Index of content:
Volume 58, Issue 3, May 2014
58(2014); http://dx.doi.org/10.1122/1.4866049View Description Hide Description
Rheology has achieved a strong position for the characterization of polymeric materials during the last 40 years. Dynamic-mechanical measurements are widely used for this purpose. On several examples, this paper demonstrates the potential of creep-recovery whose application has still been rather limited. In many cases, dynamic-mechanical experiments suffer from the fact that for several reasons, the angular frequencies applied are not chosen low enough to reach the terminal regime for which relationships between rheological quantities and molecular parameters have been established. In creep and a subsequent recovery, the time scales can be extended into the stationary regime in the linear range of deformation, and therefore, creep recovery is an efficient method to directly determine the zero-shear viscosity η 0 and the linear steady-state recoverable compliance . For a polymer melt with long relaxation times, it is shown how time-dependent creep data converted into dynamic-mechanical quantities can be used to extend the frequency scale to the terminal regime. The power of and its temperature dependence is demonstrated for the analysis of the branching structure of a polymer. Furthermore, from such kind of measurements, interesting insights into the interactions between particles and matrix molecules in filled polymeric materials were obtained. As shown in elongational experiments, the steady state of deformation at a constant stress is reached at shorter times than at the corresponding constant strain rate. The experimental consequences are discussed. Another interesting aspect of creep is that a constant stress implies a constant capillary number. The advantage of this experimental condition for investigations of the droplet deformation in polymer blends is demonstrated.
Strain hardening of molten thermoplastic polymers reinforced with poly(tetrafluoroethylene) nanofibers58(2014); http://dx.doi.org/10.1122/1.4867389View Description Hide Description
The influence of poly(tetrafluoroethylene) (PTFE) nanofibers on the extensional viscosity of various molten thermoplastic polymers, including isotactic polypropylene (iPP), high density polyethylene (HDPE), low density polyethylene (LDPE), and atactic polystyrene (PS), has been investigated. It has been shown that PTFE nanofibers, generated in situ by shearing of crystalline PTFE inclusions during compounding with another molten polymer, formed an entangled network, which in turn drastically changed the rheological behavior of polymers studied. The entangled network of PTFE nanofibers induced the strain hardening effect in the nanocomposites based on iPPs, HDPE, and PS, which do not show the strain hardening themselves. Moreover, the strain hardening in the nanocomposite with LDPE was enhanced in comparison to neat LDPE. The higher the content of PTFE nanofibers and the larger the strain rates applied, the more pronounced the strain hardening occurred. Additionally, the presence of PTFE nanofibers significantly improved the melt strength of studied thermoplastic polymers.
58(2014); http://dx.doi.org/10.1122/1.4866296View Description Hide Description
We undertake here a systematic study of the rheology of blood in steady-state shear flows. As blood is a complex fluid, the first question that we try to answer is whether, even in steady-state shear flows, we can model it as a rheologically simple fluid, i.e., we can describe its behavior through a constitutive model that involves only local kinematic quantities. Having answered that question positively, we then probe as to which non-Newtonian model best fits available shear stress vs shear-rate literature data. We show that under physiological conditions blood is typically viscoplastic, i.e., it exhibits a yield stress that acts as a minimum threshold for flow. We further show that the Casson model emerges naturally as the best approximation, at least for low and moderate shear-rates. We then develop systematically a parametric dependence of the rheological parameters entering the Casson model on key physiological quantities, such as the red blood cell volume fraction (hematocrit). For the yield stress, we base our description on its critical, percolation-originated nature. Thus, we first determine onset conditions, i.e., the critical threshold value that the hematocrit has to have in order for yield stress to appear. It is shown that this is a function of the concentration of a key red blood cell binding protein, fibrinogen. Then, we establish a parametric dependence as a function of the fibrinogen and the square of the difference of the hematocrit from its critical onset value. Similarly, we provide an expression for the Casson viscosity, in terms of the hematocrit and the temperature. A successful validation of the proposed formula is performed against additional experimental literature data. The proposed expression is anticipated to be useful not only for steady-state blood flow modeling but also as providing the starting point for transient shear, or more general flow modeling.
Large amplitude oscillatory shear and uniaxial extensional rheology of blends from linear and long-chain branched polyethylene and polypropylene58(2014); http://dx.doi.org/10.1122/1.4867555View Description Hide Description
In this article, normal stresses and shear stresses in oscillatory shear flow are measured at small and large deformation amplitudes. New material parameters are then introduced based on Fourier transform rheology and stress decomposition analysis of normal and shear stress measurements. Furthermore, uniaxial extensional measurements are performed and compared to simulation results using the molecular stress function model. Different behaviors were observed for the polyethylene and polypropylene type blends, which are believed to arise from the different types of long-chain branching (LCB) topology present in each of the systems. The use of the new material parameters proposed and described within this article has the potential to allow for a better understanding of structure-property relationships in industrial LCB materials.
