Volume 53, Issue 1, January 2009
Index of content:
53(2009); http://dx.doi.org/10.1122/1.3037266View Description Hide Description
By means of a stress imposed rheometer coupled with a “vibrating cell,” generating a Brownian motion at a macroscopic scale into the samples, we have shown that dense-phase vibrated powders exhibit rheological behaviors archetypal of non-Newtonian viscoelastic fluids. These behaviors have been accurately described through a free volume structural model based on simple “stick-slip” granular interactions. As a result, the evolution of the steady-state viscosity has been accurately expressed as a function of the shear rate, the frictional stress, the granular pressure, the mass of the samples, the vibration frequency, the vibration energy, the intergranular contact network mean life, and the free volume distribution. The model is consistent with Hookean, Coulombian, and Newtonian limits and is not only descriptive but also explicative and predictive of the encountered phenomena. In particular, a “time-granular temperature superposition principle,” theoretically predicted by the model, has been experimentally verified, the “granular temperature” being controlled through the vibration energy and frequency. Moreover, this superposition principle has been precisely described by a “Vogel-Fulcher-Tammann” law, leading to very close analogies with molecular systems near their glass transition point.
Rheology of poly(sodium acrylate) hydrogels during cross-linking with and without cellulose microfibrils53(2009); http://dx.doi.org/10.1122/1.3003054View Description Hide Description
The rheology of poly(sodium acrylate) hydrogel cross-linked with -methylene (bisacrylamide), during gelation is studied. The validity of the Winter-Chambon criterion is examined for gelation. Cellulose microfibrils (CMF) of an aspect ratio ranging from 20 to 100 are used as fillers. The effect of filler CMF on the rheological properties during gelation is also investigated. The WC criterion is satisfied and the gel time increased with an increase in the filler content. This suggests the presence of a self-similar structure at the gel point. The storage and the loss moduli crossover is observed in the case of unfilled system. Whereas no crossover is observed when the filler is incorporated and from the start of the reaction, is always greater than . With the incorporation of the filler, there is a plateau initially in and . This is attributed to the physical network of fibrils in the sample mixture. Scaling behavior of rheological properties and fractal dimensions near the gel point are also examined.
53(2009); http://dx.doi.org/10.1122/1.3000732View Description Hide Description
A set of rheological equations is developed for semiconcentrated suspensions of rigid fibers in a Newtonian fluid taking into account hydrodynamic and fiber-fiber interactions. The force generated by the fiber interactions is modeled using a linear hydrodynamic friction coefficient proportional to the relative velocity at the contact point, and weighted by the probability for contacts to occur. The equation of evolution of the second-order orientation tensor, containing advection and diffusion terms due to fiber interactions, is derived to predict fiber orientation under flow. The well known fourth-order orientation tensor, related to the hydrodynamic contribution, and a newly proposed fourth-order interaction tensor are used to evaluate the total stress in the composite. A linear and a quadratic closure approximation are proposed to describe the fourth-order interaction tensor. Results are presented using the quadratic form, which is found to be more accurate than the linear one. The model is shown to describe well simple shear data of suspensions of glass fibers in a Newtonian polybutene. Moreover, fiber orientation and the average number of contacts per fiber are predicted. The newly proposed interaction coefficient varies with fiber orientation, which appears to be realistic.
53(2009); http://dx.doi.org/10.1122/1.3009299View Description Hide Description
Entangled DNAsolutions are ideal as a model system to examine nonlinear shear flow behavior. Even when the number of entanglements per chain, , is higher than 100, the solution is still soft enough with an elastic plateau modulus under and is thus amenable to experimental study by commercial rotational rheometry without ambiguity and uncertainty. We have investigated nonlinear flow behavior of three entangled DNAsolutions with , 60, and 156, respectively, using a combination of particle-tracking velocimetric (PTV) and conventional rheometric measurements. We explore questions such as (a) whether shear banding also occurs in moderately entangled solutions, (b) whether creep results in development of nonlinear velocity profile, (c) whether shear banding produced in startup shear and creep persists at long times in steady state, and (d) whether these entangled solutions exhibit homogeneous shear at the upper end of the stress plateau region. We found that the first DNAsolution only shows transient weakly inhomogeneous shear and steady linear velocity profile. In the more entangled solutions ( and 156), shear banding is observed in startup rate- and stress-controlled shear in the shear thinning regime. Shear homogeneity eventually returns at the upper end of the stress plateau (shear thinning) regime.
