Index of content:
Volume 55, Issue 1, January 2011
55(2011); http://dx.doi.org/10.1122/1.3503529View Description Hide Description
Time-dependent materialfunctions of engineering plastics within the exploitation range of temperatures extend over several decades of time. For this reason material characterization is carried out at different temperatures and/or pressures within a certain experimental window. Using the time-temperature and/or time-pressure superposition principle, these response function segments can be shifted along the logarithmic time-scale to obtain a master curve at selected reference conditions. This shifting is commonly performed manually (“by hand”) and requires some experience. Unfortunately, manual shifting is not based on a commonly agreed mathematical procedure which would, for a given set of experimental data, yield always exactly the same master curve, independent of person who executes the shifting process. Thus, starting from the same set of experimental data two different researchers could, and very likely will, construct two different master curves. In this paper, we propose a closed form mathematical methodology (CFS) which completely removes ambiguity related to the manual shifting procedures. This paper presents the derivation of the shifting algorithm and its validation using several simulated- and real- experimental data. It has been shown that error caused by shifting performed with CFS is at least 10–50 times smaller then the underlying experimental error.
55(2011); http://dx.doi.org/10.1122/1.3523538View Description Hide Description
Formulas expressing the extra stress tensor,, in fiber suspensions in terms of microstructural state variables are derived by using two types of arguments: mechanical and thermodynamical. Results are compared for the distribution function,, and the orientation tensor,, playing the role of state variables. The main results are the following: (i) In the thermodynamical analysis the formulas arise as compatibility conditions between the time evolution of the fluid velocity and the time evolution of the internal structure. (ii) A complete agreement among the formulas arising in mechanics and thermodynamics is seen only in kinetic theory (i.e., with as the state variable) and only with the Chan–Terentjev mechanical formula. (iii) Theoretical arguments as well as numerical illustrations indicate that the larger is the role of the reversible part of the time evolution of the microstructure, the larger is the difference in predicted stresses (i.e., the formulas for evaluated at solutions of the microstructural equations) calculated with the thermodynamic and the Dinh–Armstrong mechanical formulas.
55(2011); http://dx.doi.org/10.1122/1.3523477View Description Hide Description
This paper is focused on the rheology of magnetic fiber suspensions in the presence of a magnetic field applied perpendicular to the flow. At low Mason numbers, , the experimental flow curves show a steep initial section corresponding to the inclination and stretching of the gap-spanning aggregates formed upon magnetic field application. At higher Mason numbers, aggregates no longer stick to the walls and the flow curves reach a Bingham regime, with the dynamic yield stress growing with the magnetic field intensity. This yield stress appears to be about three times higher for the fiber suspensions than for the suspensions of spherical particles. Such difference, measured at relatively low magnetic field intensities, , is explained in terms of the enhanced magnetic susceptibility of the aggregates composed of fibers compared to the aggregates composed of spherical particles. For weak magnetic fields, the forces of solid friction between fibers are expected to play a minor role on the stress level of the suspension. In order to confirm these findings, we propose a new theoretical model, taking into account hydrodynamic interactions. The flow curve and the yield stress predictions are in a good agreement with the experimental results for semi-diluted suspensions.
Molecularly derived constitutive equation for low-molecular polymer melts from thermodynamically guided simulation55(2011); http://dx.doi.org/10.1122/1.3523485View Description Hide Description
We develop a systematic method for the derivation of closed-form and thermodynamically consistent constitutive equations of complex fluids from microscopic models. The method builds upon our recent work [Ilg et al., Phys. Rev. E79, 011802 (2009)] on thermodynamically guided simulations within a consistent coarse-graining scheme. These simulations are powerful at low to intermediate flow rates and have the considerable advantage that they do not require flow-adapted boundary conditions, i.e., operate at arbitrary homogeneous flows. The new method for deriving constitutive equations is illustrated for low-molecular polymer melts subjected to imposed, homogeneous flow fields. The differential constitutive equation we obtain for this model system is a simple, nonlinear equation of change for the conformation tensor, from which the stress tensor is readily obtained. The proposed constitutive model shows shear thinning (shear viscosity exhibiting fractional power laws in the range −0.40 to −0.86, the corresponding range for the first viscometric function is −1.20 to −1.43), stress overshoots, normal stress coefficients, and elongational viscosities in agreement with reference results. The constitutive equation can be interpreted as a molecularly derived, modified Giesekus model with conformation-dependent coefficients.