58(2014); http://dx.doi.org/10.1122/1.4869350View Description Hide Description
The squeeze flow behaviors (including compressive, tensile, and oscillatory squeeze behaviors) of magnetorheological plastomers (MRPs, a kind of solidlike magnetic gels) under different experimental conditions are systematically investigated. Both compression and tension processes can be classified as elastic deformation region, stress relaxation region, and plastic flow region. A squeeze flow equation is used to describe the compressive behaviors of MRP in plastic flow region from which the compressive yield stress can be obtained and compared. The results demonstrate that both compressive yield stress and tensile yield stress are sensitive to magnetic field, particle distribution, and particle concentration. The yield stress of MRP under squeeze flow is larger than that of MR fluids due to the existence of polymer matrix. Asymmetry of hysteresis loop is found under oscillatory squeeze mode. The oscillatory squeeze behaviors of MRP are also influenced by magnetic field and particle concentration, but the influence of particle distribution is not so obvious. The related results under three operational modes are compared and qualitatively analyzed, which are helpful for further understanding the MR mechanism in the solidlike magnetic gels.
A mesoscopic simulation method for predicting the rheology of semi-dilute wormlike micellar solutions58(2014); http://dx.doi.org/10.1122/1.4868875View Description Hide Description
We present a fast “pointer” simulation method that extends the model of Cates and coworkers for the rheology of entangled wormlike micelles. Our method includes not only reptation, breakage/rejoining, contour length fluctuations, and Rouse modes, which were included in Cates' model, but also constraint release, bending modes, and a cross-over to the tight entanglement regime, which had not been previously considered. Our method also contains correlations in micelle length across multiple breakage/rejoining cycles, not included in previous approaches. Our method uses “pointers” that track the ends of unrelaxed regions along each micelle, thereby allowing efficient simulations of relaxation dynamics for ensembles containing thousands of micelles, to obtain accurate results without preaveraging or neglecting correlations. A modified genetic algorithm is applied to transform the simulation data from the time to the frequency domain. The method can span several regimes of behavior depending on the relative rates of reptation, contour length fluctuations, breakage/rejoining, and high frequency modes and is suitable for predicting the rheological behavior of experimental solutions for wormlike micelles. This new simulation method allows extraction of multiple micellar parameters simultaneously by fitting experimental rheology data across the entire available frequency range. Values of average micelle length and breakage rate thereby obtained can be an order of magnitude different from previous estimates based on “local” frequency dependencies predicted by Cates' model. These differences are due to more complete physics included in our method and the fitting of data across the entire frequency range. We also provide quantitative relationships between these parameters and rheological behaviors that improve on previous simple scaling results.
Universality and speedup in equilibrium and nonlinear rheology predictions of the fixed slip-link model58(2014); http://dx.doi.org/10.1122/1.4869252View Description Hide Description
The discrete slip-link model (DSM) was developed to describe the dynamics of flexible entangled polymer melts. With just three molecular-weight- and chain-architecture-independent parameters—the molecular weight of a Kuhn step M K; entanglement activity β; and Kuhn step shuffling characteristic time τ K—DSM is able to predict simultaneously the linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. Without any adjustment, DSM shows excellent agreement with shear flow experiments and elongational flows with stretch up to ∼10–20. Universality observed between entangled melts with the notable exception of high-strain elongations suggests that the average number of entanglements per chain is the primary characteristic of the system. Therefore, theoretical predictions for systems with differing numbers of Kuhn steps per chain but roughly the same number of entanglements should be equivalent when rescaled. In this work, we present a scaling of the DSM parameters, which has no significant effect on model predictions yet reduces greatly computational cost. The idea behind the scaling is clustering several Kuhn steps together. Thus, we call this implementation of the DSM the clustered fixed slip-link model (CFSM). The model is limited to at least one cluster between entanglements. The CFSM assumes two clusters between entanglements on average, which appears to be a reasonable minimum. We find that clustering results in a loss of some of the high frequency modes in G * predictions, sometimes called “longitudinal modes” in tube models. Matching the low-frequency rubbery plateau height allows us to derive Mc —the molecular weight of a cluster, as a function of the DSM parameters β, M K. We also find an empirical relationship between timescale parameters τ K and τ c, the characteristic time for shuffling a cluster through the entanglement. We compare G * predictions of the CFSM with predictions of the DSM for monodisperse linear, polydisperse linear, and branched systems, and observe no difference. Comparison with shear flow predictions shows that only rates with a Weissenberg number based on the strand relaxation time τe of 1 and higher are affected. For elongational flow at high strains and high rates, significant difference can occur, which is perhaps not surprising given the observation above. For the systems shown in this work, we report CFSM computational savings of several hundred times. We then apply CFSM to the shear flow of a star-branched polymer melt with molecular weight not accessible to DSM without rescaling. Excellent agreement with experimental data is observed. Additionally, we report first normal stress theoretical predictions for this system.