53(2009); http://dx.doi.org/10.1122/1.3006099View Description Hide Description
Carbon fibers and composites derived from mesophase pitch exhibit ultrahigh stiffness and thermal conductivity due to a high degree of graphitic content, which is generated by the liquid crystalline state of the precursor and the molecular orientation that is developed during melt processing steps. To understand the flow and its effect on microstructure, this paper presents an integrated experimental and modeling approach for a synthetic discotic mesophase pitch (AR-HP). Careful control of shear rate and strain was exercised throughout the rheological studies. Wide-angle x-ray diffraction studies were conducted on carefully solidified rheological specimens to obtain azimuthal profiles for layer plane orientation. Cross-polarized microscopy was conducted in the reflected mode using a first-order red plate to examine the orientation in three orthogonal planes. Under the influence of steady shear, the microstructure of mesophase pitch became flow-aligned, which is similar to the fibrous structure reported in the literature. Transient stress response, however, displayed a nonmonotonic behavior. Microscopic observations indicate that the local maximum in the shear stress is likely caused by the deformation of the initial microstructure. To develop a better understanding of these complex flowdynamics, simulations based on the Landau–de Gennes nematodynamics adapted to discotic mesophases were performed, and a qualitative agreement between simulations and experiments was found. The experimentally obtained rheostructural results and the numerical simulations provide a systematic understanding of flow-microstructure relationships during transient and steady shear flow.
53(2009); http://dx.doi.org/10.1122/1.3005402View Description Hide Description
This work reports a detailed study on the shear magnetorheology of suspensions of magnetic microfibers. The steady-state regime was investigated using a controlled-stress rheometer for different concentrations of particles and under the presence of a broad range of applied magnetic fields (up to ). The results were compared with those obtained for conventional magnetorheological fluids(suspensions of magnetic microspheres). It was found that the suspensions of magnetic fibers show an enhanced magnetorheological effect. We proposed the existence of field-dependent solid friction between fibers as the main physical reason for this enhancement. In order to ascertain the relevance of the interfiber solid friction, the microscopic structure of fiber suspensions was investigated using an optical microscope. In the absence of applied field, fibers form an entangled network with approximately isotropic orientation. Upon magnetic field application, the fiber network becomes deformed and approximately aligned with the field direction. Nonetheless, interfiber solid friction hinders a complete alignment of the fibers with the field, and the fiber network remains entangled.
53(2009); http://dx.doi.org/10.1122/1.3005405View Description Hide Description
This paper reports the first predictions of the yield stress of suspensions of non-Brownian magnetic fibers in the presence of uniform magnetic fields. The quasistatic regime of the shear deformation (before the flow onset) of the suspension is studied. Four different structures of the magnetic fiber suspensions are considered—column, zigzag, three-dimensional stochastic and near-planar stochastic structures—and the yield stress is attributed to the failure of the given structure at a critical strain. The main contributions to the yield stress are found to come from the restoring magnetic torque acting on each fiber and from the solid friction between fibers. The enhanced magnetorheological effect of magnetic fiber suspensions observed experimentally [M. T. López-López et al., J. Rheol.53, 115–126 (2009)] is explained and quantified in terms of interfiber friction. Surprisingly, the dipolar magnetic interactions between fibers do not affect significantly the yield stress. The lowest yield stress is obtained for the zigzag structure and the highest one for the column structure. A reasonable agreement with the experiments is obtained for 5% and 7% fiber volume fractions in the frame of the more realistic model of near-planar stochastic structures.