55(2011); http://dx.doi.org/10.1122/1.3523626View Description Hide Description
Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flowkinematics. The rheotens model of Doufas [J. Rheol. 50, 749–769 (2006)] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the Cox–Merz [J. Polym. Sci.28, 619–621 (1958)] and Laun [J. Rheol.30, 459–501 (1986)] rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of ), problems that have been reported for other constitutive equations.
55(2011); http://dx.doi.org/10.1122/1.3523481View Description Hide Description
Silica-based inverse ferrofluids (IFFs) are synthesized and their pre-yield and post-yield rheological properties are investigated as a function of magnetic field strength (8.8–276 kA/m), volume fraction (12.6–26.1 vol %), silica particle size (104–378 nm radius), and ferrofluid Newtonian viscosity (44–559 mPa s). The Mason number (Mn) provides a good scaling of the data in the steady simple shear flow regime. Special emphasis is made on the low and moderate Mason number region. At low Mn values, two different behaviors are observed depending on the IFF formulation and magnetic field strength applied: (i) either the viscosity monotonically increases with decreasing shear rate suggesting the existence of a yield stress (ii) or a low-shear plateau is reached. At medium Mn values, a power law behavior is found with . Yielding behavior is modeled by using both macroscopic and microscopic approaches under the assumption of spheroidal, cylindrical, and single-width particle chain models.
Effect of flow history on linear viscoelastic properties and the evolution of the structure of multiwalled carbon nanotube suspensions in an epoxy55(2011); http://dx.doi.org/10.1122/1.3523628View Description Hide Description
This paper analyzes the effect of flow history on the linear viscoelasticproperties of suspensions of multiwalled carbon nanotubes in an epoxy as well as the evolution of the suspensionmicrostructure under small deformations for different concentrations and temperatures. The effect of the flow history on the microstructure is interpreted in the light of the variation of the rheological percolation threshold, which is shown to increase with the pre-shear rate. After cessation of the shear flow, the storage modulus increased with time revealing the build-up of the structure. By decreasing the pre-shear rate, the resulting storage modulus increased and the relative increase of the storage modulus with respect to the pre-shear rate was more pronounced at lower concentrations. The rate of increase in the storage modulus drastically increased with the concentration and temperature, while its variation with respect to the pre-shear rate depended on the concentration. In dilute suspensions, it decreased dramatically by increasing the rate of pre-shear, revealing a slower structure build-up while it remained almost intact in more concentrated suspensions. The increase in kinetics of structure build-up with temperature suggests the importance of Brownian forces in the absence of flow regardless of concentration or applied pre-shear rate.
55(2011); http://dx.doi.org/10.1122/1.3523627View Description Hide Description
Recently, a computational algorithm based on Bayesian data analysis was presented to invert the linear rheology of branched polymers [Shanbhag, S., Rheol. Acta49, 411–422 (2010)]. When rheological data of an unknown polymer mixture are supplied, the algorithm produces an exhaustive distribution of structures and compositions, consistent with the rheology. Frequently, it identifies multiple or degenerate structures. In this proof-of-concept paper, a resolution of the degeneracy is sought by appealing to the concept of combinatorial rheology [Larson, R. G., Macromolecules34, 4556–4571 (2001)], where the unknown sample is strategically blended with a well-characterized fraction. Experimental load is alleviated by identifying the optimal type, molecular weight, and composition of the polymer fraction to blend with the unknown sample, to discriminate between the degenerate structures, most conclusively. Two methods are proposed and tested on a particular mixture that is characterized by severe degeneracy. Both proposed methods are able to correctly identify the structure and composition of the original mixture by requiring two additional rheological experiments.