58(2014); http://dx.doi.org/10.1122/1.4869485View Description Hide Description
In a recent short communication [Read, D. J. et al., Science 333, 1871 (2011)], we showed that a computational scheme can describe the nonlinear flow properties for a series of industrial low-density polyethylene (LDPE) resins starting from the molecular architecture. The molecular architecture itself is determined by fitting parameters of a reaction kinetics model to average structural information obtained from gel-permeation chromatography and light scattering. Flow responses of these molecules in transient uniaxial extension and shear are calculated by mapping the stretch and orientation dynamics of the segments within the molecules to effective pom-pom modes. In this paper, we provide the details of the computational scheme and present additional results on a LDPE and a high-density polyethylene resin to illustrate the dependence of segmental maximum stretch variables on the flow rate.
A generalized Oldroyd's model for non-Newtonian liquids with applications to a dilute emulsion of deformable drops58(2014); http://dx.doi.org/10.1122/1.4871375View Description Hide Description
A new, general approach to constitutive modeling for non-Newtonian liquids (i.e., formulating an equation for the stress tensor in flows with arbitrary kinematics) is proposed and tested, with a particular application to a dilute emulsion of deformable drops. A generalized traceless Oldroyd model is used for the drop-phase contribution to the stress tensor, with five material parameters allowed to be functions of one instantaneous flow invariant. Two choices for this invariant are explored (i) the second invariant I 2 of the rate-of-strain tensor and (ii) the energy dissipation rate. In both versions, all five parameters are found from simultaneously fitting the Oldroyd model to viscometric and extensiometric functions for steady shear and planar extension (PE), respectively, at arbitrary flow intensities. The model predictions are compared to precise (but computationally intensive) results from boundary-integral simulations for several flows different from simple shear or PE. The energy dissipation rate is found to be generally a much better choice for the invariant than I 2, especially for comparable drop and continuous-phase viscosities, and it provides very good accuracy in a wide range of conditions (away from drop breakup). Test examples include mixed planar flow, uniaxial/biaxial extension, flow in a cavity with a moving wall, and flow past a macroscopic sphere. Unlike small-deformation theories, the present approach can be extended to large-strain flows of highly concentrated emulsions.
58(2014); http://dx.doi.org/10.1122/1.4870967View Description Hide Description
The continuous spectrum is a unique representation of the linear viscoelastic behavior of a polymer that reveals aspects of its behavior that may not be obvious in plots of the storage and loss moduli. A spectrum can in principle be inferred from experimental data, but because data are always corrupted by random error, this is one of the several ill-posed problems that arise in rheology [Honerkamp, J., Rheol. Acta 28, 363–371 (1989) and Malkin, A. Ya., Rheol. Acta 29, 512–518 (1990)], and this throws into doubt the possibility of obtaining a unique relaxation spectrum. A number of methods have been proposed to overcome the ill-posedness of the problem to arrive at a unique continuous spectrum that is a characteristic of the material. Wider use of these methods has been limited by the fact that many of them are the work of mathematicians or physicists who use languages and symbols not readily intelligible to rheologists and that the codes required to implement them are not readily available. For these reasons, continuous spectra are rarely reported. We demonstrate and compare the use of one, well-established method as well two recent ones using both simulated and actual data and provide advice to polymer rheologists as to the feasibility of inferring a meaningful continuous spectrum from data. We also evaluate the method of Baumgaertel and Winter [J. Non-Newtonian Fluid Mech. 44, 15–36 (1992)] for obtaining a discrete spectrum that is useful for calculating material functions and for flow simulation. We recommend that reports of viscoelastic behavior include plots of this revealing material function.
58(2014); http://dx.doi.org/10.1122/1.4872058View Description Hide Description
The flow of a two-dimensional foam through a constriction is investigated numerically with the bubble model, and results are compared with existing experimental and numerical studies. We predict the dynamical behavior of the foam by measuring its flowrate as a function of the imposed pressure drop. We show that two flow regimes can be observed, with an affine relationship between flowrate and pressure drop. The model also shows that the flowrate increases with the width of the distribution of bubble sizes. The simulations exhibit a power law dependency of the flowrate in the width of the constriction. The local properties of the flow are also investigated by measuring the velocity field, the frequency and direction of plastic events, and main orientations of strain. We show that the main qualitative features of the plastic and strain tensors fit with existing experiments. Finally, we test a theoretical model that predicts a relationship among plasticity, deformation, and strain.