension interface at a radius . The instability arises due to the establishment of radial concentration and therefore viscosity gradients during the squeeze flow, which are susceptible to miscibleviscous fingering [Tang, H., W. Grivas, D. Hometocovschi, J. Geer, and T. Singler, “Stability considerations associated with the meniscoid particle band at advancing interfaces in Hele-Shaw suspension flows,” Phys. Rev. Lett.85, 2112–2115 (2000)]. We experimentally determine the characteristic radii and for the converging parallel plate geometry and show that both radii scale as , where is the volume of the suspension loaded into the geometry before the experiment and is the particle radius. This squeeze flow is identical to that produced in loading suspensions into the parallel plate viscometer and thus the concentration inhomogeneities identified here may play a role in the well known scatter of rheological measurements in this system. We also establish a critical parameter , the ratio of to the plate radius , which can be used to predict the degree of homogeneity of the suspension upon loading.
54(2010); http://dx.doi.org/10.1122/1.3378762View Description Hide Description
It has been shown in electrorheology that filtration occurs and that it impacts the structuring and rheology of electrorheological fluids under an electric field. This paper demonstrates the impact of filtration on the mechanical properties of these systems in compression. By varying the Pe number, it was shown that the Pe number was an effective indicator for electrorheological fluids in squeeze flow under an electric field. Finally, the study demonstrated the gradual transition from a close packed limit in compression, where filtration was significant, to a homogenous limit where filtration effects were low. This paper then proposes a comprehensive qualitative description of electrorheological squeeze flow discussing the impact filtration has on electrorheology.
An experimental study on the criteria for failure of polymer melts in uniaxial extension: The test case of a polyisobutylene melt in different deformation regimes54(2010); http://dx.doi.org/10.1122/1.3378791View Description Hide Description
Failure of polymer liquids under flow has been the subject of a relatively strong computational, theoretical, and experimental effort over the years, despite which a clear picture of the phenomenon is still nonexistent. For example, there are still arguments in the literature whether the maximum in engineering stress, also known as the Considère limit for failure, is a point of true yielding of the polymer network or simply a purely elastic mechanical instability and if this onset of yielding also corresponds to the true onset of non-homogeneous deformation, as expressed for example by necking. The main objective of the present work is to contribute to the ongoing discussion on this matter by studying a linear polyisobutylene melt in terms of its failure and rupture behavior in both the viscoelastic and purely elastic deformation regimes of deformation showing that homogeneous flow still occurs after the maximum in engineering stress and quantifying this deviation. This is ultimately connected with the observation of a limiting stress at rupture in the rubbery (elastic) regime. From the results, it is apparent that, for this particular polydisperse melt and in the viscoelastic regime, the Considère criterion underestimates by approximately 60% the point of onset of non-homogeneous deformation, i.e., necking. The calculated true onset of failure, on the other hand, agrees almost exactly with the visually determined onset. However, it is clear that a general working criterion for failure of entangled polymer melts, especially in the all-important viscoelasticdeformation regime, is still lacking.
54(2010); http://dx.doi.org/10.1122/1.3378879View Description Hide Description
Visco-elasticmodels are commonly used in modeling time dependent behavior of asphalts, polymers, and biomaterials (e.g., soft tissues). In order to ensure that these models are thermomechanically consistent, their stress-strain behavior has to be derived using a strain energy function. For a non-linear viscoelastic behavior, this appears to be a rather subtle problem: some quasi-linear viscoelasticenergy formulations presented in the literature do not use the true energy functions for the stress-strain response attributed to these models, making their mechanical interpretation and validation of thermomechanical consistency difficult. This paper represents an attempt to propose an alternative framework, which would retain simplicity and convenience in numerical applications of the quasi-linear viscoelasticity, but would have a straightforward mechanical interpretation and guarantee the thermomechanical consistency. This is achieved by using a thermomechanical approach with internal kinematic variables, where both the energy and dissipation potentials have the same kind of non-linearity, leading to a general family of non-linear visco-elasticmodels. Within this context, a simple thermomechanically consistent non-linear hyperviscoelastic model with pressure dependent bulk stiffness is proposed, with an example modeling experimental data from laboratory tests on asphalts.
54(2010); http://dx.doi.org/10.1122/1.3368724View Description Hide Description
We investigated the rheology of a series of anionically synthesized, model symmetric Cayley tree poly(methylmethacrylates) having from 1 to 4 generations of identical molar mass. The hierarchical relaxation of the different generations was assessed from the linear data by accounting for both the plateau modulus and the characteristic relaxation times. Using a tube-model time-marching analysis based on the concept of hierarchy of motion, we described quantitatively the frequency spectra without adjustable parameters. We also performed uniaxial extensional measurements using the Sentmanat extensional rheometer fixture. The samples tested exhibited significant strain hardening compared to their linear analogs at lower and intermediate Hencky strain rates. This hardening was more pronounced with increasing number of generations, hence branch points. The extracted effective steady extensional viscosity was found to scale with the extensional rate with a power exponent of about −0.5, in agreement with earlier findings with linear polystyrenes. We also extended the time-marching-algorithm to predict the extensional behavior of these polymers using the conceptual framework developed recently for pom-pom and Cayley-tree polymers. Comparison between theoretical and experimental results was satisfactory when the maximum stretch which can be supported by the molecule was estimated by accounting for the recently proposed inter-chain pressure effects.
54(2010); http://dx.doi.org/10.1122/1.3361668View Description Hide Description
This study presents an experimental investigation into particle migration behavior of concentrated suspensions of noncolloidal spheres in oscillatory torsional flows between parallel plates. Video imaging of the radial drift velocity of dyed tracer particles in a monodisperse, 0.4 bulk particle volume fraction suspension was performed during flow evolution. In conjunction with simultaneous rheological measurements, particle tracking provided insight into migration phenomena. For all of the cases studied, the average displacement of the tracer particles per cycle was directed radially outward and was approximately a linear function of the oscillatory strain amplitude while also varying with the frequency of oscillation in a nearly inverse square relationship. The measured radial migration velocity exceeded that estimated from the suspension balance continuum model for a corresponding steady flow, likely due to the increased microstructural mobility developed during oscillatory flow. Generally, the oscillatory torque increased as the flow evolved, while local minima in the torque ratio and radial drift velocity were detected at intermediate strain values, in agreement with recent studies of oscillatory flow. The results suggest the competition between radial shear-induced particle migration driven by the overall particle stress balance and rearrangement of particles into an ordered microstructure driven by local interactions.
Droplet deformation under extensional flow in immiscible and partially miscible polymer blends based on poly(styrene-co-acrylonitrile)54(2010); http://dx.doi.org/10.1122/1.3380856View Description Hide Description
In this paper, investigations on the morphology development under uniaxial extensional flow are reported for an immiscible [poly(styrene-co-acrylonitrile)/polypropylene] and a partially miscible [poly(styrene-co-acrylonitrile)/polycarbonate] blend. Creep experiments were performed on samples with various initial droplet sizes under different constant stresses using an oilbath rheometer. At the end of each experiment, the samples were quickly removed from the rheometer and quenched in liquid nitrogen to freeze in the morphology. By means of scanning electron microscopy, their morphologies were visualized and the accordance with the critical capillary number was analyzed. A satisfactory agreement was found for the immiscible blend. In contrast, the partially miscible blends exhibited much smaller dropletdeformation than expected and no fibril formation was found for any set of the parameters applied.