53(2009); http://dx.doi.org/10.1122/1.3037263View Description Hide Description
A constitutive model based on an assumption regarding the general response to hydrostatic pressure is proposed for the moderate deformations of slightly compressible (or nearly incompressible) rubber. It is shown that an excellent fit is obtained with the available experimental data for a particularly simple form of strain-energy density. The data considered are from those material characterization tests that involve only moderate deformations.
53(2009); http://dx.doi.org/10.1122/1.3037262View Description Hide Description
The practical implementation of several thixotropic rheological models has been evaluated for a prototypical industrial application. We have studied the ability of the models to predict both steady and transient rheology of a suspension of alumina particles and the suitability of those models for full transient finite element calculations. The constitutive models for thixotropic materials examined include the Carreau-Yasuda model and first and second-order indirect structure models. While all of these models were able to predict the shear-thinning behavior of the steady viscosity, the first and second-order structure models were also able to capture some aspects of the transient structure formation and fluid history. However, they were not able to predict some more complex transient behavior observed in step shear experiments. For most thixotropic suspensions, the time constant required to form structure is longer than the time constant to break it down. For this suspension, the time constant at a given shear rate was also dependent on the previous shear rate. If the previous shear rate was high, the time required to reach equilibrium was longer than if the previous shear rate was lower. This behavior was not captured by the simple initial structure dependence in the previous models. By adding an additional dependence on the initial suspensionstructure, the prediction of the transient rheology was substantially improved while maintaining an excellent agreement with the steady shear viscosity.Finite element results are presented for extrusion of a suspension to form a fiber. This model two-dimensional problem contains many of the same complexities as practical three-dimensional mold filling simulations (i.e., nonviscometric and mobile free surface). Our results show that these direct structure models exhibit oscillations near the stick-slip point in finite element calculations similar to many polymeric constitutive equations, but are otherwise suitable for implementation in complex industrial modeling applications.
53(2009); http://dx.doi.org/10.1122/1.3003570View Description Hide Description
The rheological behavior of the alkali metal salts of oligomeric sulfonated polystyrene (PS) ionomers was characterized using dynamic and steady shear measurements. The starting PS had a weight average molecular weight of and a narrow molecular weight distribution (1.06). Two sulfonation levels were examined, 2.5 and , which corresponded, respectively, to one and two sulfonate groups per chain on average. The ionomers exhibited nanophase separation of an ion-rich phase, and as a consequence, time-temperature superposition failed for all samples. Sulfonation increased the melt viscosity of the ionomers, as much as seven orders of magnitude. The zero shear viscosity scaled as , where was the concentration of the ionic groups, was the charge of the cation, and was the cation radius, and although the molecular weight of the parent polystyrene was much lower than the entanglement molecular weight, the ionomer melts exhibited strong elastic behavior. The flow activation energy of the ionomers was similar to that of high molecular weight PS and the calculated molecular weight between “entanglements” of the ionomers was the same as for PS.
53(2009); http://dx.doi.org/10.1122/1.3037267View Description Hide Description
A general stress decomposition (GSD) method is suggested to analyze the nonlinear behavior in arbitrary nonlinear oscillatory experiments. This method is based on the symmetric properties of different harmonics. For shear stress, it is found that odd harmonics can be separated into a viscous and elastic part, respectively, while even harmonics has a viscoelastic character. The GSD method is validated by a model wave, and applied in nonlinear oscillatory shear of viscousshear thinning fluid, Bingham material, viscoelastic polymers,polymer blends via theoretical analysis and polymer composites via an experiment. The nonlinear behaviors of these materials are studied by the GSD method to show characteristic scaling relations. The GSD method has an advantage of determination the contribution of even harmonics readily by the decomposed stresses under either transient or steady flow conditions.